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; ACL2 Version 3.1  A Computational Logic for Applicative Common Lisp
; Copyright (C) 2006 University of Texas at Austin
; This version of ACL2 is a descendent of ACL2 Version 1.9, Copyright
; (C) 1997 Computational Logic, Inc. See the documentation topic NOTE20.
; This program is free software; you can redistribute it and/or modify
; it under the terms of the GNU General Public License as published by
; the Free Software Foundation; either version 2 of the License, or
; (at your option) any later version.
; This program is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
; GNU General Public License for more details.
; You should have received a copy of the GNU General Public License
; along with this program; if not, write to the Free Software
; Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
; Written by: Matt Kaufmann and J Strother Moore
; email: Kaufmann@cs.utexas.edu and Moore@cs.utexas.edu
; Department of Computer Sciences
; University of Texas at Austin
; Austin, TX 787121188 U.S.A.
(inpackage "ACL2")
; Rockwell Addition: A major change is the provision of nonexecutable
; functions. These are typically functions that use stobjs but which
; are translated as though they were theorems rather than definitions.
; This is convenient (necessary?) for specifying some stobj
; properties. These functions will have executable counterparts that
; just throw. These functions will be marked with the property
; nonexecutablep.
(defconst *mutualrecursionctxstring*
"( MUTUALRECURSION ( DEFUN ~x0 ...) ...)")
(defun translatebodies1
(nonexecutablep names bodies bindings knownstobjslst ctx wrld state)
(cond ((null bodies) (transvalue nil))
(t (transerlet*
((x (translate1 (car bodies)
(if nonexecutablep t (car names))
(if nonexecutablep nil bindings)
(car knownstobjslst)
(if (and (consp ctx)
(equal (car ctx)
*mutualrecursionctxstring*))
(msg "( MUTUALRECURSION ... ( DEFUN ~x0 ...) ~
...)"
(car names))
ctx)
wrld state))
(y (translatebodies1 nonexecutablep
(cdr names)
(cdr bodies)
bindings
(cdr knownstobjslst)
ctx wrld state)))
(transvalue (cons x y))))))
(defun translatebodies
(nonexecutablep names bodies knownstobjslst ctx wrld state)
; Translate the bodies given and return a pair consisting of their
; translations and the final bindings from translate.
(declare (xargs :guard (truelistp bodies)))
(mvlet (erp lst bindings state)
(translatebodies1 nonexecutablep names bodies
(pairlis$ names names)
knownstobjslst
ctx wrld state)
(cond (erp (mv t nil state))
(nonexecutablep (value (cons lst (pairlisx2 names '(nil)))))
(t (value (cons lst bindings))))))
; The next section develops our check that mutual recursion is
; sensibly used.
(defun chkmutualrecursionbadnames (lst names bodies)
(cond ((null lst) nil)
((ffnnamesp names (car bodies))
(chkmutualrecursionbadnames (cdr lst) names (cdr bodies)))
(t
(cons (car lst)
(chkmutualrecursionbadnames (cdr lst) names (cdr bodies))))))
(defconst *chkmutualrecursionstring*
"The definition~#0~[~/s~] of ~&1 ~#0~[does~/do~] not call any of ~
the other functions being defined via ~
mutual recursion. The theorem prover ~
will perform better if you define ~&1 ~
without the appearance of mutual recursion. See ~
:DOC setbogusmutualrecursionok to get ~
ACL2 to handle this situation differently.")
(defun chkmutualrecursion1 (names bodies warnp ctx state)
(cond
((and warnp
(warningdisabledp "mutualrecursion"))
(value nil))
(t
(let ((bad (chkmutualrecursionbadnames names names bodies)))
(cond ((null bad) (value nil))
(warnp
(pprogn
(warning$ ctx ("mutualrecursion")
*chkmutualrecursionstring*
(if (consp (cdr bad)) 1 0)
bad)
(value nil)))
(t (er soft ctx
*chkmutualrecursionstring*
(if (consp (cdr bad)) 1 0)
bad)))))))
(defun chkmutualrecursion (names bodies ctx state)
; We check that names has at least 1 element and that if it has
; more than one then every body calls at least one of the fns in
; names. The idea is to ensure that mutual recursion is used only
; when "necessary." This is not necessary for soundness but since
; mutually recursive fns are not handled as well as singly recursive
; ones, it is done as a service to the user. In addition, several
; error messages and other userinterface features exploit the presence
; of this check.
(cond ((null names)
(er soft ctx
"It is illegal to use MUTUALRECURSION to define no functions."))
((null (cdr names)) (value nil))
(t
(let ((bogusmutualrecursionok
(cdr (assoceq :bogusmutualrecursionok
(tablealist 'acl2defaultstable (w state))))))
(if (eq bogusmutualrecursionok t)
(value nil)
(chkmutualrecursion1 names bodies
(eq bogusmutualrecursionok :warn)
ctx state))))))
; We now develop putinductioninfo.
(mutualrecursion
(defun ffnnamepmodmbe (fn term)
; We determine whether the function fn (possibly a lambdaexpression) is used
; as a function in term', the result of expanding mustbeequal calls in term.
; Keep this in sync with the ffnnamep nest. Unlike ffnnamep, we assume here
; that fn is a symbolp.
(cond ((variablep term) nil)
((fquotep term) nil)
((flambdaapplicationp term)
(or (ffnnamepmodmbe fn (lambdabody (ffnsymb term)))
(ffnnamepmodmbelst fn (fargs term))))
((eq (ffnsymb term) fn) t)
((eq (ffnsymb term) 'mustbeequal)
(ffnnamepmodmbe fn (fargn term 1)))
(t (ffnnamepmodmbelst fn (fargs term)))))
(defun ffnnamepmodmbelst (fn l)
(declare (xargs :guard (and (symbolp fn)
(pseudotermlistp l))))
(if (null l)
nil
(or (ffnnamepmodmbe fn (car l))
(ffnnamepmodmbelst fn (cdr l)))))
)
; Here is how we set the recursivep property.
; Rockwell Addition: The recursivep property has changed. Singly
; recursive fns now have the property (fn) instead of fn.
(defun putproprecursiveplst (names bodies wrld)
; On the property list of each function symbol is stored the 'recursivep
; property. For nonrecursive functions, the value is implicitly nil but no
; value is stored (see comment below). Otherwise, the value is a truelist of
; fn names in the ``clique.'' Thus, for singly recursive functions, the value
; is a singleton list containing the function name. For mutually recursive
; functions the value is the list of every name in the clique. This function
; stores the property for each name and body in names and bodies.
; WARNING: We rely on the fact that this function puts the same names into the
; 'recursivep property of each member of the clique, in our handling of
; beingopenedp.
(cond ((int= (length names) 1)
(cond ((ffnnamepmodmbe (car names) (car bodies))
(putprop (car names) 'recursivep names wrld))
(t
; Until we started using the 'defbodies property to answer most questions
; about recursivep (see macro recursivep), it was a good idea to put a
; 'recursivep property of nil in order to avoid having getprop walk through an
; entire association list looking for 'recursivep. Now, this lessused
; property is just in the way.
wrld)))
(t (putpropxlst1 names 'recursivep names wrld))))
(defrec testsandcall (tests call) nil)
; In nqthm this record was called TESTANDCASE and the second component was
; the arglist of a recursive call of the function being analyzed. Because of
; the presence of mutual recursion, we have renamed it testsandcall and the
; second component is a "recursive" call (possibly mutually recursive).
(mutualrecursion
(defun allcalls (names term alist ans)
; Names is a list of defined function symbols. Return a list with the
; property that if we append it to the set of all calls in the range
; of alist of any fn in names, then this list represents the set of
; all such calls in term/alist. Ans is an accumulator onto which the
; calls are pushed. (We really just explore term looking for calls,
; and instantiate them as we find them.)
; Our answer is in reverse print order (displaying lambdaapplications
; as LETs). For example, if a, b and c are all calls of fns in names,
; then if term is (foo a ((lambda (x) c) b)), which would be printed
; as (foo a (let ((x b)) c)), the answer is (c b a).
(cond ((variablep term) ans)
((fquotep term) ans)
((flambdaapplicationp term)
(allcalls names
(lambdabody (ffnsymb term))
(pairlis$ (lambdaformals (ffnsymb term))
(sublisvarlst alist (fargs term)))
(allcallslst names (fargs term) alist ans)))
(t (allcallslst names
(fargs term)
alist
(cond ((membereq (ffnsymb term) names)
(addtosetequal
(sublisvar alist term)
ans))
(t ans))))))
(defun allcallslst (names lst alist ans)
(cond ((null lst) ans)
(t (allcallslst names
(cdr lst)
alist
(allcalls names (car lst) alist ans)))))
)
(defun allcallsalist (names alist ans)
; This function processes an alist and computes all the calls of fns
; in names in the range of the alist and accumulates them onto ans.
(cond ((null alist) ans)
(t (allcallsalist names (cdr alist)
(allcalls names (cdar alist) nil ans)))))
(defun terminationmachine1 (tests calls ans)
; This function makes a testsandcall with tests tests for every call
; in calls. It accumulates them onto ans so that if called initially
; with ans=nil the result is a list of testsandcall in the reverse
; order of the calls.
(cond ((null calls) ans)
(t (terminationmachine1 tests
(cdr calls)
(cons (make testsandcall
:tests tests
:call (car calls))
ans)))))
(defun terminationmachine (names body alist tests)
; This function builds a list of testsandcall records for some
; fnname in names with body body/alist, with the following property:
; if we append to the result the set of all testsandcall records
; (tests c), where c varies over all calls in the range of alist of
; any fn in names, then this list represents the set of all such
; records for term/alist. Note that we don't need to know the
; function symbol to which the body belongs; all the functions in
; names are considered "recursive" calls. Names is a list of all the
; mutually recursive fns in the clique. Alist maps variables in body
; to actuals and is used in the exploration of lambda applications.
; For each recursive call in body a testsandcall is returned
; whose tests are all the tests that "rule" the call and whose call is
; the call. If a rules b then a governs b but not vice versa. For
; example, in (if (g (if a b c)) d e) a governs b but does not rule b.
; The reason for taking this weaker notion of governance is that we
; can show easily that the testsandcalls are together sufficient to
; imply the testsandcalls generated by inductionmachine.
(cond
((or (variablep body)
(fquotep body))
nil)
((flambdaapplicationp body)
(terminationmachine1
(reverse tests)
(allcallslst names
(fargs body)
alist
nil)
(terminationmachine names
(lambdabody (ffnsymb body))
(pairlis$ (lambdaformals (ffnsymb body))
(sublisvarlst alist (fargs body)))
tests)))
((eq (ffnsymb body) 'if)
(let ((insttest (sublisvar alist
; Since (removeguardholders x) is provably equal to x, the machine we
; generate using it below is equivalent to the machine generated without it.
(removeguardholders (fargn body 1)))))
(terminationmachine1
(reverse tests)
(allcalls names (fargn body 1) alist nil)
(append (terminationmachine names
(fargn body 2)
alist
(cons insttest tests))
(terminationmachine names
(fargn body 3)
alist
(cons (dumbnegatelit insttest)
tests))))))
((eq (ffnsymb body) 'prog2$)
; Here we handle type declaration forms in mvlet; see translate1.
; Note that there is nothing special here about prog2$; we could
; extend the notion of "rules" further towards the notion of "governs"
; by allowing such an extension for other function symbols as well.
(let ((allcalls1 (allcalls names (fargn body 1) alist nil)))
(cond (allcalls1
; If there are recursive calls of the function in the first argument, then the
; user is presumably intending to continue the termination and induction
; analyses through that first argument as well. Otherwise, we want to keep the
; induction scheme simple, so we do not extend that analysis into the first
; argument, either here or in inductionmachineforfn1; so keep the handling
; of prog2$ for that function in sync with the handling of prog2$ here.
(append (terminationmachine names
(fargn body 1)
alist
tests)
(terminationmachine names
(fargn body 2)
alist
tests)))
(t (terminationmachine1 (reverse tests)
nil ; allcalls1
(terminationmachine names
(fargn body 2)
alist
tests))))))
((eq (ffnsymb body) 'mustbeequal)
; It is sound to treat mustbeequal like a macro for logic purposes. We do so
; both for induction and for termination.
(terminationmachine names
(fargn body 1)
alist
tests))
(t (terminationmachine1 (reverse tests)
(allcalls names body alist nil)
nil))))
(defun terminationmachines (names bodies)
; This function builds the termination machine for each function defined
; in names with the corresponding body in bodies. A list of machines
; is returned.
(cond ((null bodies) nil)
(t (cons (terminationmachine names (car bodies) nil nil)
(terminationmachines names (cdr bodies))))))
; We next develop the function that guesses measures when the user has
; not supplied them.
(defun properdumboccurasoutput (x y)
; We determine whether the term x properly occurs within the term y, insisting
; in addition that if y is an IF expression then x occurs properly within each
; of the two output branches.
; For example, X does not properly occur in X or Z. It does properly occur in
; (CDR X) and (APPEND X Y). It does properly occur in (IF a (CDR X) (CAR X))
; but not in (IF a (CDR X) 0) or (IF a (CDR X) X).
; This function is used in alwaystestedandchangedp to identify a formal to
; use as the measured formal in the justification of a recursive definition.
; We seek a formal that is tested on every branch and changed in every
; recursion. But if (IF a (CDR X) X) is the new value of X in some recursion,
; then it is not really changed, since if we distributed the IF out of the
; recursive call we would see a call in which X did not change.
(cond ((equal x y) nil)
((variablep y) nil)
((fquotep y) nil)
((eq (ffnsymb y) 'if)
(and (properdumboccurasoutput x (fargn y 2))
(properdumboccurasoutput x (fargn y 3))))
(t (dumboccurlst x (fargs y)))))
(defun alwaystestedandchangedp (var pos tmachine)
; Is var involved in every tests component of tmachine and changed
; and involved in every call, in the appropriate argument position?
; In some uses of this function, var may not be a variable symbol
; but an arbitrary term.
(cond ((null tmachine) t)
((and (dumboccurlst var
(access testsandcall
(car tmachine)
:tests))
(let ((argn (nth pos
(fargs (access testsandcall
(car tmachine)
:call)))))
; If argn is nil then it means there was no enough args to get the one at pos.
; This can happen in a mutually recursive clique not all clique members have the
; same arity.
(and argn
(properdumboccurasoutput var argn))))
(alwaystestedandchangedp var pos (cdr tmachine)))
(t nil)))
(defun guessmeasure (name defunflg args pos tmachine ctx wrld state)
; Tmachine is a termination machine, i.e., a lists of testsandcall.
; Because of mutual recursion, we do not know that the call of a
; testsandcall is a call of name; it may be a call of a sibling of
; name. We look for the first formal that is (a) somehow tested in
; every test and (b) somehow changed in every call. Upon finding such
; a var, v, we guess the measure (acl2count v). But what does it
; mean to say that v is "changed in a call" if we are defining (foo x
; y v) and see a call of bar? We mean that v occurs in an argument to
; bar and is not equal to that argument. Thus, v is not changed in
; (bar x v) and is changed in (bar x (mumble v)). The difficulty here
; of course is that (mumble v) may not be being passed as the new
; value of v. But since this is just a heuristic guess intended to
; save the user the burden of typing (acl2count x) a lot, it doesn't
; matter.
; If we fail to find a measure we cause an error.
; Pos is initially 0 and is the position in the formals list of the first
; variable listed in args. Defunflg is t if we are guessing a measure on
; behalf of a function definition and nil if we are guessing on behalf of a
; :definition rule. It affects only the error message printed.
(cond ((null args)
(cond
((null tmachine)
; Presumably guessmeasure was called here with args = NIL, for example if
; :setbogusmutualrecursion allowed it. We pick a silly measure that will
; work. If it doesn't work (hard to imagine), well then, we'll find out when
; we try to prove termination.
(value (mconsterm* (defaultmeasurefunction wrld) *0*)))
(t
(er soft ctx
"No ~#0~[:MEASURE~/:CONTROLLERALIST~] was supplied with the ~
~#0~[definition of~/:DEFINITION rule~] ~x1. Our heuristics ~
for guessing one have not made any suggestions. No argument ~
of the function is tested along every branch and occurs as a ~
proper subterm at the same argument position in every ~
recursive call. You must specify a ~#0~[:MEASURE. See :DOC ~
defun.~/:CONTROLLERALIST. See :DOC definition.~]"
(if defunflg 0 1)
name))))
((alwaystestedandchangedp (car args) pos tmachine)
(value (mconsterm* (defaultmeasurefunction wrld) (car args))))
(t (guessmeasure name defunflg (cdr args) (1+ pos)
tmachine ctx wrld state))))
(defun guessmeasurealist (names arglists measures tmachines ctx wrld state)
; We either cause an error or return an alist mapping the names in
; names to their measures (either user suggested or guessed).
(cond ((null names) (value nil))
((equal (car measures) *0*)
(erlet* ((m (guessmeasure (car names)
t
(car arglists)
0
(car tmachines)
ctx wrld state)))
(erlet* ((alist (guessmeasurealist (cdr names)
(cdr arglists)
(cdr measures)
(cdr tmachines)
ctx wrld state)))
(value (cons (cons (car names) m)
alist)))))
(t (erlet* ((alist (guessmeasurealist (cdr names)
(cdr arglists)
(cdr measures)
(cdr tmachines)
ctx wrld state)))
(value (cons (cons (car names) (car measures))
alist))))))
; We now embark on the development of provetermination, which must
; prove the justification theorems for each termination machine and
; the measures supplied/guessed.
(defun addliteraltoclausesegments (lit segments atendflg)
(cond ((null segments) nil)
(t (conjoinclausetoclauseset
(addliteral lit (car segments) atendflg)
(addliteraltoclausesegments lit (cdr segments) atendflg)))))
(defun removebuiltinclauses (clset ens oncepoverride wrld state ttree)
; We return two results. The first is a subset of clset obtained by deleting
; all builtinclauseps and the second is the accumulated ttrees for the
; clauses we deleted.
(cond
((null clset) (mv nil ttree))
(t (mvlet
(builtinclausep ttree1)
(builtinclausep (car clset) ens oncepoverride wrld state)
; Ttree is known to be 'assumption free.
(mvlet
(newset ttree)
(removebuiltinclauses (cdr clset) ens oncepoverride wrld state
(constagtrees ttree1 ttree))
(cond (builtinclausep (mv newset ttree))
(t (mv (cons (car clset) newset) ttree))))))))
(defun lengthexceedsp (lst n)
(cond ((null lst) nil)
((= n 0) t)
(t (lengthexceedsp (cdr lst) (1 n)))))
(defun cleanupclauseset (clset ens wrld ttree state)
; Warning: The set of clauses returned by this function only implies the input
; set. They are thought to be equivalent only if the input set contains no
; tautologies. See the caution in subsumptionreplacementloop.
; This function removes subsumed clauses from clset, does replacement
; (e.g., if the set includes the clauses {~q p} and {q p} replace them
; both with {p}), and removes builtin clauses. It returns two
; results, the cleaned up clause set and a ttree justifying the
; deletions and extending ttree. The returned ttree is 'assumption
; free (provided the incoming ttree is also) because all necessary
; splitting is done internally.
; Bishop Brock has pointed out that it is unclear what is the best order in
; which to do these two checks. Subsumptionreplacement first and then
; builtin clauses? Or vice versa? We do a very trivial analysis here to
; order the two. Bishop is not to blame for this trivial analysis!
; Suppose there are n clauses in the initial clset. Suppose there are b
; builtin clauses. The cost of the subsumptionreplacement loop is roughly
; n*n and that of the builtin check is n*b. Contrary to all common sense let
; us suppose that the subsumptionreplacement loop eliminates redundant clauses
; at the rate, r, so that if we do the subsumption replacement loop first at a
; cost of n*n we are left with n*r clauses. Note that the worst case for r is
; 1 and the smaller r is, the better; if r were 1/100 it would mean that we
; could expect subsumptionreplacement to pare down a set of 1000 clauses to
; just 10. More commonly perhaps, r is just below 1, e.g., 99 out of 100
; clauses are unaffected. To make the analysis possible, let's assume that
; builtin clauses crop up at the same rate! So,
; n^2 + bnr = cost of doing subsumptionreplacement first = subfirst
; bn + (nr)^2 = cost of doing builtin clauses first = bicfirst
; Observe that when r=1 the two costs are the same, as they should be. But
; generally, r can be expected to be slightly less than 1.
; Here is an example. Let n = 10, b = 100 and r = 99/100. In this example we
; have only a few clauses to consider but lots of built in clauses, and we have
; a realistically low expectation of hits. The cost of subfirst is 1090 but
; the cost of bicfirst is 1098. So we should do subfirst.
; On the other hand, if n=100, b=20, and r=99/100 we see subfirst costs 11980
; but bicfirst costs 11801, so we should do builtin clauses first. This is a
; more common case.
; In general, we should do builtin clauses first when subfirst exceeds
; bicfirst.
; n^2 + bnr >= bn + (nr)^2 = when we should do builtin clauses first
; Solving we get:
; n > b/(1+r).
; Indeed, if n=50 and b=100 and r=99/100 we see the costs of the two equal
; at 7450.
(cond
((let ((srlimit (srlimit wrld)))
(and srlimit (> (length clset) srlimit)))
(pstk
(removebuiltinclauses
clset ens (matchfreeoverride wrld) wrld state
(addtotagtree 'srlimit t ttree))))
((lengthexceedsp clset (globalval 'halflengthbuiltinclauses wrld))
(mvlet (clset ttree)
(pstk
(removebuiltinclauses clset ens
(matchfreeoverride wrld)
wrld state ttree))
(mv (pstk
(subsumptionreplacementloop
(mergesortlength clset) nil nil))
ttree)))
(t (pstk
(removebuiltinclauses
(pstk
(subsumptionreplacementloop
(mergesortlength clset) nil nil))
ens (matchfreeoverride wrld) wrld state ttree)))))
(defun measureclauseforbranch (name tc measurealist rel wrld)
; Name is the name of some function, say f0, in a mutually recursive
; clique. Tc is a testsandcall in the termination machine of f0 and hence
; contains some tests and a call of some function in the clique, say,
; f1. Measurealist supplies the measures m0 and m1 for f0 and f1.
; Rel is the wellfounded relation we are using.
; We assume that the 'formals for all the functions in the clique have
; already been stored in wrld.
; We create a set of clauses equivalent to
; tests > (rel m1' m0),
; where m1' is m1 instantiated as indicated by the call of f1.
(let* ((f0 name)
(m0 (cdr (assoceq f0 measurealist)))
(tests (access testsandcall tc :tests))
(call (access testsandcall tc :call))
(f1 (ffnsymb call))
(m1prime (subcorvar
(formals f1 wrld)
(fargs call)
(cdr (assoceq f1 measurealist))))
(concl (mconsterm* rel m1prime m0)))
(addliteral concl
(dumbnegatelitlst tests)
t)))
(defun measureclausesforfn1 (name tmachine measurealist rel wrld)
(cond ((null tmachine) nil)
(t (conjoinclausetoclauseset
(measureclauseforbranch name
(car tmachine)
measurealist
rel
wrld)
(measureclausesforfn1 name
(cdr tmachine)
measurealist
rel
wrld)))))
(defun measureclausesforfn (name tmachine measurealist mp rel wrld)
; We form all of the clauses that are required to be theorems for the admission
; of name with the given termination machine and measures. Mp is the "domain
; predicate" for the wellfounded relation rel, or else mp is t meaning rel is
; wellfounded on the universe. (For example, mp is op when rel is o<.) For
; the sake of illustration, suppose the defun of name is simply
; (defun name (x)
; (declare (xargs :guard (guard x)))
; (if (test x) (name (d x)) x))
; Assume mp and rel are op and o<. Then we will create clauses equivalent
; to:
; (op (m x))
; and
; (test x) > (o< (m (d x)) (m x)).
; Observe that the guard of the function is irrelevant!
; We return a set of clauses which are implicitly conjoined.
(cond
((eq mp t)
(measureclausesforfn1 name tmachine measurealist rel wrld))
(t (conjoinclausetoclauseset
(addliteral (mconsterm* mp (cdr (assoceq name measurealist)))
nil t)
(measureclausesforfn1 name tmachine measurealist rel wrld)))))
(defun measureclausesforclique (names tmachines measurealist mp rel wrld)
; We assume we can obtain from wrld the 'formals for each fn in names.
(cond ((null names) nil)
(t (conjoinclausesets
(measureclausesforfn (car names)
(car tmachines)
measurealist
mp rel
wrld)
(measureclausesforclique (cdr names)
(cdr tmachines)
measurealist
mp rel
wrld)))))
(defun tilde*measurephrase1 (alist wrld)
(cond ((null alist) nil)
(t (cons (msg (cond ((null (cdr alist)) "~p1 for ~x0.")
(t "~p1 for ~x0"))
(caar alist)
(untranslate (cdar alist) nil wrld))
(tilde*measurephrase1 (cdr alist) wrld)))))
(defun tilde*measurephrase (alist wrld)
; Let alist be an alist mapping function symbols, fni, to measure terms, mi.
; The fmt directive ~*0 will print the following, if #\0 is bound to
; the output of this fn:
; "m1 for fn1, m2 for fn2, ..., and mk for fnk."
; provided alist has two or more elements. If alist contains
; only one element, it will print just "m1."
; Note the final period at the end of the phrase! In an earlier version
; we did not add the period and saw a linebreak between the ~x1 below
; and its final period.
; Thus, the following fmt directive will print a grammatically correct
; sentence ending with a period: "For the admission of ~&1 we will use
; the measure ~*0"
(list* "" "~@*" "~@* and " "~@*, "
(cond
((null (cdr alist))
(list (cons "~p1."
(list (cons #\1
(untranslate (cdar alist) nil wrld))))))
(t (tilde*measurephrase1 alist wrld)))
nil))
(defun find?measure (measurealist)
(cond ((endp measurealist) nil)
((let* ((entry (car measurealist))
(measure (cdr entry)))
(and (consp measure)
(eq (car measure) :?)
entry)))
(t (find?measure (cdr measurealist)))))
(defun provetermination (names tmachines measurealist mp rel
hints otfflg ctx ens wrld state ttree)
; Given a list of the functions introduced in a mutually recursive
; clique, their tmachines, the measurealist for the clique, a domain
; predicate mp on which a certain relation, rel, is known to be
; wellfounded, a list of hints in 1:1 correspondence with each of the
; above, and a world in which we can find the 'formals of
; each function in the clique, we prove the theorems required by the
; definitional principle. In particular, we prove that each measure
; is an op and that in every testsandcall in the tmachine
; of each function, the measure of the recursive calls is strictly
; less than that of the incoming arguments. If we fail, we cause an
; error.
; This function produces output describing the proofs. It should be
; the first outputproducing function in the defun processing on every
; branch through defun. It always prints something and leaves you in a
; clean state ready to begin a new sentence, but may leave you in the
; middle of a line (i.e., col > 0).
; If we succeed we return two values, consed together as "the" value
; in this error/value/state producing function. The first value is
; the column produced by our output. The second value is a ttree in
; which we have accumulated all of the ttrees associated with each
; proof done.
; This function is specially coded so that if tmachines is nil then
; it is a signal that there is only one element of names and it is a
; nonrecursive function. In that case, we shortcircuit all of the
; proof machinery and simply do the associated output. We coded it this
; way to preserve the invariant that provetermination is THE place
; the defun output is initiated.
; This function increments timers. Upon entry, any accumulated time
; is charged to 'othertime. The printing done herein is charged
; to 'printtime and the proving is charged to 'provetime.
(mvlet
(clset clsetttree)
(cond ((and (not (ldskipproofsp state))
tmachines)
(cleanupclauseset
(measureclausesforclique names
tmachines
measurealist
mp rel
wrld)
ens
wrld ttree state))
(t (mv nil ttree)))
(cond
((and (not (ldskipproofsp state))
(find?measure measurealist))
(let* ((entry (find?measure measurealist))
(fn (car entry))
(measure (cdr entry)))
(er soft ctx
"A :measure of the form (:? v1 ... vk) is only legal when the ~
defun is redundant (see :DOC redundantevents) or when skipping ~
proofs (see :DOC ldskipproofsp). The :measure ~x0 supplied for ~
function symbol ~x1 is thus illegal."
measure fn)))
(t
(erlet*
((clsetttree (accumulatettreeintostate clsetttree state)))
(pprogn
(incrementtimer 'othertime state)
(let ((displayedgoal (prettyifyclauseset clset
(let*abstractionp state)
wrld))
(simpphrase (tilde*simpphrase clsetttree)))
(mvlet
(col state)
(cond
((ldskipproofsp state)
(mv 0 state))
((null tmachines)
(io? event nil (mv col state)
(names)
(fmt "Since ~&0 is nonrecursive, its admission is trivial. "
(list (cons #\0 names))
(proofsco state)
state
nil)
:defaultbindings ((col 0))))
((null clset)
(io? event nil (mv col state)
(measurealist wrld rel names)
(fmt "The admission of ~&0 ~#0~[is~/are~] trivial, using ~@1 ~
and the measure ~*2 "
(list (cons #\0 names)
(cons #\1 (tilde@wellfoundedrelationphrase
rel wrld))
(cons #\2 (tilde*measurephrase
measurealist wrld)))
(proofsco state)
state
nil)
:defaultbindings ((col 0))))
(t
(io? event nil (mv col state)
(clsetttree displayedgoal simpphrase measurealist wrld
rel names)
(fmt "For the admission of ~&0 we will use ~@1 and the ~
measure ~*2 The nontrivial part of the measure ~
conjecture~#3~[~/, given ~*4,~] is~@6~%~%Goal~%~q5."
(list (cons #\0 names)
(cons #\1 (tilde@wellfoundedrelationphrase
rel wrld))
(cons #\2 (tilde*measurephrase
measurealist wrld))
(cons #\3 (if (nth 4 simpphrase) 1 0))
(cons #\4 simpphrase)
(cons #\5 displayedgoal)
(cons #\6 (if (taggedobject 'srlimit clsetttree)
" as follows (where the ~
subsumption/replacement limit ~
affected this analysis; see :DOC ~
casesplitlimitations)."
"")))
(proofsco state)
state
nil)
:defaultbindings ((col 0)))))
(pprogn
(incrementtimer 'printtime state)
(cond
((null clset)
; If the io? above did not print because 'event is inhibited, then col is nil.
; Just to keep ourselves sane, we will set it to 0.
(value (cons (or col 0) clsetttree)))
(t
(mvlet (erp ttree state)
(prove (termifyclauseset clset)
(makepspv ens wrld
:displayedgoal displayedgoal
:otfflg otfflg)
hints ens wrld ctx state)
(cond (erp
(er soft ctx
"The proof of the measure conjecture for ~&0 ~
has failed.~"
names))
(t
(mvlet (col state)
(io? event nil (mv col state)
(names clset)
(fmt "That completes the proof of ~
the measure theorem for ~&1. ~
Thus, we admit ~#1~[this ~
function~/these functions~] ~
under the principle of ~
definition."
(list (cons #\0 clset)
(cons #\1 names))
(proofsco state)
state
nil)
:defaultbindings ((col 0)))
(pprogn
(incrementtimer 'printtime state)
(value
(cons
(or col 0)
(constagtrees
clsetttree ttree)))))))))))))))))))
; When we succeed in proving termination, we will store the
; justification properties.
(defun putpropjustificationlst (measurealist mp rel wrld)
; Each function has a 'justification property. The value of the property
; is a justification record.
(cond ((null measurealist) wrld)
(t (putpropjustificationlst
(cdr measurealist) mp rel
(putprop (caar measurealist)
'justification
(make justification
:subset (allvars (cdar measurealist))
:mp mp
:rel rel
:measure (cdar measurealist))
wrld)))))
(defun crosstestsandcalls1 (toptests tests calls taclist)
; See the comment in crosstestsandcalls. Here, we cross a single
; testsandcalls record, having the given tests and calls, with such records
; in taclist.
(cond ((endp taclist)
nil)
(t (cons (make testsandcalls
:tests (append
toptests ; prettier if toptests comes first
(setdifferenceequal
(unionequal
tests
(access testsandcalls (car taclist)
:tests))
toptests))
:calls (unionequal
calls
(access testsandcalls (car taclist)
:calls)))
(crosstestsandcalls1 toptests tests calls
(cdr taclist))))))
(defun crosstestsandcalls (toptests tacs1 tacs2)
; We are given two nonempty lists, tacs1 and tacs2, of testsandcalls
; records. Each such record represents a list of tests together with a
; corresponding list of calls. For each <tests1, calls1> in tacs1 and <tests2,
; calls2> in tacs2, we can form a record by taking the union of toptests,
; tests1, and tests2 for the tests, and the union of calls1 and calls2 for the
; calls.
; Here, we view a testsandcalls record as the universal closure of an
; implication. Its hypothesis is the conjunction of its toptests and its
; tests. Its conclusion is the conjunction formed from each call by creating
; the usual corresponding formula, stating that the measure decreases for the
; indicated substitution. Moreover, the disjunction of all such hypotheses is
; the same for both tacs1 and tacs2.
; Thus, inputs tacs1 and tacs2 represent conjunctions C1 and C2 (respectively)
; of such formulas. The returned list of testsandcalls records then
; represents a formula equivalent to (and C1 C2), for which the disjunction of
; all hypotheses is equivalent to that for C1 and for C2, but with toptests
; included explicitly.
; In the context of induction, we have presumably proved each measure
; conjecture mentioned above. Moreover, the hypotheses completely cover the
; possibilities; that is, the disjunctions of the hypotheses for tacsi is
; equivalent to t (i=1,2), and thus the disjunction of the hypotheses for the
; returned testsandcalls is equivalent to the conjunction of toptests, which
; are the tests governing a toplevel call of this function.
(cond ((endp tacs1)
nil)
(t (append (crosstestsandcalls1
toptests
(access testsandcalls (car tacs1) :tests)
(access testsandcalls (car tacs1) :calls)
tacs2)
(crosstestsandcalls toptests (cdr tacs1) tacs2)))))
(defun inductionmachineforfn1 (names body alist tests calls)
; This function builds a list of testsandcalls for the fnname in
; names with the given body/alist, assuming that all calls in alist
; are among the given calls and that it is justified to
; add all the additional calls in calls. Note that we don't need to
; know the function symbol to which the body belongs; all the
; functions in names are considered "recursive" calls. Names is a
; list of all the mutually recursive fns in the clique.
(cond
((or (variablep body)
(fquotep body)
(and (not (flambdaapplicationp body))
(not (eq (ffnsymb body) 'if))
(not (eq (ffnsymb body) 'prog2$))
(not (eq (ffnsymb body) 'mustbeequal))))
(let ((reversetests (reverse tests)))
(list
(make testsandcalls
:tests reversetests
:calls (reverse
(allcalls names body alist
(allcallslst names
reversetests
nil
calls)))))))
((flambdaapplicationp body)
; Observe that we just go straight into the body of the lambda (with the
; appropriate alist) but that we modify calls so that every testsandcalls
; we build will contain all of the calls in the actuals to the lambda
; application.
(inductionmachineforfn1 names
(lambdabody (ffnsymb body))
(pairlis$
(lambdaformals (ffnsymb body))
(sublisvarlst alist (fargs body)))
tests
(allcallslst names (fargs body) alist
calls)))
((eq (ffnsymb body) 'prog2$)
(cond ((allcalls names (fargn body 1) alist nil)
; If there are recursive calls of the function in the first argument, then the
; user is presumably intending to continue the termination and induction
; analyses through that first argument as well. Otherwise, we want to keep the
; induction scheme simple, so we do not extend that analysis into the first
; argument, either here or in terminationmachine; so keep the handling
; of prog2$ for that function in sync with the handling of prog2$ here.
(crosstestsandcalls
tests
; Note that each of the following arguments to crosstestsandcalls is
; nonnil, by an easy induction on inductionmachineforfn1.
(inductionmachineforfn1 names
(fargn body 1)
alist
nil ; fresh tests
calls)
(inductionmachineforfn1 names
(fargn body 2)
alist
nil ; fresh tests
calls)))
(t (inductionmachineforfn1
names
(fargn body 2)
alist
tests
calls ; equal to (allcalls names (fargn body 1) alist calls)
))))
((eq (ffnsymb body) 'mustbeequal)
; It is sound to treat mustbeequal like a macro for logic purposes. We do so
; both for induction and for termination.
(inductionmachineforfn1 names
(fargn body 1)
alist
tests
calls))
(t
(let ((insttest (sublisvar alist
; Since (removeguardholders x) is provably equal to x, the machine we
; generate using it below is equivalent to the machine generated without it.
(removeguardholders (fargn body 1)))))
(append
(inductionmachineforfn1 names
(fargn body 2)
alist
(cons insttest tests)
calls)
(inductionmachineforfn1 names
(fargn body 3)
alist
(cons (dumbnegatelit insttest)
tests)
calls))))))
(defun inductionmachineforfn (names body)
; We build an induction machine for the function in names with the given body.
; We claim the soundness of the induction schema suggested by this machine is
; easily seen from the proof done by provetermination. See
; terminationmachine.
; Note: The induction machine built for a clique of more than 1
; mutually recursive functions is probably unusable. We do not know
; how to do inductions on such functions now.
(inductionmachineforfn1 names
body
nil
nil
nil))
(defun inductionmachines (names bodies)
; This function builds the induction machine for each function defined
; in names with the corresponding body in bodies. A list of machines
; is returned. See terminationmachine.
; Note: If names has more than one element we return nil because we do
; not know how to interpret the inductionmachines that would be
; constructed from a nontrivial clique of mutually recursive
; functions. As a matter of fact, as of this writing,
; inductionmachineforfn constructs the "natural" machine for
; mutually recursive functions, but there's no point in consing them
; up since we can't use them. So all that machinery is
; shortcircuited here.
(cond ((null (cdr names))
(list (inductionmachineforfn names (car bodies))))
(t nil)))
(defun putpropinductionmachinelst (names machines wrld)
; Note: If names has more than one element we do nothing. We only
; know how to interpret induction machines for singly recursive fns.
(cond ((null (cdr names))
(putprop (car names)
'inductionmachine
(car machines)
wrld))
(t wrld)))
(defun quickblockinitialsettings (formals)
(cond ((null formals) nil)
(t (cons 'uninitialized
(quickblockinitialsettings (cdr formals))))))
(defun quickblockinfo1 (var term)
(cond ((eq var term) 'unchanging)
((dumboccur var term) 'selfreflexive)
(t 'questionable)))
(defun quickblockinfo2 (setting info1)
(case setting
(questionable 'questionable)
(uninitialized info1)
(otherwise
(cond ((eq setting info1) setting)
(t 'questionable)))))
(defun quickblocksettings (settings formals args)
(cond ((null settings) nil)
(t (cons (quickblockinfo2 (car settings)
(quickblockinfo1 (car formals)
(car args)))
(quickblocksettings (cdr settings)
(cdr formals)
(cdr args))))))
(defun quickblockdowntmachine (name settings formals tmachine)
(cond ((null tmachine) settings)
((not (eq name
(ffnsymb (access testsandcall (car tmachine) :call))))
(er hard 'quickblockdowntmachine
"When you add induction on mutually recursive functions don't ~
forget about QUICKBLOCKINFO!"))
(t (quickblockdowntmachine
name
(quickblocksettings
settings
formals
(fargs (access testsandcall (car tmachine) :call)))
formals
(cdr tmachine)))))
(defun quickblockinfo (name formals tmachine)
; This function should be called a singly recursive function, name, and
; its termination machine. It should not be called on a function
; in a nontrivial mutually recursive clique because the we don't know
; how to analyze a call to a function other than name in the tmachine.
; We return a list in 1:1 correspondence with the formals of name.
; Each element of the list is either 'unchanging, 'selfreflexive,
; or 'questionable. The list is used to help quickly decide if a
; blocked formal can be tolerated in induction.
(quickblockdowntmachine name
(quickblockinitialsettings formals)
formals
tmachine))
(defun putpropquickblockinfolst (names tmachines wrld)
; We do not know how to compute quickblockinfo for nontrivial
; mutuallyrecursive cliques. We therefore don't do anything for
; those functions. If names is a list of length 1, we do the
; computation. We assume we can find the formals of the name in wrld.
(cond ((null (cdr names))
(putprop (car names)
'quickblockinfo
(quickblockinfo (car names)
(formals (car names) wrld)
(car tmachines))
wrld))
(t wrld)))
(deflabel subversiverecursions
:doc
":DocSection Miscellaneous
why we restrict ~il[encapsulate]d recursive functions~/
Subtleties arise when one of the ``constrained'' functions, ~c[f],
introduced in the ~il[signature] of an ~ilc[encapsulate] event, is
involved in the termination argument for a nonlocal recursively
defined function, ~c[g], in that ~c[encapsulate]. During the
processing of the encapsulated events, ~c[f] is locally defined to
be some witness function, ~c[f']. Properties of ~c[f'] are
explicitly proved and exported from the encapsulate as the
constraints on the undefined function ~c[f]. But if ~c[f] is used
in a recursive ~c[g] defined within the encapsulate, then the
termination proof for ~c[g] may use properties of ~c[f']  the
witness  that are not explicitly set forth in the constraints
stated for ~c[f].
Such recursive ~c[g] are said be ``subversive'' because if naively
treated they give rise to unsound induction schemes or (via
functional instantiation) recurrence equations that are impossible
to satisfy. We illustrate what could go wrong below.
Subversive recursions are not banned outright. Instead, they are
treated as part of the constraint. That is, in the case above, the
definitional equation for ~c[g] becomes one of the constraints on
~c[f]. This is generally a severe restriction on future functional
instantiations of ~c[f]. In addition, ACL2 removes from its knowledge
of ~c[g] any suggestions about legal inductions to ``unwind'' its
recursion.
What should you do? Often, the simplest response is to move the
offending recursive definition, e.g., ~c[g], out of the encapsulate.
That is, introduce ~c[f] by constraint and then define ~c[g] as an
``independent'' event. You may need to constrain ``additional''
properties of ~c[f] in order to admit ~c[g], e.g., constrain it to
reduce some ordinal measure. However, by separating the
introduction of ~c[f] from the admission of ~c[g] you will clearly
identify the necessary constraints on ~c[f], functional
instantiations of ~c[f] will be simpler, and ~c[g] will be a useful
function which suggests inductions to the theorem prover.
Note that the functions introduced in the ~il[signature] should not
even occur ancestrally in the termination proofs for nonlocal
recursive functions in the encapsulate. That is, the constrained
functions of an encapsulate should not be reachable in the
dependency graph of the functions used in the termination arguments
of recursive functions in encapsulate. If they are reachable, their
definitions become part of the constraints.~/
The following event illustrates the problem posed by subversive
recursions.
~bv[]
(encapsulate (((f *) => *))
(local (defun f (x) (cdr x)))
(defun g (x)
(if (consp x) (not (g (f x))) t)))
~ev[]
Suppose, contrary to how ACL2 works, that the encapsulate above
were to introduce no constraints on ~c[f] on the bogus grounds that
the only use of ~c[f] in the encapsulate is in an admissible function.
We discuss the plausibility of this bogus argument in a moment.
Then it would be possible to prove the theorem:
~bv[]
(defthm fnotidentity
(not (equal (f '(a . b)) '(a . b)))
:ruleclasses nil
:hints ((\"Goal\" :use (:instance g (x '(a . b))))))
~ev[]
simply by observing that if ~c[(f '(a . b))] were ~c['(a . b)], then
~c[(g '(a . b))] would be ~c[(not (g '(a . b)))], which is impossible.
But then we could functionally instantiate ~c[fnotidentity], replacing
~c[f] by the identity function, to prove ~c[nil]! This is bad.
~bv[]
(defthm bad
nil
:ruleclasses nil
:hints
((\"Goal\" :use (:functionalinstance fnotidentity (f identity)))))
~ev[]
This sequence of events was legal in versions of ACL2 prior to Version 1.5.
When we realized the problem we took steps to make it illegal. However,
our steps were insufficient and it was possible to sneak in a subversive
function (via mutual recursion) as late as Version 2.3.
We now turn to the plausibility of the bogus argument above. Why might
one even be tempted to think that the definition of ~c[g] above poses
no constraint on ~c[f]? Here is a very similar encapsulate.
~bv[]
(encapsulate (((f *) => *))
(local (defun f (x) (cdr x)))
(defun map (x)
(if (consp x)
(cons (f x) (map (cdr x)))
nil)))
~ev[]
Here ~c[map] plays the role of ~c[g] above. Like ~c[g], ~c[map]
calls the constrained function ~c[f]. But ~c[map] truly does not
constrain ~c[f]. In particular, the definition of ~c[map] could be
moved ``out'' of the encapsulate so that ~c[map] is introduced
afterwards. The difference between ~c[map] and ~c[g] is that the
constrained function plays no role in the termination argument for
the one but does for the other.
As a ``userfriendly'' gesture, ACL2 implicitly moves ~c[map]like
functions out of encapsulations; logically speaking, they are
introduced after the encapsulation. This simplifies the constraint.
This is done only for ``toplevel'' encapsulations. When an
~c[encapsulate] containing a nonempty ~il[signature] list is
embedded in another ~c[encapsulate] with a nonempty signature list,
no attempt is made to move ~c[map]like functions out. The user is
advised, via the ``infected'' warning, to phrase the encapsulation
in the simplest way possible.
The lingering bug between Versions 1.5 and 2.3 mentioned above was
due to our failure to detect the ~c[g]like nature of some functions
when they were defined in mutually recursively cliques with other
functions. The singly recursive case was recognized. The bug arose
because our detection ``algorithm'' was based on the ``suggested
inductions'' left behind by successful definitions. We failed to
recall that mutuallyrecursive definitions do not, as of this
writing, make any suggestions about inductions and so did not leave
any traces of their subversive natures.~/")
(deflabel subversiveinductions
:doc
":DocSection Miscellaneous
why we restrict ~il[encapsulate]d recursive functions~/
~l[subversiverecursions]. ~/
")
(defmacro bigmutrec (names)
; All mutual recursion nests with more than the indicated number of defuns will
; be processed by installing intermediate worlds, for improved performance. We
; have seen an improvement of roughly two orders of magnitude in such a case.
; The value below is merely heuristic, chosen with very little testing; we
; should feel free to change it.
`(> (length ,names) 20))
(defmacro updatew (condition neww &optional retractp)
; WARNING: This function installs a world, so it may be necessary to call it
; only in the (dynamic) context of revertworldonerror. For example, its
; calls during definitional processing are all under the call of
; revertworldonerror in defunsfn.
`(let ((wrld ,neww))
(cond
(,condition
(pprogn ,(if retractp
'(setw 'retraction wrld state)
'(setw 'extension wrld state))
(value wrld)))
(t (value wrld)))))
(defun putinductioninfo
(names arglists measures bodies mp rel hints otfflg bigmutrec ctx ens wrld
state)
; WARNING: This function installs a world. That is safe at the time of this
; writing because this function is only called by defunsfn0, which is only
; called by defunsfn, where that call is protected by a revertworldonerror.
; We are processing a clique of mutually recursive functions with the
; names, arglists, measures, and bodies given. All of the
; above lists are in 1:1 correspondence. The hints is the result
; of appending together all of the hints provided. Mp and rel are the
; domain predicate and wellfounded relation to be used. We attempt to
; prove the admissibility of the recursions. We cause an error if any
; proof fails. We put a lot of properties under the function symbols,
; namely:
; recursivep all fns in names
; justification all recursive fns in names
; inductionmachine the singly recursive fn in name*
; quickblockinfo the singly recursive fn in name*
; symbolclass :ideal all fns in names
; *If names consists of exactly one recursive fn, we store its
; inductionmachine and its quickblockinfo, otherwise we do not.
; If no error occurs, we return a triple consisting of the column the
; printer is in, the final value of wrld and a tag tree documenting
; the proofs we did.
; Note: The function could be declared to return 5 values, but we
; would rather use the standard state and error primitives and so
; it returns 3 and lists together the three "real" answers.
(let* ((wrld1 (putproprecursiveplst names bodies wrld)))
; The put above stores a note on each function symbol as to whether it is
; recursive or not. An important question arises: have we inadventently
; assumed something axiomatically about inadmissible functions? We say no.
; None of the functions in question have bodies yet, so the simplifier doesn't
; care about properties such as 'recursivep. However, we make use of this
; property below to decide if we need to prove termination.
(cond ((and (null (cdr names))
(null (getprop (car names) 'recursivep nil
'currentacl2world wrld1)))
; If only one function is being defined and it is nonrecursive, we can quit.
; But we have to store the symbolclass and we have to print out the admission
; message with provetermination so the rest of our processing is uniform.
(erprogn
(cond
(hints
(er soft ctx
"Since ~x0 is nonrecursive it is odd that you have ~
supplied :hints (which are used only during ~
termination proofs). We suspect something is ~
amiss, e.g., you meant to supply :guardhints or ~
the body of the definition is incorrect."
(car names)))
(t (value nil)))
(erlet*
((wrld1 (updatew bigmutrec wrld1))
(pair (provetermination names nil nil mp rel nil
otfflg ctx ens wrld1 state nil)))
; We know that pair is of the form (col . ttree), where col is the column
; the output state is in.
(value (list (car pair)
(putpropxlst1 names 'symbolclass :ideal wrld1)
(cdr pair))))))
(t
; Otherwise we first construct the termination machines for all the
; functions in the clique.
(let*
((tmachines (terminationmachines names bodies)))
; Next we get the measures for each function. That may cause an error
; if we couldn't guess one for some function.
(erlet*
((wrld1 (updatew bigmutrec wrld1))
(measurealist
(guessmeasurealist names arglists
measures
tmachines
ctx wrld1 state))
(hints (if hints
(value hints)
(let ((defaulthints (defaulthints wrld1)))
(if defaulthints ; then we haven't yet translated
(translatehints
(cons "Measure Lemma for" (car names))
defaulthints ctx wrld1 state)
(value hints)))))
(pair (provetermination names
tmachines
measurealist
mp
rel
hints
otfflg
ctx
ens
wrld1
state
nil)))
; Ok, we have managed to prove termination! Pair is a pair of the form (col .
; ttree), where col tells us what column the printer is in and ttree describes
; the proofs done. We now store the 'justification of each function, the
; induction machine for each function, and the quickblockinfo.
(let* ((wrld2
(putpropjustificationlst measurealist mp rel wrld1))
(wrld3 (putpropinductionmachinelst
names
(inductionmachines names bodies)
wrld2))
(wrld4 (putpropquickblockinfolst names
tmachines
wrld3))
(wrld5 (putpropxlst1 names
'symbolclass :ideal wrld4)))
; We are done. We will return the final wrld and the ttree describing
; the proofs we did.
(value
(list (car pair)
wrld5
(pushlemma
(cddr (assoceq rel
(globalval
'wellfoundedrelationalist
wrld5)))
(cdr pair)))))))))))
; We next worry about storing the normalized bodies.
(defconst *equalityaliases* '(eq eql =))
(defun destructuredefinition (term installbody ens wrld ttree)
; Term is a translated term that is the :corollary of a :definition rule. If
; installbody is nonnil then we intend to update the 'defbodies
; property; and if moreover, installbody is :normalize, then we want to
; normalize the resulting new body. Ens is an enabled structure if
; installbody is :normalize; otherwise ens is ignored.
; We return (mv hyps equiv fn args body newbody ttree) or else nils if we fail
; to recognize the form of term. Hyps results flattening the hypothesis of
; term, when a call of implies, into a list of hypotheses. Failure can be
; detected by checking for (null fn) since nil is not a legal fn symbol.
(mvlet
(hyps equiv fnargs body)
(casematch term
(('implies hyp (equiv fnargs body))
(mv (flattenandsinlit hyp)
equiv
fnargs
body))
((equiv fnargs body)
(mv nil
equiv
fnargs
body))
(& (mv nil nil nil nil)))
(let ((equiv (if (membereq equiv *equalityaliases*)
'equal
equiv))
(fn (and (consp fnargs) (car fnargs))))
(cond
((and fn
(symbolp fn)
(not (membereq fn
; Hide is disallowed in chkacceptabledefinitionrule.
'(quote if)))
(equivalencerelationp equiv wrld))
(mvlet (body ttree)
(cond ((eq installbody :NORMALIZE)
(normalize (removeguardholders body)
nil ; iffflg
nil ; typealist
ens
wrld
ttree))
(t (mv body ttree)))
(mv hyps
equiv
fn
(cdr fnargs)
body
ttree)))
(t (mv nil nil nil nil nil nil))))))
(defun memberrewriterulerune (rune lst)
; Lst is a list of :rewrite rules. We determine whether there is a
; rule in lst with the :rune rune.
(cond ((null lst) nil)
((equal rune (access rewriterule (car lst) :rune)) t)
(t (memberrewriterulerune rune (cdr lst)))))
(defun replacerewriterulerune (rune rule lst)
; Lst is a list of :rewrite rules and one with :rune rune is among them.
; We replace that rule with rule.
(cond ((null lst) nil)
((equal rune (access rewriterule (car lst) :rune))
(cons rule (cdr lst)))
(t (cons (car lst) (replacerewriterulerune rune rule (cdr lst))))))
; We massage the hyps with this function to speed rewrite up.
(defun preprocesshyp (hyp)
; In nqthm, this function also replaced (not (zerop x)) by
; ((numberp x) (not (equal x '0))).
(casematch hyp
(('atom x) (list (mconsterm* 'not (mconsterm* 'consp x))))
(& (list hyp))))
(defun preprocesshyps (hyps)
(cond ((null hyps) nil)
(t (append (preprocesshyp (car hyps))
(preprocesshyps (cdr hyps))))))
(defun adddefinitionrulewithttree (rune nume clique controlleralist
installbody term ens wrld ttree)
; We make a :rewrite rule of subtype 'definition (or 'abbreviation)
; and add it to the 'lemmas property of the appropriate fn. This
; function is defined the way it is (namely, taking term as an arg and
; destructuring it rather than just taking term in pieces) because it
; is also used as the function for adding a usersupplied :REWRITE
; rule of subclass :DEFINITION.
(mvlet
(hyps equiv fn args body ttree)
(destructuredefinition term installbody ens wrld ttree)
(let* ((varsbag (allvarsbaglst args nil))
(abbreviationp (and (null hyps)
(null clique)
; Rockwell Addition: We have changed the notion of when a rule is an
; abbreviation. Our new concern is with stobjs and lambdas.
; If fn returns a stobj, we don't consider it an abbreviation unless
; it contains no lambdas. Thus, the updaters are abbreviations but
; lambdanests built out of them are not. We once tried the idea of
; letting a lambda in a function body disqualify the function as an
; abbreviation, but that made FLOOR no longer an abbreviation and some
; of the fp proofs failed. So we made the question depend on stobjs
; for compatibility's sake.
(abbreviationp
(not (allnils (stobjsout fn wrld)))
varsbag
body)))
(rule
(make rewriterule
:rune rune
:nume nume
:hyps (preprocesshyps hyps)
:equiv equiv
:lhs (mconsterm fn args)
:freevarsplhs (not (null varsbag))
:rhs body
:subclass (cond (abbreviationp 'abbreviation)
(t 'definition))
:heuristicinfo
(cond (abbreviationp nil)
(t (cons clique controlleralist)))
; Backchainlimitlst does not make much sense for definitions.
:backchainlimitlst nil)))
(let ((wrld0 (if (eq fn 'hide)
wrld
(putprop fn 'lemmas
(cons rule (getprop fn 'lemmas nil
'currentacl2world wrld))
wrld))))
(cond (installbody
(mv (putprop fn
'defbodies
(cons (make defbody
:nume nume
:hyp (and hyps (conjoin hyps))
:concl body
:rune rune
:formals args
:recursivep clique
:controlleralist controlleralist)
(getprop fn 'defbodies nil
'currentacl2world wrld))
wrld0)
ttree))
(t (mv wrld0 ttree)))))))
(defun adddefinitionrule (rune nume clique controlleralist installbody term
ens wrld)
(mvlet (wrld ttree)
(adddefinitionrulewithttree rune nume clique controlleralist
installbody term ens wrld nil)
(declare (ignore ttree))
wrld))
#+:nonstandardanalysis
(defun listofstandardnumberpmacro (lst)
; If the guard for standardnumberp is changed from t, consider changing
; the corresponding calls of mconsterm* to fconsterm*.
(if (consp lst)
(if (consp (cdr lst))
(mconsterm*
'if
(mconsterm* 'standardnumberp (car lst))
(listofstandardnumberpmacro (cdr lst))
*nil*)
(mconsterm* 'standardnumberp (car lst)))
*t*))
(defun putpropbodylst (names arglists bodies normalizeps
clique controlleralist
#+:nonstandardanalysis stdp
ens wrld installedwrld ttree)
#
; Rockwell Addition: A major change is the handling of PROG2$ and THE
; below.
; We store the body property for each name in names. It is set to the
; normalized body. Normalization expands some nonrecursive functions,
; namely those on *expandablebootstrapnonrecfns*, which includes
; old favorites like EQ and ATOM. In addition, we eliminate all the
; PROG2$s, MUSTBEEQUALs and THEs from the body. This can be seen as
; just an optimization of expanding nonrec fns.
; We add a definition rule equating the call of name with its
; normalized body.
; We store the unnormalized body under the property
; 'unnormalizedbody.
; We return two results: the final wrld and a ttree justifying the
; normalization, which is an extension of the input ttree.
; Essay on the Normalization of Bodies
; We normalize the bodies of functions to speed up typeset
; and rewriting. But there are some subtle issues here. Let term be
; a term and let term' be its normalization. We will ignore iffflg
; and typealist here. First, we claim that term and term' are
; equivalent. Thus, if we are allowed to add the axiom (fn x) = term
; then we may add (fn x) = term' too. But while term and term' are
; equivalent they are not interchangeable from the perspective of
; defun processing. For example, as nqthm taught us, the measure
; conjectures generated from term' may be inadequate to justify the
; admission of a function whose body is term. A classic example is
; (fn x) = (if (fn x) t t), where the normalized body is just t. The
; Hisorical Plaque below contains a proof that if (fn x) = term' is
; admissible then there exists one and only one function satisfying
; (fn x) = term. Thus, while the latter definition may not actually
; be admissible it at least will not get us into trouble and in the
; end the issue visavis admissibility seems to be the technical one
; of exactly how we wish to define the Principle of Definition.
; Historical Plaque from Nqthm
; The following extensive comment used to guard the definition of
; DEFN0 in nqthm and is placed here partly as a nostalgic reminder of
; decades of work and partly because it has some good statistics in it
; that we might still want to look at.
; This function is FUNCALLed and therefore may not be made a MACRO.
; The list of comments on this function do not necessarily describe
; the code below. They have been left around in reverse chronology
; order to remind us of the various combinations of preprocessing
; we have tried.
; If we ever get blown out of the water while normalizing IFs in a
; large defn, read the following comment before abandoning
; normalization.
; 18 August 1982. Here we go again! At the time of this writing
; the preprocessing of defns is as follows, we compute the
; induction and type info on the translated body and store under
; sdefn the translated body. This seems to slow down the system a
; lot and we are going to change it so that we store under sdefn
; the result of expanding boot strap nonrec fns and normalizing
; IFs. As nearly as we can tell from the comments below, we have
; not previously tried this. According to the record, we have
; tried expanding all nonrec fns, and we have tried expanding boot
; strap fns and doing a little normalization. The data that
; suggests this will speed things up is as follows. Consider the
; first call of SIMPLIFYCLAUSE in the proof of PRIMELISTTIMES
; LIST. The first three literals are trivial but the fourth call
; of SIMPLIFYCLAUSE1 is on (NOT (PRIME1 C (SUB1 C))). With SDEFNs
; not expanded and normalized  i.e., under the processing as it
; was immediately before the current change  there are 2478 calls
; of REWRITE and 273 calls of RELIEVEHYPS for this literal. With
; all defns preprocessed as described here those counts drop to
; 1218 and 174. On a sample of four theorems, PRIMELISTTIMES
; LIST, PRIMELISTPRIMEFACTORS, FALSIFY1FALSIFIES, and ORDERED
; SORT, the use of normalized and expanded sdefns saves us 16
; percent of the conses over the use of untouched sdefns, reducing
; the cons counts for those theorems from 880K to 745K. It seems
; unlikely that this preprocessing will blow us out of the water on
; large defns. For the EV used in UNSOLV and for the 386L M with
; subroutine call this new preprocessing only marginally increases
; the size of the sdefn. It would be interesting to see a function
; that blows us out of the water. When one is found perhaps the
; right thing to do is to so preprocess small defns and leave big
; ones alone.
; 17 December 1981. Henceforth we will assume that the very body
; the user supplies (modulo translation) is the body that the
; theoremprover uses to establish that there is one and only one
; function satisfying the definition equation by determining that
; the given body provides a method for computing just that
; function. This prohibits our "improving" the body of definitions
; such as (f x) = (if (f x) a a) to (f x) = a.
; 18 November 1981. We are sick of having to disable nonrec fns in
; order to get large fns processed, e.g., the interpreter for our
; 386L class. Thus, we have decided to adopt the policy of not
; touching the user's typein except to TRANSLATE! it. The
; induction and type analysis as well as the final SDEFN are based
; on the translated typein.
; Before settling with the preprocessing used below we tried
; several different combinations and did provealls. The main issue
; was whether we should normalize sdefns. Unfortunately, the
; incorporation of META0LEMMAS was also being experimented with,
; and so we do not have a precise breakdown of who is responsible
; for what. However, below we give the total stats for three
; separate provealls. The first, called 1PROVEALL, contained
; exactly the code below  except that the ADDDCELL was given the
; SDEFN with all the fn names replaced by *1*Fns instead of a fancy
; TRANSLATETOINTERLISP call. Here are the 1PROVEALL stats.
; Elapsed time = 9532.957, CPU time = 4513.88, GC time = 1423.261,
; IO time = 499.894, CONSes consumed = 6331517.
; We then incorporated META0LEMMAS. Simultaneously, we tried
; running the RUN fns through DEFN and found that we exploded. The
; expansion of nonrec fns and the normalization of IFs before the
; induction analysis transformed functions of CONSCOUNT 300 to
; functions of CONSCOUNT exceeding 18K. We therefore decided to
; expand only BOOTSTRAP fns  and not NORMALIZEIFS for the
; purposes of induction analysis. After the induction and type
; analyses were done, we put down an SDEFN with some trivial IF
; simplification performed  e.g., IF X Y Y => Y and IF bool T F
; => bool  but not a NORMALIZEIFs version. We then ran a
; proveall with CANCEL around as a META0LEMMA. The result was
; about 20 percent slower than the 1PROVEALL and used 15 percent
; more CONSes. At first this was attributed to CANCEL. However,
; we then ran two simultaneous provealls, one with META0LEMMAS set
; to NIL and one with it set to ((1CANCEL . CORRECTNESSOFCANCEL)).
; The result was that the version with CANCEL available used
; slightly fewer CONSes than the other one  7303311 to 7312505
; That was surprising because the implementation of META0LEMMAS
; uses no CONSes if no META0LEMMAS are available, so the entire 15
; percent more CONSes had to be attributed to the difference in the
; defn processing. This simultaneous run was interesting for two
; other reasons. The times  while still 20 percent worse than
; 1PROVEALL  were one half of one percent different, with CANCEL
; being the slower. That means having CANCEL around does not cost
; much at all  and the figures are significant despite the slop
; in the operating system's timing due to thrashing because the two
; jobs really were running simultaneously. The second interesting
; fact is that CANCEL can be expected to save us a few CONSes
; rather than cost us.
; We therefore decided to return the DEFN0 processing to its
; original state. Only we did it in two steps. First, we put
; NORMALIZEIFs into the preinduction processing and into the
; final SDEFN processing. Here are the stats on the resulting
; proveall, which was called PROVEALLWITHNORMANDCANCEL but not
; saved. Elapsed time = 14594.01, CPU time = 5024.387, GC time =
; 1519.932, IO time = 593.625, CONSes consumed = 6762620.
; While an improvement, we were still 6 percent worse than
; 1PROVEALL on CONSes. But the only difference between 1PROVEALL
; and PROVEALLWITHNORMANDCANCEL  if you discount CANCEL which
; we rightly believed was paying for itself  was that in the
; former induction analyses and type prescriptions were being
; computed from fully expanded bodies while in the latter they were
; computed from only BOOTSTRAPexpanded bodies. We did not
; believe that would make a difference of over 400,000 CONSes, but
; had nothing else to believe. So we went to the current state,
; where we do the induction and type analyses on the fully expanded
; and normalized bodies  bodies that blow us out of the water on
; some of the RUN fns. Here are the stats for
; PROVEALLPROOFS.79101, which was the proveall for that version.
; Elapsed time = 21589.84, CPU time = 4870.231, GC time = 1512.813,
; IO time = 554.292, CONSes consumed= 6356282.
; Note that we are within 25K of the number of CONSes used by
; 1PROVEALL. But to TRANSLATETOINTERLISP all of the defns in
; question costs 45K. So  as expected  CANCEL actually saved
; us a few CONSes by shortening proofs. It takes only 18 seconds
; to TRANSLATETOINTERLISP the defns, so a similar argument does
; not explain why the latter proveall is 360 seconds slower than
; 1PROVEALL. But since the elapsed time is over twice as long, we
; believe it is fair to chalk that time up to the usual slop
; involved in measuring cpu time on a time sharing system.
; We now explain the formal justification of the processing we do
; on the body before testing it for admissibility.
; We do not work with the body that is typed in by the user but
; with an equivalent body' produced by normalization and the
; expansion of nonrecursive function calls in body. We now prove
; that if (under no assumptions about NAME except that it is a
; function symbol of the correct arity) (a) body is equivalent to
; body' and (b) (name . args) = body' is accepted under our
; principle of definition, then there exists exactly one function
; satisfying the original equation (name . args) = body.
; First observe that since the definition (name . args) = body' is
; accepted by our principle of definition, there exists a function
; satisfying that equation. But the accepted equation is
; equivalent to the equation (name . args) = body by the
; hypothesis that body is equivalent to body'.
; We prove that there is only one such function by induction.
; Assume that the definition (name . args) = body has been accepted
; under the principle of definition. Suppose that f is a new name
; and that (f . args) = bodyf, where bodyf results from replacing
; every use of name as a function symbol in body with f. It
; follows that (f . args) = bodyf', where bodyf' results from
; replacing every use of name as a function symbol in body' with f.
; We can now easily prove that (f . args) = (name . args) by
; induction according to the definition of name. Q.E.D.
; One might be tempted to think that if the defn with body' is
; accepted under the principle of definition then so would be the
; defn with body and that the use of body' was merely to make the
; implementation of the defn principle more powerful. This is not
; the case. For example
; (R X) = (IF (R X) T T)
; is not accepted by the definitional principle, but we would
; accept the body'version (R X) = T, and by our proof, that
; function uniquely satisfies the equation the user typed in.
; One might be further tempted to think that if we changed
; normalize so that (IF X Y Y) = Y was not applied, then the two
; versions were interacceptable under the defn principle. This is
; not the case either. The function
; (F X) = (IF (IF (X.ne.0) (F X1) F) (F X1) T)
; is not accepted under the principle of defn. Consider its
; normalized body.
#
(cond ((null names) (mv wrld ttree))
(t (let* ((fn (car names))
(args (car arglists))
(body (car bodies))
(normalizep (car normalizeps))
(rune (fnrunenume fn nil nil installedwrld))
(nume (fnrunenume fn t nil installedwrld)))
(let* ((eqterm (fconsterm* 'equal
(fconsterm fn args)
body))
(term #+:nonstandardanalysis
(if (and stdp (consp args))
(fconsterm*
'implies
(listofstandardnumberpmacro args)
eqterm)
eqterm)
#:nonstandardanalysis
eqterm)
#+:nonstandardanalysis
(wrld (if stdp
(putprop fn 'constrainedp t wrld)
wrld)))
(mvlet
(wrld ttree)
(adddefinitionrulewithttree
rune nume clique controlleralist
(if normalizep :NORMALIZE t) ; installbody
term ens
(putprop fn
'unnormalizedbody
body
wrld)
ttree)
(putpropbodylst (cdr names)
(cdr arglists)
(cdr bodies)
(cdr normalizeps)
clique controlleralist
#+:nonstandardanalysis stdp
ens
wrld installedwrld ttree)))))))
; We now develop the facility for guessing the typeprescription of a defuned
; function. When guards were part of the logic, the first step was to guess
; the types implied by the guard. We no longer have to do that, but the
; utility written for it is used elsewhere and so we keep it here.
; Suppose you are trying to determine the type implied by term for some
; variable x. The key trick is to normalize the term and replace every true
; output by x and every nil output by a term with an empty typeset. Then take
; the type of that term. For example, if term is (if (if p q) r nil) then it
; normalizes to (if p (if q (if r t nil) nil) nil) and so produces the
; intermediate term (if p (if q (if r x e ) e ) e ), where x is the formal in
; whose type we are interested and e is a new variable assumed to be of empty
; type.
(defun typesetimpliedbyterm1 (term tvar fvar)
; Term is a normalized propositional term. Tvar and fvar are two variable
; symbols. We return a normalized term equivalent to (if term tvar fvar)
; except we drive tvar and fvar as deeply into term as possible.
(cond ((variablep term)
(fconsterm* 'if term tvar fvar))
((fquotep term)
(if (equal term *nil*) fvar tvar))
((eq (ffnsymb term) 'if)
(fconsterm* 'if
(fargn term 1)
(typesetimpliedbyterm1 (fargn term 2) tvar fvar)
(typesetimpliedbyterm1 (fargn term 3) tvar fvar)))
(t
; We handle all nonIF applications here, even lambda applications.
; Once upon a time we considered driving into the body of a lambda.
; But that introduces a free var in the body, namely fvar (or whatever
; the new variable symbol is) and there are no guarantees that typeset
; works on such a nonterm.
(fconsterm* 'if term tvar fvar))))
(defun typesetimpliedbyterm (var notflg term ens wrld ttree)
; Given a variable and a term, we determine a type set for the
; variable under the assumption that the term is nonnil. If notflg
; is t, we negate term before using it. This function is not used in
; the guard processing but is needed in the compoundrecognizer work.
; The ttree returned is 'assumptionfree (provided the initial ttree
; is also).
(let* ((newvar (genvar 'genvar "EMPTY" nil (allvars term)))
(typealist (list (list* newvar *tsempty* nil))))
(mvlet (normalterm ttree)
(normalize term t nil ens wrld ttree)
(typeset
(typesetimpliedbyterm1 normalterm
(if notflg newvar var)
(if notflg var newvar))
nil nil typealist nil ens wrld ttree
nil nil))))
(defun putpropinitialtypeprescriptions (names wrld)
; Suppose we have a clique of mutually recursive fns, names. Suppose
; that we can recover from wrld both the formals and body of each
; name in names.
; This function adds to the front of each 'typeprescriptions property
; of the names in names an initial, empty guess at its
; typeprescription. These initial rules are unsound and are only the
; starting point of our iterative guessing mechanism. Oddly, the
; :rune and :nume of each rule is the same! We use the
; *fakeruneforanonymousenabledrule* for the rune and the nume
; nil. We could create the proper runes and numes (indeed, we did at
; one time) but those runes then find their way into the ttrees of the
; various guesses (and not just the rune of the function being typed
; but also the runes of its cliquemates). By adopting this fake
; rune, we prevent that.
; The :term and :hyps we create for each rule are appropriate and survive into
; the final, accurate guess. But the :basicts and :vars fields are initially
; empty here and are filled out by the iteration.
(cond
((null names) wrld)
(t (let ((fn (car names)))
(putpropinitialtypeprescriptions
(cdr names)
(putprop fn
'typeprescriptions
(cons (make typeprescription
:rune *fakeruneforanonymousenabledrule*
:nume nil
:term (mconsterm fn (formals fn wrld))
:hyps nil
:basicts *tsempty*
:vars nil
:corollary *t*)
(getprop fn
'typeprescriptions
nil
'currentacl2world
wrld))
wrld))))))
; We now turn to the problem of iteratively guessing new
; typeprescriptions. The root of this guessing process is the
; computation of the typeset and formals returned by a term.
(defun mapreturnedformalsviaformals (formals pockets returnedformals)
; Formals is the formals list of a lambda expression, (lambda formals
; body). Pockets is a list in 1:1 correspondence with formals. Each
; pocket in pockets is a set of vars. Finally, returnedformals is a
; subset of formals. We return the set of vars obtained by unioning
; together the vars in those pockets corresponding to those in
; returnedformals.
; This odd little function is used to help determine the returned
; formals of a function defined in terms of a lambdaexpression.
; Suppose foo is defined in terms of ((lambda formals body) arg1 ...
; argn) and we wish to determine the returned formals of that
; expression. We first determine the returned formals in each of the
; argi. That produces our pockets. Then we determine the returned
; formals of body  note however that the formals returned by body
; are not the formals of foo but the formals of the lambda. The
; returned formals of body are our returnedformals. This function
; can then be used to convert the returned formals of body into
; returned formals of foo.
(cond ((null formals) nil)
((membereq (car formals) returnedformals)
(unioneq (car pockets)
(mapreturnedformalsviaformals (cdr formals)
(cdr pockets)
returnedformals)))
(t (mapreturnedformalsviaformals (cdr formals)
(cdr pockets)
returnedformals))))
(defun maptypesetsviaformals (formals tslst returnedformals)
; This is just like the function above except instead of dealing with
; a list of lists which are unioned together we deal with a list of
; typesets which are tsunioned.
(cond ((null formals) *tsempty*)
((membereq (car formals) returnedformals)
(tsunion (car tslst)
(maptypesetsviaformals (cdr formals)
(cdr tslst)
returnedformals)))
(t (maptypesetsviaformals (cdr formals)
(cdr tslst)
returnedformals))))
(defun vectortsunion (tslst1 tslst2)
; Given two lists of typesets of equal lengths we tsunion
; corresponding elements and return the resulting list.
(cond ((null tslst1) nil)
(t (cons (tsunion (car tslst1) (car tslst2))
(vectortsunion (cdr tslst1) (cdr tslst2))))))
(defun mapconstagtrees (lst ttree)
; Constagtree every element of lst into ttree.
(cond ((null lst) ttree)
(t (mapconstagtrees
(cdr lst)
(constagtrees (car lst) ttree)))))
(defun typesetandreturnedformalswithrule1
(alist rulevars typealist ens wrld basicts varsts vars ttree)
; See typesetwithrule1 for a slightly simpler version of this.
; Note: This function is really just a loop that finishes off the
; computation done by typesetandreturnedformalswithrule, below.
; It would be best not to try to understand this function until you
; have read that function and typesetandreturnedformals.
; Alist maps variables in a typeprescription to terms. The context in which
; those terms occur is described by typealist. Rulevars is the list of :vars
; of the rule.
; The last four arguments are accumulators that will become four of the
; answers delivered by typesetandreturnedformalswithrule, i.e.,
; a basicts, the typeset of a set of vars, the set of vars, and the
; justifying ttree. We assemble these four answers by sweeping over
; alist, considering each var and its image term. If the var is not
; in the rulevars, we go on. If the var is in the rulevars, then
; its image is a possible value of the term for which we are computing
; a typeset. If its image is a variable, we accumulate it and its
; typeset into vars and varsts. If its image is not a variable, we
; accumulate its typeset into basicts.
; The ttree returned is 'assumptionfree (provided the initial ttree
; is also).
(cond
((null alist) (mv basicts varsts vars typealist ttree))
((membereq (caar alist) rulevars)
(mvlet (ts ttree)
(typeset (cdar alist) nil nil typealist nil ens wrld ttree
nil nil)
(let ((variablepimage (variablep (cdar alist))))
(typesetandreturnedformalswithrule1
(cdr alist) rulevars
typealist ens wrld
(if variablepimage
basicts
(tsunion ts basicts))
(if variablepimage
(tsunion ts varsts)
varsts)
(if variablepimage
(addtoseteq (cdar alist) vars)
vars)
ttree))))
(t
(typesetandreturnedformalswithrule1
(cdr alist) rulevars
typealist ens wrld
basicts
varsts
vars
ttree))))
(defun typesetandreturnedformalswithrule
(tp term typealist ens wrld ttree)
; This function is patterned after typesetwithrule, which the
; reader might understand first.
; The ttree returned is 'assumptionfree (provided the initial ttree
; and typealist are also).
(cond
((enablednumep (access typeprescription tp :nume) ens)
(mvlet
(unifyans unifysubst)
(onewayunify (access typeprescription tp :term)
term)
(cond
(unifyans
(withaccumulatedpersistence
(access typeprescription tp :rune)
(basicts varsts vars typealist ttree)
(let ((typealist (extendtypealistwithbindings unifysubst
nil
nil
typealist
nil
ens wrld
nil
nil nil)))
(mvlet
(relievehypsans typealist ttree)
(typesetrelievehyps (access typeprescription tp :rune)
term
(access typeprescription tp :hyps)
nil
nil
unifysubst
typealist
nil ens wrld nil ttree
nil nil)
(cond
(relievehypsans
; Subject to the conditions in ttree, we now know that the type set of term is
; either in :basicts or else that term is equal to the image under unifysubst
; of some var in the :vars of the rule. Our charter is to return five results:
; basicts, varsts, vars, typealist and ttree. We do that with the
; subroutine below. It sweeps over the unifysubst, considering each vi and
; its image, ai. If ai is a variable, then it accumulates ai into the returned
; vars (which is initially nil below) and the typeset of ai into varsts
; (which is initially *tsempty* below). If ai is not a variable, it
; accumulates the typeset of ai into basicts (which is initially :basicts
; below).
(typesetandreturnedformalswithrule1
unifysubst
(access typeprescription tp :vars)
typealist ens wrld
(access typeprescription tp :basicts)
*tsempty*
nil
(pushlemma
(access typeprescription tp :rune)
ttree)))
(t
; We could not establish the hyps of the rule. Thus, the rule tells us
; nothing about term.
(mv *tsunknown* *tsempty* nil typealist ttree)))))))
(t
; The :term of the rule does not unify with our term.
(mv *tsunknown* *tsempty* nil typealist ttree)))))
(t
; The rule is disabled.
(mv *tsunknown* *tsempty* nil typealist ttree))))
(defun typesetandreturnedformalswithrules
(tplst term typealist ens w ts varsts vars ttree)
; See typesetwithrules for a simpler model of this function. We
; try to apply each typeprescription in tplst, "conjoining" the
; results into an accumulating typeset, ts, and vars (and its
; associated typeset, varsts). However, if a rule fails to change
; the accumulating answers, we ignore it.
; However, we cannot really conjoin two typeprescriptions and get a
; third. We do, however, deduce a valid conclusion. A rule
; essentially gives us a conclusion of the form (or basicts
; varequations), where basicts is the proposition that the term is
; of one of several given types and varequations is the proposition
; that the term is one of several given vars. Two rules therefore
; tell us (or basicts1 varequations1) and (or basicts2
; varequations2). Both of these propositions are true. From them we
; deduce the truth
; (or (and basicts1 basicts2)
; (or varequations1 varequations2)).
; Note that we conjoin the basic typesets but we disjoin the vars. The
; validity of this conclusion follows from the tautology
; (implies (and (or basicts1 varequations1)
; (or basicts2 varequations2))
; (or (and basicts1 basicts2)
; (or varequations1 varequations2))).
; It would be nice if we could conjoin both sides, but that's not valid.
; Recall that we actually must also return the union of the typesets
; of the returned vars. Since the "conjunction" of two rules leads us
; to union the vars together we just union their types together too.
; The ttree returned is 'assumption free provided the initial ttree and
; typealist are also.
(cond
((null tplst)
(mvlet
(ts1 ttree1)
(typeset term nil nil typealist nil ens w ttree nil nil)
(let ((ts2 (tsintersection ts1 ts)))
(mv ts2 varsts vars (if (ts= ts2 ts) ttree ttree1)))))
(t (mvlet
(ts1 varsts1 vars1 typealist1 ttree1)
(typesetandreturnedformalswithrule (car tplst) term
typealist ens w ttree)
(let* ((ts2 (tsintersection ts1 ts))
(unchangedp (and (ts= ts2 ts)
(equal typealist typealist1))))
; If the typeset established by the new rule doesn't change (i.e.,
; narrow) what we already know, we simply choose to ignore the new
; rule. If it does change, then ts2 is smaller and we have to union
; together what we know about the vars and report the bigger ttree.
(typesetandreturnedformalswithrules
(cdr tplst)
term typealist1 ens w
ts2
(if unchangedp
varsts
(tsunion varsts1 varsts))
(if unchangedp
vars
(unioneq vars1 vars))
(if unchangedp
ttree
ttree1)))))))
(mutualrecursion
(defun typesetandreturnedformals (term typealist ens wrld ttree)
; Term is the ifnormalized body of a defined function. The
; 'typeprescriptions property of that fn (and all of its peers in its mutually
; recursive clique) may or may not be nil. If nonnil, it may contain many
; enabled rules. (When guards were part of the logic, we computed the typeset
; of a newly defined function twice, once before and once after verifying its
; guards. So during the second pass, a valid rule was present.) Among the
; rules is one that is possibly unsound and represents our current guess at the
; type. We compute, from that guess, a "basic typeset" for term and a list of
; formals that might be returned by term. We also return the union of the
; typesets of the returned formals and a ttree justifying all our work. An
; odd aspect of this ttree is that it will probably include the rune of the
; very rule we are trying to create, since its use in this process is
; essentially as an induction hypothesis.
; Terminology: Consider a term and a typealist, and the basic
; typeset and returned formals as computed here. Let a "satisfying"
; instance of the term be an instance obtained by replacing each
; formal by an actual that has as its typeset a subtype of that of
; the corresponding formal under typealist. Let the "returned
; actuals" of such an instance be the actuals corresponding to
; returned formals. We say the type set of such a satisfying instance
; of term is "described" by a basic typeset and some returned formals
; if the typeset of the instance is a subset of the union of the
; basic typeset and the typesets of the returned actuals. Claim:
; The typeset of a satisfying instance of term is given by our
; answer.
; This function returns four results. The first is the basic type
; set computed. The third is the set of returned formals. The second
; one is the union of the typesets of the returned formals. Thus,
; the typeset of the term can in fact be obtained by unioning together
; the first and second answers. However, toplevel calls of this
; function are basically unconcerned with the second answer. The fourth
; answer is a ttree justifying all the typeset reasoning done so far,
; accumulated onto the initial ttree.
; We claim that if our computation produces the typeset and formals
; that the typeprescription alleges, then the typeprescription is a
; correct one.
; The function works by walking through the if structure of the body,
; using the normal assumetruefalse to construct the governing
; typealist for each output branch. Upon arriving at an output we
; compute the type set and returned formals for that branch. If the
; output is a quote or a call to an ACL2 primitive, we just use
; typeset. If the output is a call of a defun'd function, we
; interpret its typeprescription.
; The ttree returned is 'assumptionfree provided the initial ttree
; and typealist are also.
; Historical Plaque from Nqthm.
; In nqthm, the root of the guessing processing was DEFNTYPESET,
; which was mutually recursive with DEFNASSUMETRUEFALSE. The
; following comment could be found at the entrance to the guessing
; process:
; *************************************************************
; THIS FUNCTION WILL BE COMPLETELY UNSOUND IF TYPESET IS EVER
; REACHABLE FROM WITHIN IT. IN PARTICULAR, BOTH THE TYPEALIST AND
; THE TYPEPRESCRIPTION FOR THE FN BEING PROCESSED ARE SET TO ONLY
; PARTIALLY ACCURATE VALUES AS THIS FN COMPUTES THE REAL TYPESET.
; *************************************************************
; We now believe that this dreadful warning is an overstatement of the
; case. It is true that in nqthm the typealist used in DEFNTYPESET
; would cause trouble if it found its way into TYPESET, because it
; bound vars to "defn typesets" (pairs of typesets and variables)
; instead of to typesets. But the fear of the inaccurate
; TYPEPRESCRIPTIONs above is misplaced we think. We believe that if
; one guesses a typeprescription and then confirms that it accurately
; describes the function body, then the typeprescription is correct.
; Therefore, in ACL2, far from fencing typeset away from
; "defuntypeset" we use it explicitly. This has the wonderful
; advantage that we do not duplicate the typeset code (which is even
; worse in ACL2 than it was in nqthm).
(cond
((variablep term)
; Term is a formal variable. We compute its typeset under
; typealist. If it is completely unrestricted, then we will say that
; formal is sometimes returned. Otherwise, we will say that it is not
; returned. Once upon a time we always said it was returned. But the
; term (if (integerp x) (if (< x 0) ( x) x) 0) as occurs in
; integerabs, then got the typeset "nonnegative integer or x" which
; meant that it effectively had the typeset unknown.
; Observe that the code below satisfies our Claim. If term' is a
; satisfying instance of this term, then we know that term' is in fact
; an actual being substituted for this formal. Since term' is
; satisfying, the typeset of that actual (i.e., term') is a subtype
; of ts, below. Thus, the typeset of term' is indeed described by
; our answer.
(mvlet (ts ttree)
(typeset term nil nil typealist nil ens wrld ttree
nil nil)
(cond ((ts= ts *tsunknown*)
(mv *tsempty* ts (list term) ttree))
(t (mv ts *tsempty* nil ttree)))))
((fquotep term)
; Term is a constant. We return a basic typeset consisting of the
; typeset of term. Our Claim is true because the typeset of every
; instance of term is a subtype of the returned basic typeset is a
; subtype of the basic typeset.
(mvlet (ts ttree)
(typeset term nil nil typealist nil ens wrld ttree
nil nil)
(mv ts *tsempty* nil ttree)))
((flambdaapplicationp term)
; Without loss of generality we address ourselves to a special case.
; Let term be ((lambda (...u...) body) ...arg...). Let the formals in
; term be x1, ..., xn.
; We compute a basic typeset, bts, some returned vars, vars, and the
; typesets of the vars, vts, for a lambda application as follows.
; (1) For each argument, arg, obtain btsarg, vtsarg, and varsarg,
; which are the basic typeset, the variable typeset, and the
; returned variables with respect to the given typealist.
; (2) Build a new typealist, typealistbody, by binding the formals
; of the lambda, (...u...), to the types of its arguments (...arg...).
; We know that the type of arg is the union of btsarg and the types
; of those xi in varsarg positions (which is to say, vtsarg).
; (3) Obtain btsbody, vtsbody, and varsbody, by recursively
; processing body under typealistbody.
; (4) Create the final bts by unioning btsbody and those of the
; btsargs in positions that are sometimes returned, as specified by
; varsbody.
; (5) Create the final vars by unioning together those of the
; varsargs in positions that are sometimes returned, as specified by
; varsbody.
; (6) Union together the types of the vars to create the final vts.
; We claim that the typeset of any instance of term that satisfies
; typealist is described by the bts and vars computed above and that
; the vts computed above is the union of the the types of the vars
; computed.
; Now consider an instance, term', of term, in which the formals of
; term are mapped to some actuals and typealist is satisfied. Then
; the typeset of each actual is a subtype of the type assigned each
; xi. Observe further that if term' is an instance of term satisfying
; typealist then term' is ((lambda (...u...) body) ...arg'...), where
; arg' is an instance of arg satisfying typealist.
; Thus, by induction, the typeset of arg' is a subtype of the union
; of btsarg and the typesets of those actuals in varsarg positions.
; But the union of the typesets of those actuals in varsarg
; positions is a subtype of the union of the typesets of the xi in
; varsarg. Also observe that term' is equal, by lambda expansion, to
; body', where body' is the instance of body in which each u is
; replaced by the corresponding arg'. Note that body' is an instance
; of body satisfying typealistbody: the type of arg' is a subtype of
; that assigned u in typealistbody, because the type of arg' is a
; subtype of the union of btsarg and the typesets of the actuals in
; varsarg positions, but the type assigned u in typealistbody is
; the union of btsarg and the typesets of the xi in varsarg.
; Therefore, by induction, we know that the typeset of body' is a
; subtype of btsbody and the typesets of those arg' in varsbody
; positions. But the typeset of each arg' is a subtype of btsarg
; unioned with the typesets of the actuals in varsarg positions.
; Therefore, when we union over the selected arg' we get a subtype of
; the union of the union of the selected btsargs and the union of the
; typesets of the actuals in vars positions. By the associativity
; and commutativity of union, the bts and vars created in (4) and (5)
; are correct.
(mvlet (btsargs vtsargs varsargs ttreeargs)
(typesetandreturnedformalslst (fargs term)
typealist
ens wrld)
(mvlet (btsbody vtsbody varsbody ttree)
(typesetandreturnedformals
(lambdabody (ffnsymb term))
(zipvariabletypealist
(lambdaformals (ffnsymb term))
(pairlis$ (vectortsunion btsargs vtsargs)
ttreeargs))
ens wrld ttree)
(declare (ignore vtsbody))
(let* ((bts (tsunion btsbody
(maptypesetsviaformals
(lambdaformals (ffnsymb term))
btsargs
varsbody)))
(vars (mapreturnedformalsviaformals
(lambdaformals (ffnsymb term))
varsargs
varsbody))
(tsandttreelst
(typesetlst vars nil nil typealist nil ens wrld
nil nil)))
; Below we make unconventional use of maptypesetsviaformals.
; Its first and third arguments are equal and thus every element of
; its second argument will be tsunioned into the answer. This is
; just a hackish way to union together the typesets of all the
; returned formals.
(mv bts
(maptypesetsviaformals
vars
(stripcars tsandttreelst)
vars)
vars
(mapconstagtrees (stripcdrs tsandttreelst)
ttree))))))
((eq (ffnsymb term) 'if)
; If by typeset reasoning we can see which way the test goes, we can
; clearly focus on that branch. So now we consider (if t1 t2 t3) where
; we don't know which way t1 will go. We compute the union of the
; respective components of the answers for t2 and t3. In general, the
; typeset of any instance of this if will be at most the union of the
; typesets of the instances of t2 and t3. (In the instance, t1' might
; be decidable and a smaller typeset could be produced.)
(mvlet
(mustbetrue
mustbefalse
truetypealist
falsetypealist
tsttree)
(assumetruefalse (fargn term 1)
nil nil nil typealist nil ens wrld
nil nil nil)
; Observe that tsttree does not include ttree. If mustbetrue and
; mustbefalse are both nil, tsttree is nil and can thus be ignored.
(cond
(mustbetrue
(typesetandreturnedformals (fargn term 2)
truetypealist ens wrld
(constagtrees tsttree ttree)))
(mustbefalse
(typesetandreturnedformals (fargn term 3)
falsetypealist ens wrld
(constagtrees tsttree ttree)))
(t (mvlet
(basicts2 formalsts2 formals2 ttree)
(typesetandreturnedformals (fargn term 2)
truetypealist
ens wrld ttree)
(mvlet
(basicts3 formalsts3 formals3 ttree)
(typesetandreturnedformals (fargn term 3)
falsetypealist
ens wrld ttree)
(mv (tsunion basicts2 basicts3)
(tsunion formalsts2 formalsts3)
(unioneq formals2 formals3)
ttree)))))))
(t
(let* ((fn (ffnsymb term))
(recogtuple
(mostrecentenabledrecogtuple fn
(globalval 'recognizeralist wrld)
ens)))
(cond
(recogtuple
(mvlet (ts ttree1)
(typeset (fargn term 1) nil nil typealist nil ens wrld ttree
nil nil)
(mvlet (ts ttree)
(typesetrecognizer recogtuple ts ttree1 ttree)
(mv ts *tsempty* nil ttree))))
(t
(typesetandreturnedformalswithrules
(getprop (ffnsymb term) 'typeprescriptions nil
'currentacl2world wrld)
term typealist ens wrld
*tsunknown* *tsempty* nil ttree)))))))
(defun typesetandreturnedformalslst
(lst typealist ens wrld)
(cond
((null lst) (mv nil nil nil nil))
(t (mvlet (basicts returnedformalsts returnedformals ttree)
(typesetandreturnedformals (car lst)
typealist ens wrld nil)
(mvlet (ans1 ans2 ans3 ans4)
(typesetandreturnedformalslst (cdr lst)
typealist
ens wrld)
(mv (cons basicts ans1)
(cons returnedformalsts ans2)
(cons returnedformals ans3)
(cons ttree ans4)))))))
)
(defun guesstypeprescriptionforfnstep (name body ens wrld ttree)
; This function takes one incremental step towards the type prescription of
; name in wrld. Body is the normalized body of name. We assume that the
; current guess for a typeprescription for name is the car of the
; 'typeprescriptions property. That is, initialization has occurred and every
; iteration keeps the current guess at the front of the list.
; We get the typeset of and formals returned by body. We convert the two
; answers into a new typeprescription and replace the current car of the
; 'typeprescriptions property.
; We return the new world and an 'assumptionfree ttree extending ttree.
(let* ((ttree0 ttree)
(oldtypeprescriptions
(getprop name 'typeprescriptions nil 'currentacl2world wrld))
(tp (car oldtypeprescriptions)))
(mvlet (newbasictypeset returnedvarstypeset newreturnedvars ttree)
(typesetandreturnedformals body nil ens wrld ttree)
(declare (ignore returnedvarstypeset))
(cond ((ts= newbasictypeset *tsunknown*)
; Ultimately we will delete this rule. But at the moment we wish merely to
; avoid contaminating the ttree of the ongoing process by whatever we've
; done to derive this.
(mv (putprop name
'typeprescriptions
(cons (change typeprescription tp
:basicts *tsunknown*
:vars nil)
(cdr oldtypeprescriptions))
wrld)
ttree0))
(t
(mv (putprop name
'typeprescriptions
(cons (change typeprescription tp
:basicts newbasictypeset
:vars newreturnedvars)
(cdr oldtypeprescriptions))
wrld)
ttree))))))
(defconst *cliquestepinstallinterval*
; This interval represents how many type prescriptions are computed before
; installing the resulting intermediate world. The value below is merely
; heuristic, chosen with very little testing; we should feel free to change it.
30)
(defun guessandputproptypeprescriptionlstforcliquestep
(names bodies ens wrld ttree interval state)
; Given a list of function names and their normalized bodies
; we take one incremental step toward the final typeprescription of
; each fn in the list. We return a world containing the new
; typeprescription for each fn and a ttree extending ttree.
; Note: During the initial coding of ACL2 the iteration to guess
; typeprescriptions was slightly different from what it is now. Back
; then we used wrld as the world in which we computed all the new
; typeprescriptions. We returned those new typeprescriptions to our
; caller who determined whether the iteration had repeated. If not,
; it installed the new typeprescriptions to generate a new wrld' and
; called us on that wrld'.
; It turns out that that iteration can loop indefinitely. Consider the
; mutually recursive nest of foo and bar where
; (defun foo (x) (if (consp x) (not (bar (cdr x))) t))
; (defun bar (x) (if (consp x) (not (foo (cdr x))) nil))
; Below are the successive typeprescriptions under the old scheme:
; iteration foo type bar type
; 0 {} {}
; 1 {T NIL} {NIL}
; 2 {T} {T NIL}
; 3 {T NIL} {NIL}
; ... ... ...
; Observe that the type of bar in round 1 is incomplete because it is
; based on the incomplete type of foo from round 0. This kind of
; incompleteness is supposed to be closed off by the iteration.
; Indeed, in round 2 bar has got its complete typeset. But the
; incompleteness has now been transferred to foo: the round 2
; typeprescription for foo is based on the incomplete round 1
; typeprescription of bar. Isn't this an elegant example?
; The new iteration computes the typeprescriptions in a strict linear
; order. So that the round 1 typeprescription of bar is based on the
; round 1 typeprescription of foo.
(cond ((null names) (mv wrld ttree state))
(t (mvlet
(erp val state)
(updatew (int= interval 0) wrld)
(declare (ignore erp val))
(mvlet
(wrld ttree)
(guesstypeprescriptionforfnstep
(car names)
(car bodies)
ens wrld ttree)
(guessandputproptypeprescriptionlstforcliquestep
(cdr names)
(cdr bodies)
ens
wrld
ttree
(if (int= interval 0)
*cliquestepinstallinterval*
(1 interval))
state))))))
(defun cleansetypeprescriptions
(names typeprescriptionslst defnume rmpcnt ens wrld installedwrld ttree)
; Names is a clique of function symbols. Typeprescriptionslst is in
; 1:1 correspondence with names and gives the value in wrld of the
; 'typeprescriptions property for each name. (We provide this just
; because our caller happens to be holding it.) This function should
; be called when we have completed the guessing process for the
; typeprescriptions for names. This function does two sanitary
; things: (a) it deletes the guessed rule if its :basicts is
; *tsunknown*, and (b) in the case that the guessed
; rule is kept, it is given the rune and nume described by the Essay
; on the Assignment of Runes and Numes by DEFUNS. It is assumed that
; defnume is the nume of (:DEFINITION fn), where fn is the car of
; names. We delete *tsunknown* rules just to save typeset the
; trouble of relieving their hyps or skipping them.
; Rmpcnt (which stands for "runicmappingpairs count") is the length of the
; 'runicmappingpairs entry for the functions in names (all of which have the
; same number of mapping pairs). We increment our defnume by rmpcnt on each
; iteration.
; This function knows that the defun runes for each name are laid out
; as follows, where i is defnume:
; i (:definition name) ^
; i+1 (:executablecounterpart name)
; i+2 (:typeprescription name) rmpcnt=3 or 4
; i+4 (:induction name) ; optional v
; Furthermore, we know that the nume of the :definition rune for the kth
; (0based) name in names is defnume+(k*rmpcnt); that is, we assigned
; numes to the names in the same order as the names appear in names.
(cond
((null names) (mv wrld ttree))
(t (let* ((fn (car names))
(lst (car typeprescriptionslst))
(newtp (car lst)))
(mvlet
(wrld ttree1)
(cond
((ts= *tsunknown* (access typeprescription newtp :basicts))
(mv (putprop fn 'typeprescriptions (cdr lst) wrld) nil))
(t (mvlet
(corollary ttree1)
(converttypeprescriptiontoterm newtp ens
; We use the installed world (the one before cleansing started) for efficient
; handling of large mutual recursion nests.
installedwrld)
(mv (putprop fn 'typeprescriptions
(cons (change typeprescription
newtp
:rune (list :typeprescription
fn)
:nume (+ 2 defnume)
:corollary corollary)
(cdr lst))
wrld)
ttree1))))
(cleansetypeprescriptions (cdr names)
(cdr typeprescriptionslst)
(+ rmpcnt defnume)
rmpcnt ens wrld installedwrld
(constagtrees ttree1 ttree)))))))
(defun guessandputproptypeprescriptionlstforclique
(names bodies defnume ens wrld ttree bigmutrec state)
; We assume that in wrld we find 'typeprescriptions for every fn in
; names. We compute new guesses at the typeprescriptions for each fn
; in names. If they are all the same as the currently stored ones we
; quit. Otherwise, we store the new guesses and iterate. Actually,
; when we quit, we cleanse the 'typeprescriptions as described above.
; We return the final wrld and a ttree extending ttree. Defnume is
; the nume of (:DEFINITION fn), where fn is the first element of names
; and is used in the cleaning up to install the proper numes in the
; generated rules.
(let ((oldtypeprescriptionslst
(getpropxlst names 'typeprescriptions wrld)))
(mvlet (wrld1 ttree state)
(guessandputproptypeprescriptionlstforcliquestep
names bodies ens wrld ttree *cliquestepinstallinterval* state)
(erprogn
(updatew bigmutrec wrld1)
(cond ((equal oldtypeprescriptionslst
(getpropxlst names 'typeprescriptions wrld1))
(mvlet
(wrld2 ttree)
(cleansetypeprescriptions
names
oldtypeprescriptionslst
defnume
(length (getprop (car names) 'runicmappingpairs nil
'currentacl2world wrld))
ens
wrld
wrld1
ttree)
(erprogn
; Warning: Do not use setw! here, because if we are in the middle of a
; toplevel includebook, that will roll the world back to the start of that
; includebook. We have found that reinstalling the world omits inclusion of
; the compiled files for subsidiary includebooks (see description of bug fix
; in :doc note29 (bug fixes)).
(updatew bigmutrec wrld t)
(updatew bigmutrec wrld2)
(mv wrld2 ttree state))))
(t
(guessandputproptypeprescriptionlstforclique
names
bodies
defnume ens wrld1 ttree bigmutrec state)))))))
(defun getnormalizedbodies (names wrld)
; Return the normalized bodies for names in wrld.
; WARNING: We ignore the runes and hyps for the normalized bodies returned. So
; this function is probably only of interest when names are being introduced,
; where the 'defbodies properties have been placed into wrld but no new
; :definition rules with nonnil :installbody fields have been proved for
; names.
(cond ((endp names) nil)
(t (cons (access defbody
(defbody (car names) wrld)
:concl)
(getnormalizedbodies (cdr names) wrld)))))
(defun putproptypeprescriptionlst (names defnume ens wrld ttree state)
; Names is a list of mutually recursive fns being introduced. We assume that
; for each fn in names we can obtain from wrld the 'formals and the normalized
; body (from 'defbodies). Defnume must be the nume assigned (:DEFINITION
; fn), where fn is the first element of names. See the Essay on the Assignment
; of Runes and Numes by DEFUNS. We compute typeprescriptions for each fn in
; names and store them. We return the new wrld and a ttree extending ttree
; justifying what we've done.
; This function knows that HIDE should not be given a
; 'typeprescriptions property.
; Historical Plaque for Versions Before 1.8
; In 1.8 we "eliminated guards from the ACL2 logic." Prior to that guards were
; essentially hypotheses on the definitional equations. This complicated many
; things, including the guessing of typeprescriptions. After a function was
; known to be Common Lisp compliant we could recompute its typeprescription
; based on the fact that we knew that every subfunction in it would return its
; "expected" type. Here is a comment from that era, preserved for posterity.
; On Guards: In what way is the computed typeprescription influenced
; by the changing of the 'guardschecked property from nil to t?
; The key is illustrated by the following fact: typeset returns
; *tsunknown* if called on (+ x y) with gcflg nil but returns a
; subset of *tsacl2number* if called with gcflg t. To put this into
; context, suppose that the guard for (fn x y) is (g x y) and that it
; is not known by typeset that (g x y) implies that both x and y are
; acl2numberps. Suppose the body of fn is (+ x y). Then the initial
; typeprescription for fn, computed when the 'guardschecked property
; is nil, will have the basictypeset *tsunknown*. After the guards
; have been checked the basic typeset will be *tsacl2number*.
(cond
((and (consp names)
(eq (car names) 'hide)
(null (cdr names)))
(mv wrld ttree state))
(t
(let ((bodies (getnormalizedbodies names wrld))
(bigmutrec (bigmutrec names)))
(erlet*
((wrld1 (updatew bigmutrec
(putpropinitialtypeprescriptions names wrld))))
(guessandputproptypeprescriptionlstforclique
names
bodies
defnume
ens
wrld1
ttree
bigmutrec
state))))))
; So that finishes the typeprescription business. Now to levelno...
(defun putproplevelnolst (names wrld)
; We compute the levelno properties for all the fns in names, assuming they
; have no such properties in wrld (i.e., we take advantage of the fact that
; when maxlevelno sees a nil 'levelno it acts like it saw 0). Note that
; induction and rewriting do not use heuristics for 'levelno, so it seems
; reasonable not to recompute the 'levelno property when adding a :definition
; rule with nonnil :installbody value. We assume that we can get the
; 'recursivep and the 'defbodies property of each fn in names from wrld.
(cond ((null names) wrld)
(t (let ((maximum (maxlevelno (body (car names) t wrld) wrld)))
(putproplevelnolst (cdr names)
(putprop (car names)
'levelno
(if (getprop (car names)
'recursivep nil
'currentacl2world
wrld)
(1+ maximum)
maximum)
wrld))))))
; Next we put the primitiverecursivedefun property
(defun primitiverecursiveargp (var term wrld)
; Var is some formal of a recursively defined function. Term is the actual in
; the var position in a recursive call in the definition of the function.
; I.e., we are recursively replacing var by term in the definition. Is this
; recursion in the p.r. schema? Well, that is impossible to tell by just
; looking at the recursion, because we need to know that the tests governing
; the recursion are also in the scheme. In fact, we don't even check that; we
; just rely on the fact that the recursion was justified and so some governing
; test does the job. So, ignoring tests, what is a p.r. function? It is one
; in which every formal is replaced either by itself or by an application of a
; (nest of) primitive recursive destructors to itself. The primitive recursive
; destructors recognized here are all unary function symbols with levelno 0
; (e.g., car, cdr, nqthm::sub1, etc) as well as terms of the form (+ & n) and
; (+ n &), where n is negative.
; A consequence of this definition (before we turned 1+ into a macro) is that
; 1+ is a primitive recursive destructor! Thus, the classic example of a
; terminating function not in the classic p.r. scheme,
; (fn x y) = (if (< x y) (fn (1+ x) y) 0)
; is now in the "p.r." scheme. This is a crock!
; Where is this notion used? The detection that a function is "p.r." is made
; after its admittance during the defun principle. The appropriate flag is
; stored under the property 'primitiverecursivedefunp. This property is only
; used (as of this writing) by inductioncomplexity1, where we favor induction
; candidates suggested by non"p.r." functions. Thus, the notion of "p.r." is
; entirely heuristic and only affects which inductions we choose.
; Why don't we define it correctly? That is, why don't we only recognize
; functions that recurse via car, cdr, etc.? The problem is the
; introduction of the "NQTHM" package, where we want NQTHM::SUB1 to be a p.r.
; destructor  even in the defn of NQTHM::LESSP which must happen before we
; prove that NQTHM::SUB1 decreases according to NQTHM::LESSP. The only way to
; fix this, it seems, would be to provide a world global variable  perhaps a
; new field in the acl2defaultstable  to specify which function symbols are
; to be considered p.r. destructors. We see nothing wrong with this solution,
; but it seems cumbersome at the moment. Thus, we adopted this hackish notion
; of "p.r." and will revisit the problem if and when we see counterexamples to
; the induction choices caused by this notion.
(cond ((variablep term) (eq var term))
((fquotep term) nil)
(t (let ((fn (ffnsymb term)))
(case
fn
(binary+
(or (and (nvariablep (fargn term 1))
(fquotep (fargn term 1))
(rationalp (cadr (fargn term 1)))
(< (cadr (fargn term 1)) 0)
(primitiverecursiveargp var (fargn term 2) wrld))
(and (nvariablep (fargn term 2))
(fquotep (fargn term 2))
(rationalp (cadr (fargn term 2)))
(< (cadr (fargn term 2)) 0)
(primitiverecursiveargp var (fargn term 1) wrld))))
(otherwise
(and (symbolp fn)
(fargs term)
(null (cdr (fargs term)))
(= (getlevelno fn wrld) 0)
(primitiverecursiveargp var (fargn term 1) wrld))))))))
(defun primitiverecursivecallp (formals args wrld)
(cond ((null formals) t)
(t (and (primitiverecursiveargp (car formals) (car args) wrld)
(primitiverecursivecallp (cdr formals) (cdr args) wrld)))))
(defun primitiverecursivecallsp (formals calls wrld)
(cond ((null calls) t)
(t (and (primitiverecursivecallp formals (fargs (car calls)) wrld)
(primitiverecursivecallsp formals (cdr calls) wrld)))))
(defun primitiverecursivemachinep (formals machine wrld)
; Machine is an induction machine for a singly recursive function with
; the given formals. We return t iff every recursive call in the
; machine has the property that every argument is either equal to the
; corresponding formal or else is a primitive recursive destructor
; nest around that formal.
(cond ((null machine) t)
(t (and
(primitiverecursivecallsp formals
(access testsandcalls
(car machine)
:calls)
wrld)
(primitiverecursivemachinep formals (cdr machine) wrld)))))
(defun putpropprimitiverecursivedefunplst (names wrld)
; The primitiverecursivedefun property of a function name indicates
; whether the function is defined in the primitive recursive schema 
; or, to be precise, in a manner suggestive of the p.r. schema. We do
; not actually check for syntactic adherence to the rules and this
; property is of heuristic use only. See the comment in
; primitiverecursiveargp.
; We say a defun'd function is p.r. iff it is not recursive, or else it
; is singly recursive and every argument position of every recursive call
; is occupied by the corresponding formal or else a nest of primitive
; recursive destructors around the corresponding formal.
; Observe that our notion doesn't include any inspection of the tests
; governing the recursions and it doesn't include any check of the
; subfunctions used. E.g., the function that collects all the values of
; Ackerman's functions is p.r. if it recurses on cdr's.
(cond ((null names) wrld)
((cdr names) wrld)
((primitiverecursivemachinep (formals (car names) wrld)
(getprop (car names)
'inductionmachine nil
'currentacl2world wrld)
wrld)
(putprop (car names)
'primitiverecursivedefunp
t
wrld))
(t wrld)))
; Onward toward defuns... Now we generate the controlleralists.
(defun makecontrollerpocket (formals vars)
; Given the formals of a fn and a measured subset, vars, of formals,
; we generate a controllerpocket for it. A controller pocket is a
; list of t's and nil's in 1:1 correspondence with the formals, with
; t in the measured slots.
(cond ((null formals) nil)
(t (cons (if (member (car formals) vars)
t
nil)
(makecontrollerpocket (cdr formals) vars)))))
(defun makecontrolleralist1 (names wrld)
; Given a clique of recursive functions, we return the controller alist built
; for the 'justification. A controller alist is an alist that maps fns in the
; clique to controller pockets. The controller pockets describe the measured
; arguments in a justification. We assume that all the fns in the clique have
; been justified (else none would be justified).
; This function should not be called on a clique consisting of a single,
; nonrecursive fn (because it has no justification).
(cond ((null names) nil)
(t (cons (cons (car names)
(makecontrollerpocket
(formals (car names) wrld)
(access justification
(getprop (car names)
'justification
'(:error
"See MAKECONTROLLERALIST1.")
'currentacl2world wrld)
:subset)))
(makecontrolleralist1 (cdr names) wrld)))))
(defun makecontrolleralist (names wrld)
; We store a controlleralists property for every recursive fn in names. We
; assume we can get the 'formals and the 'justification for each fn from wrld.
; If there is a fn with no 'justification, it means the clique consists of a
; single nonrecursive fn and we store no controlleralists. We generate one
; controller pocket for each fn in names.
; The controlleralist associates a fn in the clique to a controller pocket. A
; controller pocket is a list in 1:1 correspondence with the formals of the fn
; with a t in slots that are controllers. The controllers assigned for the fns
; in the clique by a given controlleralist were used jointly in the
; justification of the clique.
(and (getprop (car names) 'justification nil 'currentacl2world wrld)
(makecontrolleralist1 names wrld)))
(defun maxnumeexceedederror (ctx)
(er hard ctx
"ACL2 assumes that no nume exceeds ~x0. It is very surprising that ~
this bound is about to be exceeded. We are causing an error because ~
for efficiency, ACL2 assumes this bound is never exceeded. Please ~
contact the ACL2 implementors with a request that this assumption be ~
removed from enablednumep."
(fixnumbound)))
(defun putpropdefunrunicmappingpairs1 (names defnume tpflg indflg wrld)
; Names is a list of function symbols. For each fn in names we store some
; runic mapping pairs. We always create (:DEFINITION fn) and (:EXECUTABLE
; COUNTERPART fn). If tpflg is t, we create (:TYPEPRESCRIPTION fn). If
; indflg is t we create (:INDUCTION fn). However, indflg is t only if tpflg
; is t (that is, tpflg = nil and indflg = t never arises). Thus, we may
; store 2 (tpflg = nil; indflg = nil), 3 (tpflg = t; indflg = nil), or 4
; (tpflg = t; indflg = t) runes. As of this writing, we never call this
; function with tpflg nil but indflg t and the function is not prepared for
; that possibility.
; WARNING: Don't change the layout of the runicmappingpairs without
; considering all the places that talk about the Essay on the Assignment of
; Runes and Numes by DEFUNS.
(cond ((null names) wrld)
(t (putpropdefunrunicmappingpairs1
(cdr names)
(+ 2 (if tpflg 1 0) (if indflg 1 0) defnume)
tpflg
indflg
(putprop
(car names) 'runicmappingpairs
(list* (cons defnume (list :DEFINITION (car names)))
(cons (+ 1 defnume)
(list :EXECUTABLECOUNTERPART (car names)))
(if tpflg
(list* (cons (+ 2 defnume)
(list :TYPEPRESCRIPTION (car names)))
(if indflg
(list (cons (+ 3 defnume)
(list :INDUCTION (car names))))
nil))
nil))
wrld)))))
(defun putpropdefunrunicmappingpairs (names tpflg wrld)
; Essay on the Assignment of Runes and Numes by DEFUNS
; Names is a clique of mutually recursive function names. For each
; name in names we store a 'runicmappingpairs property. Each name
; gets either four (tpflg = t) or two (tpflg = nil) mapping pairs:
; ((n . (:definition name))
; (n+1 . (:executablecounterpart name))
; (n+2 . (:typeprescription name)) ; only if tpflg
; (n+3 . (:induction name))) ; only if tpflg and name is
; ; recursively defined
; where n is the next available nume. Important aspects to this
; include:
; * Fnrunenume knows where the :definition and :executablecounterpart
; runes are positioned.
; * Several functions (e.g. augmentrunictheory) exploit the fact
; that the mapping pairs are ordered ascending.
; * functiontheoryfn1 knows that if the token of the first rune in
; the 'runicmappingpairs is not :DEFINITION then the base symbol
; is not a function symbol.
; * Getnextnume implicitly exploits the fact that the numes are
; consecutive integers  it adds the length of the list to
; the first nume to get the next available nume.
; * Cleansetypeprescriptions knows that the same number of numes are
; consumed by each function in a DEFUNS. We have consistently used
; the formal parameter defnume when we were enumerating numes for
; definitions.
; * Converttheorytounorderedmappingpairs1 knows that if the first rune in
; the list is a :definition rune, then the length of this list is 4 if and
; only if the list contains an :induction rune, in which case that rune is
; last in the list.
; In short, don't change the layout of this property unless you
; inspect every occurrence of 'runicmappingpairs in the system!
; (Even that won't find the defnume uses.) Of special note is the
; fact that all nonconstrained function symbols are presumed to have
; the same layout of 'runicmappingpairs as shown here. Constrained
; symbols have a nil 'runicmappingpairs property.
; We do not allocate the :typeprescription or :induction runes or their numes
; unless tpflg is nonnil. This way we can use this same function to
; initialize the 'runicmappingpairs for primitives like car and cdr, without
; wasting runes and numes. We like reusing this function for that purpose
; because it isolates the place we create the 'runicmappingpairs for
; functions.
(let ((nextnume (getnextnume wrld)))
(prog2$ (or (<= (thefixnum nextnume)
( (thefixnum (fixnumbound))
(thefixnum (* (thefixnum 4)
(thefixnum (length names))))))
(maxnumeexceedederror 'putpropdefunrunicmappingpairs))
(putpropdefunrunicmappingpairs1
names
nextnume
tpflg
(and tpflg
(getprop (car names) 'recursivep nil 'currentacl2world wrld))
wrld))))
; Before completing the implementation of defun we turn to the implementation
; of the verifyguards event. The idea is that one calls (verifyguards name)
; and we will generate the guard conditions for all the functions in the
; mutually recursive clique with name, prove them, and then exploit those
; proofs by resetting their symbolclasss. This process is optionally available
; as part of the defun event and hence we must define it before defun.
; While reading this code it is best to think of ourselves as having completed
; defun. Imagine a wrld in which a defun has just been done: the
; 'unnormalizedbody is b, the unnormalized 'guard is g, the 'symbolclass is
; :ideal. The user then calls (verifyguards name) and we want to prove that
; every guard encountered in the mutually recursive clique containing name is
; satisfied.
; We have to collect every subroutine mentioned by any member of the clique and
; check that its guards have been checked. We cause an error if not. Once we
; have checked that all the subroutines have had their guards checked, we
; generate the guard clauses for the new functions.
(defun guardclausesforbody (hypsegments body stobjoptp wrld ttree)
; Hypsegments is a list of clauses derived from the guard for body. We
; generate the guard clauses for the unguarded body, body, under each of the
; different hyp segments. We return a clause set and a ttree justifying all
; the simplification and extending ttree.
(cond
((null hypsegments) (mv nil ttree))
(t (mvlet
(clset1 ttree)
(guardclauses body stobjoptp (car hypsegments) wrld ttree)
(mvlet
(clset2 ttree)
(guardclausesforbody (cdr hypsegments)
body
stobjoptp
wrld ttree)
(mv (conjoinclausesets clset1 clset2) ttree))))))
(defun guardclausesforfn (name ens wrld state ttree)
; Given a function name we generate the clauses that establish that
; all the guards in both the unnormalized guard and unnormalized body are
; satisfied. While processing the guard we assume nothing. But we
; generate the guards for the unnormalized body under each of the
; possible guardhypsegments derived from the assumption of the
; normalized 'guard. We return the resulting clause set and an extension
; of ttree justifying it. The resulting ttree is 'assumptionfree,
; provided the initial ttree is also.
; Notice that in the two calls of guard below, used while computing
; the guard conjectures for the guard of name itself, we use stobjopt
; = nil.
(mvlet
(clset1 ttree)
(guardclauses (guard name nil wrld)
nil nil wrld ttree)
(mvlet
(normalguard ttree)
(normalize (guard name nil wrld)
t ; iffflg
nil ; typealist
ens wrld ttree)
(mvlet
(changedp body ttree)
(evalgroundsubexpressions
(getprop name 'unnormalizedbody
'(:error "See GUARDCLAUSESFORFN.")
'currentacl2world wrld)
ens wrld state ttree)
(declare (ignore changedp))
(mvlet
(clset2 ttree)
; Should we expand lambdas here? I say ``yes,'' but only to be
; conservative with old code. Perhaps we should change the t to nil?
(guardclausesforbody (clausify (dumbnegatelit normalguard)
nil t wrld)
body
; Observe that when we generate the guard clauses for the body we optimize
; the stobj recognizers away, provided the named function is executable.
(not (getprop name 'nonexecutablep nil
'currentacl2world wrld))
wrld ttree)
(mv (conjoinclausesets clset1 clset2) ttree))))))
(defun guardclausesforclique (names ens wrld state ttree)
; Given a mutually recursive clique of fns we generate all of the
; guard conditions for every function in the clique and return that
; set of clauses and a ttree extending ttree and justifying its
; construction. The resulting ttree is 'assumptionfree, provided the
; initial ttree is also.
(cond ((null names) (mv nil ttree))
(t (mvlet
(clset1 ttree)
(guardclausesforfn (car names) ens wrld state ttree)
(mvlet
(clset2 ttree)
(guardclausesforclique (cdr names) ens wrld state ttree)
(mv (conjoinclausesets clset1 clset2) ttree))))))
; That completes the generation of the guard clauses. We will prove
; them with prove.
(defun printverifyguardsmsg (names col state)
; Note that names is either a singleton list containing a theorem name
; or is a mutually recursive clique of function names.
; This function increments timers. Upon entry, the accumulated time
; is charged to 'othertime. The time spent in this function is
; charged to 'printtime.
(cond
((ldskipproofsp state) state)
(t
(pprogn
(incrementtimer 'othertime state)
(mvlet (col state)
(io? event nil (mv col state)
(col names)
(fmt1 "~&0 ~#0~[is~/are~] compliant with Common Lisp.~"
(list (cons #\0 names))
col
(proofsco state)
state nil)
:defaultbindings ((col 0)))
(declare (ignore col))
(incrementtimer 'printtime state))))))
(defun collectideals (names wrld acc)
(cond ((null names) acc)
((eq (symbolclass (car names) wrld) :ideal)
(collectideals (cdr names) wrld (cons (car names) acc)))
(t (collectideals (cdr names) wrld acc))))
(defun collectnonideals (names wrld)
(cond ((null names) nil)
((eq (symbolclass (car names) wrld) :ideal)
(collectnonideals (cdr names) wrld))
(t (cons (car names) (collectnonideals (cdr names) wrld)))))
(defun collectnoncommonlispcompliants (names wrld)
(cond ((null names) nil)
((eq (symbolclass (car names) wrld) :commonlispcompliant)
(collectnoncommonlispcompliants (cdr names) wrld))
(t (cons (car names)
(collectnoncommonlispcompliants (cdr names) wrld)))))
(defun allfnnames1mbeexec (flg x acc)
; Keep this in sync with allfnnames1.
(cond (flg ; x is a list of terms
(cond ((null x) acc)
(t (allfnnames1mbeexec nil (car x)
(allfnnames1mbeexec t (cdr x) acc)))))
((variablep x) acc)
((fquotep x) acc)
((flambdaapplicationp x)
(allfnnames1mbeexec nil (lambdabody (ffnsymb x))
(allfnnames1mbeexec t (fargs x) acc)))
((eq (ffnsymb x) 'mustbeequal)
(allfnnames1mbeexec nil (fargn x 2) acc))
(t
(allfnnames1mbeexec t (fargs x)
(addtoseteq (ffnsymb x) acc)))))
(defmacro allfnnamesmbeexec (term)
`(allfnnames1mbeexec nil ,term nil))
(defun chkcommonlispcompliantsubfunctions
(names0 names terms wrld str ctx state)
; Assume we are defining (or have defined) names in terms of terms
; (1:1 correspondence). We wish to make the definitions
; :commonlispcompliant. Then we insist that every function used in
; terms (other than names0) be :commonlispcompliant. Str is a
; string used in our error message and is "guard", "body" or
; "auxiliary function". Note that this function is used by
; chkacceptabledefuns and by chkacceptableverifyguards and
; chkstobjfielddescriptor. In the first usage, names have not been
; defined yet; in the other two they have. So be careful about using
; wrld to get properties of names.
(cond ((null names) (value nil))
(t (let ((bad (collectnoncommonlispcompliants
(setdifferenceeq (allfnnamesmbeexec (car terms))
names0)
wrld)))
(cond
(bad
(er soft ctx
"The ~@0 for ~x1 calls the function~#2~[ ~&2~/s ~&2~], the ~
guards of which have not yet been verified. See :DOC ~
verifyguards."
str (car names) bad))
(t (chkcommonlispcompliantsubfunctions
names0 (cdr names) (cdr terms)
wrld str ctx state)))))))
(defun chkacceptableverifyguards (name ctx wrld state)
; We check that name is acceptable input for verifyguards. We return either
; the list of names in the clique of name (if name and every peer in the clique
; is :ideal and every subroutine of every peer is :commonlispcompliant), the
; symbol 'redundant (if name and every peer is :commonlispcompliant), or
; cause an error.
; One might wonder when two peers in a clique can have different symbolclasss,
; e.g., how is it possible (as implied above) for name to be :ideal but for one
; of its peers to be :commonlispcompliant or :program? Redefinition. For
; example, the clique could have been admitted as :logic and then later one
; function in it redefined as :program. Because redefinition invalidates the
; system, we could do anything in this case. What we choose to do is to cause
; an error and say you can't verify the guards of any of the functions in the
; nest.
(cond
((not (symbolp name))
(er soft ctx
"Verifyguards can only be applied to a name theorem or function ~
symbol. ~x0 is neither. See :DOC verifyguards."
name))
((getprop name 'theorem nil 'currentacl2world wrld)
; Theorems are of either symbolclass :ideal or :commonlispcompliant.
(mvlet (erp term state)
(translate (getprop name 'untranslatedtheorem nil
'currentacl2world wrld)
t t t ctx wrld state)
; knownstobjs = t (stobjsout = t)
(declare (ignore term))
(cond
(erp
(er soft ctx
"The guards for ~x0 cannot be verified because the theorem ~
has the wrong syntactic form. See :DOC verifyguards."
name))
(t
(value (if (eq (symbolclass name wrld) :ideal)
(list name)
'redundant))))))
((functionsymbolp name wrld)
(let ((symbolclass (symbolclass name wrld)))
(case symbolclass
(:program
(er soft ctx
"~x0 is :program. Only :logic functions can have their guards ~
verified. See :DOC verifyguards."
name))
(:ideal
(let* ((recp (getprop name 'recursivep nil
'currentacl2world wrld))
(names (cond
((null recp)
(list name))
(t recp)))
(nonidealnames (collectnonideals names wrld)))
(cond (nonidealnames
(er soft ctx
"One or more of the mutuallyrecursive peers of ~
~x0 either was not defined in :logic mode or ~
has already had its guards verified. The ~
offending function~#1~[ is~/s are~] ~&1. We ~
thus cannot verify the guards of ~x0. This ~
situation can arise only through redefinition."
name
nonidealnames))
(t
(erprogn
(chkcommonlispcompliantsubfunctions
names names
(guardlst names nil wrld)
wrld "guard" ctx state)
(chkcommonlispcompliantsubfunctions
names names
(getpropxlst names 'unnormalizedbody wrld)
wrld "body" ctx state)
(value names))))))
(:commonlispcompliant
(let ((recp (getprop name 'recursivep nil
'currentacl2world wrld)))
(cond
((null recp) (value 'redundant))
((null (cdr recp)) (value 'redundant))
(t (let ((noncommonlispcompliantnames
(collectnoncommonlispcompliants recp wrld)))
(cond ((null noncommonlispcompliantnames)
(value 'redundant))
(t (er soft ctx
"While the guards for ~x0 have already been ~
verified, those for ~&1, which ~#1~[is~/are~] ~
mutuallyrecursive peers of ~x0, have not been ~
verified. This can only happen through ~
redefinition."
name
noncommonlispcompliantnames))))))))
(otherwise
(er soft ctx
"The argument to VERIFYGUARDS must be the name of a function ~
defined in :logic mode. ~x0 is thus illegal. See :DOC ~
verifyguards."
name)))))
(t (er soft ctx
"~x0 is not a theorem name or a function symbol in the current ACL2 ~
world. See :DOC verifyguards."
name))))
(defun proveguardclauses (names hints otfflg ctx ens wrld state)
; Names is either a clique of mutually recursive functions or else a singleton
; list containing a theorem name. We generate and attempt to prove the guard
; conjectures for the formulas in names. We generate suitable output
; explaining what we are doing. This is an error/value/state producing
; function that returns a pair of the form (col . ttree) when nonerroneous.
; Col is the column in which the printer is left. We always output something
; and we always leave the printer reader to start a new sentence. Ttree is a
; tag tree describing the proof.
; This function increments timers. Upon entry, any accumulated time
; is charged to 'othertime. The printing done herein is charged
; to 'printtime and the proving is charged to 'provetime.
(mvlet
(clset clsetttree state)
(cond ((not (ldskipproofsp state))
(pprogn
(io? event nil state
(names)
(fms "Computing the guard conjecture for ~&0....~"
(list (cons #\0 names))
(proofsco state)
state
nil))
(cond ((and (consp names)
(null (cdr names))
(getprop (car names) 'theorem nil
'currentacl2world wrld))
(mvlet (clset clsetttree)
(guardclauses
(getprop (car names) 'theorem nil
'currentacl2world wrld)
nil ;stobjoptp = nil
nil wrld nil)
(mv clset clsetttree state)))
(t (mvlet
(erp pair state)
(stategloballet*
((guardcheckingon :all))
(mvlet (clset clsetttree)
(guardclausesforclique names ens wrld state
nil)
(value (cons clset clsetttree))))
(declare (ignore erp))
(mv (car pair) (cdr pair) state))))))
(t (mv nil nil state)))
; Clsetttree is 'assumptionfree.
(mvlet
(clset clsetttree)
(cleanupclauseset clset ens wrld clsetttree state)
; Clsetttree is still 'assumptionfree.
(pprogn
(incrementtimer 'othertime state)
(let ((displayedgoal (prettyifyclauseset clset
(let*abstractionp state)
wrld))
(simpphrase (tilde*simpphrase clsetttree)))
(cond
((ldskipproofsp state) (value '(0 . nil)))
((null clset)
(mvlet (col state)
(io? event nil (mv col state)
(names simpphrase)
(fmt "The guard conjecture for ~&0 is trivial to ~
prove~#1~[~/, given ~*2~]. "
(list (cons #\0 names)
(cons #\1 (if (nth 4 simpphrase) 1 0))
(cons #\2 simpphrase))
(proofsco state)
state
nil)
:defaultbindings ((col 0)))
(pprogn
(incrementtimer 'printtime state)
(value (cons (or col 0) clsetttree)))))
(t
(pprogn
(io? event nil state
(displayedgoal simpphrase names)
(fms "The nontrivial part of the guard conjecture for ~
~&0~#1~[~/, given ~*2,~] is~%~%Goal~%~q3."
(list (cons #\0 names)
(cons #\1 (if (nth 4 simpphrase) 1 0))
(cons #\2 simpphrase)
(cons #\3 displayedgoal))
(proofsco state)
state
nil))
(incrementtimer 'printtime state)
(mvlet (erp ttree state)
(prove (termifyclauseset clset)
(makepspv ens wrld
:displayedgoal displayedgoal
:otfflg otfflg)
hints
ens wrld ctx state)
(cond
(erp
(er soft ctx
"The proof of the guard conjecture for ~&0 has ~
failed.~"
names))
(t
(mvlet (col state)
(io? event nil (mv col state)
(names)
(fmt "That completes the proof of the guard ~
theorem for ~&0. "
(list (cons #\0 names))
(proofsco state)
state
nil)
:defaultbindings ((col 0)))
(pprogn
(incrementtimer 'printtime state)
(value
(cons (or col 0)
(constagtrees clsetttree
ttree))))))))))))))))
(defun verifyguardsfn1 (names hints otfflg ctx state)
; This function is called on a clique of mutually recursively defined
; fns whose guards have not yet been verified. Hints is a properly
; translated hints list. This is an error/value/state producing
; function. We cause an error if some subroutine of names has not yet
; had its guards checked or if we cannot prove the guards. Otherwise,
; the "value" is a pair of the form (wrld . ttree), where wrld results
; from storing symbolclass :commonlispcompliant for each name and
; ttree is the ttree proving the guards.
; Note: In a series of conversations started around 13 Jun 94, with Bishop
; Brock, we came up with a new proposal for the form of guard conjectures.
; However, we have decided to delay the experiementation with this proposal
; until we evaluate the new logic of Version 1.8. But, the basic idea is this.
; Consider two functions, f and g, with guards a and b, respectively. Suppose
; (f (g x)) occurs in a context governed by q. Then the current guard
; conjectures are
; (1) q > (b x) ; guard for g holds on x
; (2) q > (a (g x)) ; guard for f holds on (g x)
; Note that (2) contains (g x) and we might need to know that x satisfies the
; guard for g here. Another way of putting it is that if we have to prove both
; (1) and (2) we might imagine forward chaining through (1) and reformulate (2)
; as (2') q & (b x) > (a (g x)).
; Now in the days when guards were part of the logic, this was a pretty
; compelling idea because we couldn't get at the definition of (g x) in (2)
; without establisthing (b x) and thus formulation (2) forced us to prove
; (1) all over again during the proof of (2). But it is not clear whether
; we care now, because the smart user will define (g x) to "do the right thing"
; for any x and thus f will approve of (g x). So it is our expectation that
; this whole issue will fall by the wayside. It is our utter conviction of
; this that leads us to write this note. Just in case...
#
++++++++++++++++++++++++++++++
Date: Sun, 2 Oct 94 17:31:10 CDT
From: kaufmann (Matt Kaufmann)
To: moore
Subject: proposal for handling generalized booleans
Here's a pretty simple idea, I think, for handling generalized Booleans. For
the rest of this message I'll assume that we are going to implement the
abouttobeproposed handling of guards. This proposal doesn't address
functions like member, which could be thought of as returning generalized
booleans but in fact are completely specified (when their guards are met).
Rather, the problem we need to solve is that certain functions, including EQUAL
and RATIONALP, only specify the propositional equivalence class of the value
returned, and no more. I'll call these "problematic functions" for the rest of
this note.
The fundamental ideas of this proposal are as follows.
====================
(A) Problematic functions are completely a nonissue except for guard
verification. The ACL2 logic specifies Boolean values for functions that are
specified in dpANS to return generalized Booleans.
(B) Guard verification will generate not only the current proof obligations,
but also appropriate proof obligations to show that for all values returned by
relevant problematic functions, only their propositional equivalence class
matters. More on this later.
(C) If a function is problematic, it had better only be used in propositional
contexts when used in functions or theorems that are intended to be
:commonlispcompliant. For example, consider the following.
(defun foo (x y z)
(if x
(equal y z)
(cons y z)))
This is problematic, and we will never be able to use it in a
:commonlispcompliant function or formula for other than its propositional
value (unfortunately).
====================
Elaborating on (B) above:
So for example, if we're verifying guards on
(... (foo (rationalp x) ...) ...)
then there will be a proof obligation to show that under the appropriate
hypotheses (from governing IF tests),
(implies (and a b)
(equal (foo a ...) (foo b ...)))
Notice that I've assumed that a and b are nonNIL. The other case, where a and
b are both NIL, is trivial since in that case a and b are equal.
Finally, most of the time no such proof obligation will be generated, because
the context will make it clear that only the propositional equivalence class
matters. In fact, for each function we'll store information that gives
``propositional arguments'' of the function: arguments for which we can be
sure that only their propositional value matters. More on this below.
====================
Here are details.
====================
1. Every function will have a ``propositional signature,'' which is a list of
T's and NIL's. The CAR of this list is T when the function is problematic.
The CDR of the list is in 11 correspondence with the function's formals (in
the same order, of course), and indicates whether the formal's value only
matters propositionally for the value of the function.
For example, the function
(defun bar (x y z)
(if x
(equal y z)
(equal y nil)))
has a propositional signature of (T T NIL NIL). The first T represents the
fact that this function is problematic. The second T represents the fact that
only the propositional equivalence class of X is used to compute the value of
this function. The two NILs say that Y and Z may have their values used other
than propositionally.
An argument that corresponds to a value of T will be called a ``propositional
argument'' henceforth. An OBSERVATION will be made any time a function is
given a propositional signature that isn't composed entirely of NILs.
(2) Propositional signatures will be assigned as follows, presumably hung on
the 'propositionalsignature property of the function. We intend to ensure
that if a function is problematic, then the CAR of its propositional signature
is T. The converse could fail, but it won't in practice.
a. The primitives will have their values set using a fixed alist kept in sync
with *primitiveformalsandguards*, e.g.:
(defconst *primitivepropositionalsignatures*
'((equal (t nil nil))
(cons (nil nil nil))
(rationalp (t nil))
...))
In particular, IF has propositional signature (NIL T NIL NIL): although IF is
not problematic, it is interesting to note that its first argument is a
propositional argument.
b. Defined functions will have their propositional signatures computed as
follows.
b1. The CAR is T if and only if some leaf of the IFtree of the body is the
call of a problematic function. For recursive functions, the function itself
is considered not to be problematic for the purposes of this algorithm.
b2. An argument, arg, corresponds to T (i.e., is a propositional argument in
the sense defined above) if and only if for every subterm for which arg is an
argument of a function call, arg is a propositional argument of that function.
Actually, for recursive functions this algorithm is iterative, like the type
prescription algorithm, in the sense that we start by assuming that every
argument is propositional and iterate, continuing to cut down the set of
propositional arguments until it stabilizes.
Consider for example:
(defun atomlistp (lst)
(cond ((atom lst) (eq lst nil))
(t (and (atom (car lst))
(atomlistp (cdr lst))))))
Since EQ returns a generalized Boolean, ATOMLISTP is problematic. Since
the first argument of EQ is not propositional, ATOMLISTP has propositional
signature (T NIL).
Note however that we may want to replace many such calls of EQ as follows,
since dpANS says that NULL really does return a Boolean [I guess because it's
sort of synonymous with NOT]:
(defun atomlistp (lst)
(cond ((atom lst) (null lst))
(t (and (atom (car lst))
(atomlistp (cdr lst))))))
Now this function is not problematic, even though one might be nervous because
ATOM is, in fact, problematic. However, ATOM is in the test of an IF (because
of how AND is defined). Nevertheless, the use of ATOM here is of issue, and
this leads us to the next item.
(3) Certain functions are worse than merely problematic, in that their value
may not even be determined up to propositional equivalence class. Consider for
example our old favorite:
(defun bad (x)
(equal (equal x x) (equal x x)))
In this case, we can't really say anything at all about the value of BAD, ever.
So, every function is checked that calls of problematic functions in its body
only occur either at the toplevel of its IF structure or in propositional
argument positions. This check is done after the computation described in (2)b
above.
So, the second version of the definition of ATOMLISTP above,
(defun atomlistp (lst)
(cond ((atom lst) (null lst))
(t (and (atom (car lst))
(atomlistp (cdr lst))))))
is OK in this sense, because both calls of ATOM occur in the first argument of
an IF call, and the first argument of IF is propositional.
Functions that fail this check are perfectly OK as :ideal functions; they just
can't be :commonlispcompliant. So perhaps they should generate a warning
when submitted as :ideal, pointing out that they can never be
:commonlispcompliant.
 Matt
#
(let ((wrld (w state))
(ens (ens state)))
(erlet*
((pair (proveguardclauses names hints otfflg ctx ens wrld state)))
; Pair is of the form (col . ttree)
(let* ((col (car pair))
(ttree1 (cdr pair))
(wrld1 (putpropxlst1 names 'symbolclass
:commonlispcompliant wrld)))
(pprogn
(printverifyguardsmsg names col state)
(value (cons wrld1 ttree1)))))))
(defun appendlst (lst)
(cond ((null lst) nil)
(t (append (car lst) (appendlst (cdr lst))))))
(defun verifyguardsfn (name state hints otfflg doc eventform)
; Important Note: Don't change the formals of this function without
; reading the *initialeventdefmacros* discussion in axioms.lisp.
(whenlogic
"VERIFYGUARDS"
(withctxsummarized
(if (outputininfixp state)
eventform
(cond ((and (null hints)
(null otfflg)
(null doc))
(msg "( VERIFYGUARDS ~x0)"
name))
(t (cons 'verifyguards name))))
(let ((wrld (w state))
(eventform (or eventform
(list* 'verifyguards
name
(append
(if hints
(list :hints hints)
nil)
(if otfflg
(list :otfflg otfflg)
nil)
(if doc
(list :doc doc)
nil)))))
(assumep (or (eq (ldskipproofsp state) 'includebook)
(eq (ldskipproofsp state) 'includebookwithlocals)
(eq (ldskipproofsp state) 'initializeacl2))))
(erlet*
((names (chkacceptableverifyguards name ctx wrld state)))
(cond
((eq names 'redundant)
(stopredundantevent state))
(t (enforceredundancy
eventform ctx wrld
(erlet*
((hints (if assumep
(value nil)
(translatehints
(cons "Guard Lemma for" name)
(append hints (defaulthints wrld))
ctx wrld state)))
(docpair (translatedoc nil doc ctx state))
; Docpair is guaranteed to be nil because of the nil name supplied to
; translatedoc.
(pair (verifyguardsfn1 names hints otfflg ctx state)))
; pair is of the form (wrld1 . ttree)
(erprogn
(chkassumptionfreettree (cdr pair) ctx state)
(installevent name
eventform
'verifyguards
0
(cdr pair)
nil
nil
nil
(car pair)
state)))))))))))
; That completes the implementation of verifyguards. We now return
; to the development of defun itself.
; Here is the shortcut used when we are introducing :program functions.
; The superdefunwart operations are not so much concerned with the
; :program defunmode as with system functions that need special treatment.
; The wonderful superdefunwart operations should not, in general, mess with
; the primitive state accessors and updaters. They have to do with a
; bootstrapping problem that is described in more detail in STATESTATE in
; axioms.lisp.
; The following table has gives the proper STOBJSIN and STOBJSOUT
; settings for the indicated functions.
; Warning: If you ever change this table so that it talks about stobjs other
; than STATE, then reconsider oneifycltlcode. These functions assume that if
; stobjsin from this table is nonnil then special handling of STATE is
; required; or, at least, they did before Version_2.6.
(defconst *superdefunwarttable*
; fn stobjsin stobjsout
'((COERCESTATETOOBJECT (STATE) (NIL))
(COERCEOBJECTTOSTATE (NIL) (STATE))
(USERSTOBJALIST (STATE) (NIL))
(UPDATEUSERSTOBJALIST (NIL STATE) (STATE))
(BIGCLOCKNEGATIVEP (STATE) (NIL))
(DECREMENTBIGCLOCK (STATE) (STATE))
(STATEP (STATE) (NIL))
(OPENINPUTCHANNELP (NIL NIL STATE) (NIL))
(OPENOUTPUTCHANNELP (NIL NIL STATE) (NIL))
(OPENINPUTCHANNELANYP (NIL STATE) (NIL))
(OPENOUTPUTCHANNELANYP (NIL STATE) (NIL))
(READCHAR$ (NIL STATE) (NIL STATE))
(PEEKCHAR$ (NIL STATE) (NIL))
(READBYTE$ (NIL STATE) (NIL STATE))
(READOBJECT (NIL STATE) (NIL NIL STATE))
(READACL2ORACLE (STATE) (NIL NIL STATE))
(READRUNTIME (STATE) (NIL STATE))
(READIDATE (STATE) (NIL STATE))
(LISTALLPACKAGENAMES (STATE) (NIL STATE))
(PRINC$ (NIL NIL STATE) (STATE))
(WRITEBYTE$ (NIL NIL STATE) (STATE))
(PRINTOBJECT$ (NIL NIL STATE) (STATE))
(GETGLOBAL (NIL STATE) (NIL))
(BOUNDPGLOBAL (NIL STATE) (NIL))
(MAKUNBOUNDGLOBAL (NIL STATE) (STATE))
(PUTGLOBAL (NIL NIL STATE) (STATE))
(GLOBALTABLECARS (STATE) (NIL))
(TSTACKLENGTH (STATE) (NIL))
(EXTENDTSTACK (NIL NIL STATE) (STATE))
(SHRINKTSTACK (NIL STATE) (STATE))
(AREFTSTACK (NIL STATE) (NIL))
(ASETTSTACK (NIL NIL STATE) (STATE))
(32BITINTEGERSTACKLENGTH (STATE) (NIL))
(EXTEND32BITINTEGERSTACK (NIL NIL STATE) (STATE))
(SHRINK32BITINTEGERSTACK (NIL STATE) (STATE))
(AREF32BITINTEGERSTACK (NIL STATE) (NIL))
(ASET32BITINTEGERSTACK (NIL NIL STATE) (STATE))
(OPENINPUTCHANNEL (NIL NIL STATE) (NIL STATE))
(OPENOUTPUTCHANNEL (NIL NIL STATE) (NIL STATE))
(CLOSEINPUTCHANNEL (NIL STATE) (STATE))
(CLOSEOUTPUTCHANNEL (NIL STATE) (STATE))
(SYSCALLSTATUS (STATE) (NIL STATE))))
(defun projectoutcolumnsiandj (i j table)
(cond
((null table) nil)
(t (cons (cons (nth i (car table)) (nth j (car table)))
(projectoutcolumnsiandj i j (cdr table))))))
(defconst *superdefunwartbindingalist*
(projectoutcolumnsiandj 0 2 *superdefunwarttable*))
(defconst *superdefunwartstobjsinalist*
(projectoutcolumnsiandj 0 1 *superdefunwarttable*))
(defun superdefunwartbindings (bindings)
(cond ((null bindings) nil)
(t (cons (or (assoceq (caar bindings)
*superdefunwartbindingalist*)
(car bindings))
(superdefunwartbindings (cdr bindings))))))
(defun storestobjsins (names stobjsins w)
(cond ((null names) w)
(t (storestobjsins (cdr names) (cdr stobjsins)
(putprop (car names) 'stobjsin
(car stobjsins) w)))))
(defun storesuperdefunwartsstobjsin (names wrld)
; Store the builtin stobjsin values of the super defuns among names, if any.
(cond
((null names) wrld)
((assoceq (car names) *superdefunwartstobjsinalist*)
(storesuperdefunwartsstobjsin
(cdr names)
(putprop (car names) 'stobjsin
(cdr (assoceq (car names) *superdefunwartstobjsinalist*))
wrld)))
(t (storesuperdefunwartsstobjsin (cdr names) wrld))))
(defun collectoldnameps (names wrld)
(cond ((null names) nil)
((newnamep (car names) wrld)
(collectoldnameps (cdr names) wrld))
(t (cons (car names) (collectoldnameps (cdr names) wrld)))))
(defun defunsfnshortcut (names docs pairs guards bodies
wrld state)
; This function is called by defunsfn when the functions to be defined are
; :program. It short cuts the normal putinductioninfo and other such
; analysis of defuns. The function essentially makes the named functions look
; like primitives in the sense that they can be used in formulas and they can
; be evaluated on explicit constants but no axioms or rules are available about
; them. In particular, we do not store 'defbodies, typeprescriptions, or
; any of the recursion/induction properties normally associated with defuns and
; the prover will not execute them on explicit constants.
; We do take care of the documentation data base.
; Like defunsfn0, this function returns a pair consisting of the new world and
; a tag tree recording the proofs that were done.
(let ((wrld (updatedocdatabaselst
names docs pairs
(putpropxlst2unless
names 'guard guards *t*
(putpropxlst1
names 'symbolclass :program
(if (globalval 'bootstrapflg wrld)
wrld
(putpropxlst2 names 'unnormalizedbody bodies wrld)))))))
(value (cons wrld nil))))
; Now we develop the output for the defun event.
(defun printdefunmsg/collecttypeprescriptions (names wrld)
; This function returns two lists, a list of names in names with
; trivial typeprescriptions (i.e., NIL 'typeprescriptions property)
; and an alist that pairs names in names with the term representing
; their (nontrivial) type prescriptions.
(cond
((null names) (mv nil nil))
(t (mvlet (fns alist)
(printdefunmsg/collecttypeprescriptions (cdr names) wrld)
(let ((lst (getprop (car names) 'typeprescriptions nil
'currentacl2world wrld)))
(cond
((null lst)
(mv (cons (car names) fns) alist))
(t (mv fns
(cons
(cons (car names)
(untranslate
(access typeprescription (car lst) :corollary)
t wrld))
alist)))))))))
(defun printdefunmsg/typeprescriptions1 (alist simpphrase col state)
; See printdefunmsg/typeprescriptions. We print out a string of
; phrases explaining the alist produced above. We return the final
; col and state. This function used to be a tilde* phrase, but
; you cannot get the punctuation after the ~xt commands.
(cond ((null alist) (mv col state))
((null (cdr alist))
(fmt1 "the type of ~xn is described by the theorem ~pt. ~#p~[~/We ~
used ~*s.~]~"
(list (cons #\n (caar alist))
(cons #\t (cdar alist))
(cons #\p (if (nth 4 simpphrase) 1 0))
(cons #\s simpphrase))
col
(proofsco state)
state nil))
((null (cddr alist))
(fmt1 "the type of ~xn is described by the theorem ~pt ~
and the type of ~xm is described by the theorem ~ps.~"
(list (cons #\n (caar alist))
(cons #\t (cdar alist))
(cons #\m (caadr alist))
(cons #\s (cdadr alist)))
col
(proofsco state)
state nil))
(t
(mvlet (col state)
(fmt1 "the type of ~xn is described by the theorem ~pt, "
(list (cons #\n (caar alist))
(cons #\t (cdar alist)))
col
(proofsco state)
state nil)
(printdefunmsg/typeprescriptions1 (cdr alist) simpphrase
col state)))))
(defun printdefunmsg/typeprescriptions (names ttree wrld col state)
; This function prints a description of each nontrivial
; typeprescription for the functions names. It assumes that at the
; time it is called, it is printing in col. It returns the final col,
; and the final state.
(let ((simpphrase (tilde*simpphrase ttree)))
(mvlet
(fns alist)
(printdefunmsg/collecttypeprescriptions names wrld)
(cond
((null alist)
(fmt1
"We could deduce no constraints on the type of ~#0~[~&0.~/any of the ~
functions in the clique.~]~#1~[~/ However, in normalizing the ~
definition~#0~[~/s~] we used ~*2.~]~%"
(list (cons #\0 names)
(cons #\1 (if (nth 4 simpphrase) 1 0))
(cons #\2 simpphrase))
col
(proofsco state)
state nil))
(fns
(mvlet
(col state)
(fmt1
"We could deduce no constraints on the type of ~#f~[~vf,~/any of ~
~vf,~] but we do observe that "
(list (cons #\f fns))
col
(proofsco state)
state nil)
(printdefunmsg/typeprescriptions1 alist simpphrase col state)))
(t
(mvlet
(col state)
(fmt1
"We observe that " nil col (proofsco state)
state nil)
(printdefunmsg/typeprescriptions1 alist simpphrase
col state)))))))
(defun simplesignaturep (fn wrld)
; A simple signature is one in which no stobjs are involved and the
; output is a single value.
(and (allnils (stobjsin fn wrld))
(null (cdr (stobjsout fn wrld)))))
(defun allsimplesignaturesp (names wrld)
(cond ((endp names) t)
(t (and (simplesignaturep (car names) wrld)
(allsimplesignaturesp (cdr names) wrld)))))
(defun printdefunmsg/signatures1 (names wrld state)
(cond
((endp names) state)
((not (simplesignaturep (car names) wrld))
(pprogn
(fms "~x0 => ~x1."
(list
(cons #\0
(cons (car names)
(prettyifystobjflags (stobjsin (car names) wrld))))
(cons #\1 (prettyifystobjsout (stobjsout (car names) wrld))))
(proofsco state)
state
nil)
(printdefunmsg/signatures1 (cdr names) wrld state)))
(t (printdefunmsg/signatures1 (cdr names) wrld state))))
(defun printdefunmsg/signatures (names wrld state)
(cond ((allsimplesignaturesp names wrld)
state)
((cdr names)
(pprogn
(fms "The Nonsimple Signatures" nil (proofsco state) state nil)
(printdefunmsg/signatures1 names wrld state)
(newline (proofsco state) state)))
(t (pprogn
(printdefunmsg/signatures1 names wrld state)
(newline (proofsco state) state)))))
(defun printdefunmsg (names ttree wrld col state)
; Once upon a time this function printed more than just the type
; prescription message. We've left the function here to handle that
; possibility in the future. This function returns the final state.
; This function increments timers. Upon entry, the accumulated time
; is charged to 'othertime. The time spent in this function is
; charged to 'printtime.
(cond ((ldskipproofsp state)
state)
(t
(io? event nil state
(names ttree wrld col)
(pprogn
(incrementtimer 'othertime state)
(mvlet (erp ttree state)
(accumulatettreeintostate ttree state)
(declare (ignore erp))
(mvlet (col state)
(printdefunmsg/typeprescriptions names ttree
wrld col state)
(declare (ignore col))
(pprogn
(printdefunmsg/signatures names wrld state)
(incrementtimer 'printtime state)))))))))
(defun getignores (lst)
(cond ((null lst) nil)
(t (cons (ignorevars
(fourth (car lst)))
(getignores (cdr lst))))))
(defun getignorables (lst)
(cond ((null lst) nil)
(t (cons (ignorablevars
(fourth (car lst)))
(getignorables (cdr lst))))))
(defun chkallstobjnames (lst msg ctx wrld state)
; Cause an error if any element of lst is not a legal stobj name in wrld.
(cond ((endp lst) (value nil))
((not (stobjp (car lst) t wrld))
(er soft ctx
"Every name used as a stobj (whether declared explicitly ~
via the :STOBJ keyword argument or implicitly via ~
*notation) must have been previously defined as a ~
singlethreaded object with defstobj. ~x0 is used as ~
stobj name ~#1~[~/in ~@1 ~]but has not been defined as ~
a stobj."
(car lst)
msg))
(t (chkallstobjnames (cdr lst) msg ctx wrld state))))
(defun getdeclaredstobjnames (edcls ctx wrld state)
; Each element of edcls is the cdr of a DECLARE form. We look for the
; ones of the form (XARGS ...) and find the first :stobjs keyword
; value in each such xargs. We know there is at most one :stobjs
; occurrence in each xargs by chkdcllst. We union together all the
; values of that keyword, after checking that each value is legal. We
; return the list of declared stobj names or cause an error.
; Keep this in sync with getdeclaredstobjs (which does not do any checking
; and returns a single value).
(cond ((endp edcls) (value nil))
((eq (caar edcls) 'xargs)
(let* ((temp (assockeyword :stobjs (cdar edcls)))
(lst (cond ((null temp) nil)
((null (cadr temp)) nil)
((atom (cadr temp))
(list (cadr temp)))
(t (cadr temp)))))
(cond
(lst
(cond
((not (symbollistp lst))
(er soft ctx
"The value specified for the :STOBJS xarg ~
must be a true list of symbols and ~x0 is ~
not."
lst))
(t (erprogn
(chkallstobjnames lst
(msg "... :stobjs ~x0 ..."
(cadr temp))
ctx wrld state)
(erlet*
((rst (getdeclaredstobjnames (cdr edcls)
ctx wrld state)))
(value (unioneq lst rst)))))))
(t (getdeclaredstobjnames (cdr edcls) ctx wrld state)))))
(t (getdeclaredstobjnames (cdr edcls) ctx wrld state))))
(defun getstobjsinlst (lst ctx wrld state)
; Lst is a list of ``fives'' as computed in chkacceptabledefuns.
; Each element is of the form (fn args "doc" edcls body). We know the
; args are legal arg lists, but nothing else.
; Unless we cause an error, we return a list in 1:1 correspondence
; with lst containing the STOBJSIN flags for each fn. This involves
; three steps. First we recover from the edcls the declared :stobjs.
; We augment those with STATE, if STATE is in formals, which is always
; implicitly a stobj, if STATE is in the formals. We confirm that all
; the declared stobjs are indeed stobjs in wrld. Then we compute the
; stobj flags using the formals and the declared stobjs.
(cond ((null lst) (value nil))
(t (let ((fn (first (car lst)))
(formals (second (car lst))))
(erlet* ((dclstobjnames
(getdeclaredstobjnames (fourth (car lst))
ctx wrld state))
(dclstobjnamesx
(cond ((and (membereq 'state formals)
(not (membereq 'state dclstobjnames)))
(erprogn
(chkstateok ctx wrld state)
(value (cons 'state dclstobjnames))))
(t (value dclstobjnames)))))
(cond
((not (subsetpeq dclstobjnamesx formals))
(er soft ctx
"The stobj name~#0~[ ~&0 is~/s ~&0 are~] ~
declared but not among the formals of ~x1. ~
This generally indicates some kind of ~
typographical error and is illegal. Declare ~
only those stobj names listed in the formals. ~
The formals list of ~x1 is ~x2."
(setdifferenceequal dclstobjnamesx formals)
fn
formals))
(t (erlet* ((others (getstobjsinlst (cdr lst)
ctx wrld state)))
; Note: Wrld is irrelevant below because dclstobjnamesx is not T so
; we simply look for the formals that are in dclstobjnamesx.
(value
(cons (computestobjflags formals
dclstobjnamesx
wrld)
others))))))))))
(defun chkstobjsoutbound (names bindings ctx state)
(cond ((null names) (value nil))
((translateunbound (car names) bindings)
(er soft ctx
"Translate failed to determine the output signature of ~
~x0." (car names)))
(t (chkstobjsoutbound (cdr names) bindings ctx state))))
(defun storestobjsout (names bindings w)
(cond ((null names) w)
(t (storestobjsout
(cdr names)
bindings
(putprop (car names) 'stobjsout
(translatederef (car names)
bindings) w)))))
(defun unparsesignature (x)
; Suppose x is an internal form signature, i.e., (fn formals stobjsin
; stobjsout). Then we return an external version of it, e.g., ((fn
; . stobjsin) => (mv . stobjsout)). This is only used in error
; reporting.
(let* ((fn (car x))
(prettyflags1 (prettyifystobjflags (caddr x)))
(output (prettyifystobjsout (cadddr x))))
`((,fn ,@prettyflags1) => ,output)))
(defconst *builtinprogrammodefns* '(syscall gc$))
(defun chkdefunmode (defunmode names ctx state)
(cond ((eq defunmode :program)
(value nil))
((eq defunmode :logic)
(cond ((intersectpeq names *builtinprogrammodefns*)
(er soft ctx
"The builtin function~#0~[~/s~] ~&0 must ~
remain in :PROGRAM mode."
(intersectioneq names *builtinprogrammodefns*)))
(t (value nil))))
(t (er soft ctx
"The legal defunmodes are :program and :logic. ~x0 is ~
not a recognized defunmode."
defunmode))))
(defun scantocltlcommand (wrld)
; Scan to the next binding of 'cltlcommand or to the end of this event block.
; Return either nil or the globalvalue of cltlcommand for this event.
(cond ((null wrld) nil)
((and (eq (caar wrld) 'eventlandmark)
(eq (cadar wrld) 'globalvalue))
nil)
((and (eq (caar wrld) 'cltlcommand)
(eq (cadar wrld) 'globalvalue))
(cddar wrld))
(t (scantocltlcommand (cdr wrld)))))
(defun plausibledclsp1 (lst)
; We determine whether lst is a plausible cdr for a DECLARE form. Ignoring the
; order of presentation and the number of occurrences of each element
; (including 0), we ensure that lst is of the form (... (TYPE ...) ... (IGNORE
; ...) ... (XARGS ... :key val ...) ...) where the :keys are our xarg keys,
; :GUARD, :MEASURE, :WELLFOUNDEDRELATION :HINTS, :GUARDHINTS, :MODE,
; :VERIFYGUARDS and :OTFFLG.
(cond ((atom lst) (null lst))
((and (consp (car lst))
(truelistp (car lst))
(or (membereq (caar lst) '(type ignore))
(and (eq (caar lst) 'xargs)
(keywordvaluelistp (cdar lst))
(subsetpeq (evens (cdar lst))
'(:guard :measure :wellfoundedrelation
:hints :guardhints :mode
:verifyguards :otfflg)))))
(plausibledclsp1 (cdr lst)))
(t nil)))
(defun plausibledclsp (lst)
; We determine whether lst is a plausible thing to include between the formals
; and the body in a defun, e.g., a list of doc strings and DECLARE forms. We
; do not insist that the DECLARE forms are "perfectly legal"  for example, we
; would approve (DECLARE (XARGS :measure m1 :measure m2))  but they are
; wellenough formed to permit us to walk through them with the fetchfromdcls
; functions below.
; Note: This predicate is not actually used by defuns but is used by
; verifytermination in order to guard its exploration of the proposed dcls
; to merge them with the existing ones. After we define the predicate we
; define the exploration functions, which implicitly assume this fn as their
; guard. The exploration functions below are used in defuns, in particular,
; in the determination of whether a proposed defun is redundant.
(cond ((atom lst) (null lst))
((stringp (car lst)) (plausibledclsp (cdr lst)))
((and (consp (car lst))
(eq (caar lst) 'declare)
(plausibledclsp1 (cdar lst)))
(plausibledclsp (cdr lst)))
(t nil)))
; The above function, plausibledclsp, is the guard and the role model for the
; following functions which explore plausibledcls and either collect all the
; "fields" used or delete certain fields.
(defun dclfields1 (lst)
(cond ((null lst) nil)
((or (eq (caar lst) 'type)
(eq (caar lst) 'ignore))
(addtoseteq (caar lst) (dclfields1 (cdr lst))))
(t (unioneq (evens (cdar lst)) (dclfields1 (cdr lst))))))
(defun dclfields (lst)
; Lst satisfies plausibledclsp, i.e., is the sort of thing you would find
; between the formals and the body of a DEFUN. We return a list of all the
; "field names" used in lst. Our answer is a subset of the following list of
; symbols: COMMENT, TYPE, IGNORE, :GUARD, :MEASURE, :WELLFOUNDEDRELATION,
; :HINTS, :GUARDHINTS, :MODE, :VERIFYGUARDS, and :OTFFLG.
(cond ((null lst) nil)
((stringp (car lst))
(addtoseteq 'comment (dclfields (cdr lst))))
(t (unioneq (dclfields1 (cdar lst))
(dclfields (cdr lst))))))
(defun stripkeywordlist (fields lst)
; Lst is a keywordvaluelistp, i.e., (:key1 val1 ...). We remove any key/val
; pair whose key is in fields.
(cond ((null lst) nil)
((membereq (car lst) fields)
(stripkeywordlist fields (cddr lst)))
(t (cons (car lst)
(cons (cadr lst)
(stripkeywordlist fields (cddr lst)))))))
(defun stripdcls1 (fields lst)
(cond ((null lst) nil)
((or (eq (caar lst) 'type)
(eq (caar lst) 'ignore))
(cond ((membereq (caar lst) fields) (stripdcls1 fields (cdr lst)))
(t (cons (car lst) (stripdcls1 fields (cdr lst))))))
(t
(let ((temp (stripkeywordlist fields (cdar lst))))
(cond ((null temp) (stripdcls1 fields (cdr lst)))
(t (cons (cons 'xargs temp)
(stripdcls1 fields (cdr lst)))))))))
(defun stripdcls (fields lst)
; Lst satisfies plausibledclsp. Fields is a list as returned by dclfields,
; i.e., a subset of the symbols COMMENT, TYPE, IGNORE, :GUARD, :MEASURE,
; :WELLFOUNDEDRELATION, :HINTS, :GUARDHINTS, :MODE, :VERIFYGUARDS, and
; :OTFFLG. We copy lst deleting any part of it that specifies a value for one
; of the fields named. The result satisfies plausibledclsp.
(cond ((null lst) nil)
((stringp (car lst))
(cond ((membereq 'comment fields) (stripdcls fields (cdr lst)))
(t (cons (car lst) (stripdcls fields (cdr lst))))))
(t (let ((temp (stripdcls1 fields (cdar lst))))
(cond ((null temp) (stripdcls fields (cdr lst)))
(t (cons (cons 'declare temp)
(stripdcls fields (cdr lst)))))))))
(defun fetchdclfield1 (fieldname lst)
(cond ((null lst) nil)
((or (eq (caar lst) 'type)
(eq (caar lst) 'ignore))
(if (eq (caar lst) fieldname)
(cons (cdar lst) (fetchdclfield1 fieldname (cdr lst)))
(fetchdclfield1 fieldname (cdr lst))))
(t (let ((temp (assockeyword fieldname (cdar lst))))
(cond (temp (cons (cadr temp)
(fetchdclfield1 fieldname (cdr lst))))
(t (fetchdclfield1 fieldname (cdr lst))))))))
(defun fetchdclfield (fieldname lst)
; Lst satisfies plausibledclsp, i.e., is the sort of thing you would find
; between the formals and the body of a DEFUN. Fieldname is one of the
; symbols: COMMENT, TYPE, IGNORE, :GUARD, :MEASURE, :WELLFOUNDEDRELATION,
; :HINTS, :GUARDHINTS, :MODE, :VERIFYGUARDS, and :OTFFLG. We return the
; list of the contents of all fields with that name. We assume we will find at
; most one specification per XARGS entry for a given keyword.
; For example, if fieldname is :GUARD and there are two XARGS among the
; DECLAREs in lst, one with :GUARD g1 and the other with :GUARD g2 we return
; (g1 g2). Similarly, if fieldname is TYPE and lst contains (DECLARE (TYPE
; INTEGER X Y)) then our output will be (... (INTEGER X Y) ...) where the ...
; are the other TYPE entries.
(cond ((null lst) nil)
((stringp (car lst))
(if (eq fieldname 'comment)
(cons (car lst) (fetchdclfield fieldname (cdr lst)))
(fetchdclfield fieldname (cdr lst))))
(t (append (fetchdclfield1 fieldname (cdar lst))
(fetchdclfield fieldname (cdr lst))))))
(defun setequalpeq (lst1 lst2)
(declare (xargs :guard (and (symbollistp lst1)
(symbollistp lst2))))
(and (subsetpeq lst1 lst2)
(subsetpeq lst2 lst1)))
(defun nonidenticaldefp (def1 def2 chkmeasurep wrld)
; This predicate is used in recognizing redundant definitions. In our intended
; application, def2 will have been successfully processed and def1 is merely
; proposed, where def1 and def2 are each of the form (fn args ...dcls... body)
; and everything is untranslated. Two such tuples are "identical" if their
; fns, args, bodies, types, stobjs, measures, and guards are equal  except
; that the new measure can be (:? v1 ... vk) if (v1 ... vk) is the measured
; subset for the old definition. We return nil if def1 is thus redundant
; ("identical" to) with def2. Otherwise we return a message suitable for
; printing using " Note that ~@k.".
; Note that def1 might actually be syntactically illegal, e.g., it might
; specify two different :measures. But it is possible that we will still
; recognize it as identical to def2 because the args and body are identical.
; Thus, the syntactic illegality of def1 might not be discovered if def1 is
; avoided because it is redundant. This happens already in redundancy checking
; in defthm: a defthm event is redundant if it introduces an identical theorem
; with the same name  even if the :hints in the new defthm are illformed.
; The idea behind redundancy checking is to allow books to be loaded even if
; they share some events. The assumption is that def1 is in a book that got
; (or will get) processed by itself sometime and the illformedness will be
; detected there. That will change the check sum on the book and cause
; certification to lapse in the book that considered def1 redundant.
(cond
((equal def1 def2) ; optimization
nil)
((not (eq (car def1) (car def2))) ; check same fn (can this fail?)
(msg "the name of the new event, ~x0, differs from the name of the ~
corresponding existing event, ~x1."
(car def1) (car def2)))
((not (equal (cadr def1) (cadr def2))) ; check same args
(msg "the proposed argument list for ~x0, ~x1, differs from the existing ~
argument list, ~x2."
(car def1) (cadr def1) (cadr def2)))
((not (equal (car (last def1)) (car (last def2)))) ; check same body
(msg "the proposed body for ~x0,~~%~p1,~~%differs from the existing ~
body,~~%~p2.~~%"
(car def1) (car (last def1)) (car (last def2))))
(t
(let ((allbutbody1 (butlast (cddr def1) 1))
(allbutbody2 (butlast (cddr def2) 1)))
(cond
((not (equal (fetchdclfield :nonexecutable allbutbody1)
(fetchdclfield :nonexecutable allbutbody2)))
(msg "the proposed and existing definitions for ~x0 differ on their ~
:nonexecutable declarations."
(car def1)))
((not (equal (fetchdclfield :stobjs allbutbody1)
(fetchdclfield :stobjs allbutbody2)))
; We insist that the :STOBJS of the two definitions be identical. Vernon
; Austel pointed out the following bug.
#
; Define a :program mode function with a nonstobj argument.
(defun stobjlessfn (stobjtobe)
(declare (xargs :mode :program))
stobjtobe)
; Use it in the definition of another :program mode function.
(defun mycalleeisstobjless (x)
(declare (xargs :mode :program))
(stobjlessfn x))
; Then introduce a the argument name as a stobj:
(defstobj stobjtobe
(afield :type integer :initially 0))
; And reclassify the first function into :logic mode.
(defun stobjlessfn (stobjtobe)
(declare (xargs :stobjs stobjtobe))
stobjtobe)
; If you don't notice the different use of :stobjs then the :program
; mode function mycalleeisstobjless [still] treats the original
; function as though its argument were NOT a stobj! For example,
; (mycalleeisstobjless 3) is a wellformed :program mode term
; that treats 3 as a stobj.
#
(msg "the proposed and existing definitions for ~x0 differ on their ~
:stobj declarations."
(car def1)))
((not (setequalpequal (fetchdclfield 'type allbutbody1)
(fetchdclfield 'type allbutbody2)))
; Once we removed the restriction that the type and :guard fields of the defs
; be setequal. But imagine that we have a strong guard on foo in our current
; ACL2 session, but that we then include a book with a much weaker guard.
; (Horrors! What if the new guard is totally unrelated!?) If we didn't make
; the tests below, then presumably the guard on foo would be unchanged by this
; includebook. Suppose that in this book, we have verified guards for a
; function bar that calls foo. Then after including the book, it will look as
; though correctly guarded calls of bar always generate only correctly guarded
; calls of foo, but now that foo has a stronger guard than it did when the book
; was certified, this might not always be the case.
(msg "the proposed and existing definitions for ~x0 differ on their ~
type declarations."
(car def1)))
((let ((guards1 (fetchdclfield :guard allbutbody1))
(guards2 (fetchdclfield :guard allbutbody2)))
(not (or (setequalpequal guards1 guards2)
; See the comment above on type and :guard fields. Here, we comprehend the
; fact that omission of a guard is equivalent to :guard t. Of course, it is
; also equivalent to :guard 't and even to :guard (not nil), but we see no need
; to be that generous with our notion of redundancy.
(and (null guards1) (equal guards2 '(t)))
(and (null guards2) (equal guards1 '(t))))))
(msg "the proposed and existing definitions for ~x0 differ on their ~
:guard declarations."
(car def1)))
((not chkmeasurep)
nil)
(t
(let ((newmeasures (fetchdclfield :measure allbutbody1))
(oldmeasures (fetchdclfield :measure allbutbody2)))
(cond
((equal newmeasures oldmeasures)
nil)
(t
(let ((oldmeasuredsubset
(let ((justification
(getprop (car def2) 'justification nil
'currentacl2world wrld)))
(and
; Consider the case that the existing definition is nonrecursive. Then we
; treat the measured subset as nil.
justification
(access justification justification :subset)))))
(cond
((and (consp newmeasures)
(null (cdr newmeasures))
(let ((newmeasure (car newmeasures)))
(or (equal newmeasure (car oldmeasures))
(and (truelistp newmeasure)
(eq (car newmeasure) :?)
(arglistp (cdr newmeasure))
(setequalpeq oldmeasuredsubset (cdr newmeasure))))))
nil)
(oldmeasures
(msg "the proposed and existing definitions for ~x0 differ on ~
their measures. The existing measure is ~x1. The new ~
measure needs to be specified explicitly with :measure ~
(see :DOC xargs), either to be identical to the ~
existing measure or to be a call of :? on the measured ~
subset; for example, ~x2 will serve as the new :measure."
(car def1)
(car oldmeasures)
(cons :? oldmeasuredsubset)))
(t
(msg "the existing definition for ~x0 does not have an ~
explicitly specified measure. Either remove the ~
:measure declaration from your proposed definition, or ~
else specify a :measure that applies :? to the existing ~
measured subset, for example, ~x1."
(car def1)
(cons :? oldmeasuredsubset))))))))))))))
(defun identicaldefp (def1 def2 chkmeasurep wrld)
; This function is probably obsolete  superseded by nonidenticaldefp  but
; we leave it here for reference by comments.
(not (nonidenticaldefp def1 def2 chkmeasurep wrld)))
(defun redundantorreclassifyingdefunp (defunmode symbolclass
ldskipproofsp def wrld)
; Def is a defuns tuple such as (fn args ...dcls... body) that has been
; submitted to defuns with mode defunmode. We determine whether fn is already
; defined in wrld and has an "identical" definition (up to defunmode). We
; return either nil, a message (cons pair suitable for printing with ~@),
; 'redundant, or 'reclassifying, or 'verifyguards. 'Redundant is returned if
; there is an existing definition for fn that is identicaldefp to def and has
; mode defunmode, except that in this case 'verifyguards is returned if the
; symbolclass was :ideal but this definition indicates promotion to
; :commonlispcompliant. 'Reclassifying is returned if there is an existing
; definition for fn that is identicaldefp to def but in defunmode :program
; while defunmode is :logic. Otherwise nil or an explanatory message,
; suitable for printing using " Note that ~@0.", is returned.
; Functions further up the call tree will decide what to do with a result of
; 'verifyguards. But a perfectly reasonable action would be to cause an error
; suggesting the use of verifyguards instead of defun.
; A successful redundancy check requires that the untranslated measure is
; identical to that of the earlier corresponding defun. Without such a check
; we can store incorrect induction information, as exhibited by the "soundness
; bug in the redundancy criterion for defun events" mentioned in :doc
; note302. The following examples, which work with Version_3.0.1 but
; (fortunately) not afterwards, build on the aforementioned proof of nil given
; in :doc note302, giving further weight to our insistence on the same
; measure if the mode isn't changing from :program to :logic.
; The following example involves redundancy only for :program mode functions.
#
(encapsulate
()
(local (defun foo (x y)
(declare (xargs :measure (acl2count y) :mode :program))
(if (and (consp x) (consp y))
(foo (cons x x) (cdr y))
y)))
(defun foo (x y)
(declare (xargs :mode :program))
(if (and (consp x) (consp y))
(foo (cons x x) (cdr y))
y))
(verifytermination foo))
(defthm bad
(atom x)
:ruleclasses nil
:hints (("Goal" :induct (foo x '(3)))))
(defthm contradiction
nil
:ruleclasses nil
:hints (("Goal" :use ((:instance bad (x '(7)))))))
#
; Note that even though we do not store induction schemes for mutualrecursion,
; the following variant of the first example shows that we still need to check
; measures in that case:
#
(setbogusmutualrecursionok t) ; ease construction of example
(encapsulate
()
(local (encapsulate
()
(local (mutualrecursion
(defun bar (x) x)
(defun foo (x y)
(declare (xargs :measure (acl2count y)))
(if (and (consp x) (consp y))
(foo (cons x x) (cdr y))
y))))
(mutualrecursion
(defun bar (x) x)
(defun foo (x y)
(if (and (consp x) (consp y))
(foo (cons x x) (cdr y))
y)))))
(defun foo (x y)
(if (and (consp x) (consp y))
(foo (cons x x) (cdr y))
y)))
(defthm bad
(atom x)
:ruleclasses nil
:hints (("Goal" :induct (foo x '(3)))))
(defthm contradiction
nil
:ruleclasses nil
:hints (("Goal" :use ((:instance bad (x '(7)))))))
# ; 
(cond ((functionsymbolp (car def) wrld)
(let* ((wrld1 (decodelogicalname (car def) wrld))
(name (car def))
(val (scantocltlcommand (cdr wrld1)))
(chkmeasurep
(and
; If we are skipping proofs, then we do not need to check the measure. Why
; not? One case is that we are explicitly skipping proofs (with skipproofs,
; rebuild, setldskipproofsp, etc.; or, inclusion of an uncertified book), in
; which case all bets are off. Otherwise we are including a certified book,
; where the measured subset was proved correct. This observation satisfies our
; concern, which is that the current redundant definition will ultimately
; become the actual definition because the earlier one is local.
(not ldskipproofsp)
; In later code, below, we disallow reclassifying :logic to :program. Now
; consider the case of going from :program to :logic. Then we ignore the
; measure of the :program mode definition when calculating the measure for the
; new :logic mode definition, so we do not need to check equality of the old
; and new measures.
(eq (cadr val) defunmode))))
; The 'cltlcommand val for a defun is (defuns :defunmode ignorep . deflst)
; where :defunmode is a keyword (rather than nil which means this was an
; encapsulate or was :nonexecutable).
(cond ((null val) nil)
((and (consp val)
(eq (car val) 'defuns)
(keywordp (cadr val)))
(cond
((nonidenticaldefp def
(assoceq name (cdddr val))
chkmeasurep
wrld))
; Else, this cltlcommand contains a member of deflst that is identical to
; def.
((eq (cadr val) defunmode)
(cond ((and (eq symbolclass :commonlispcompliant)
(eq (symbolclass name wrld) :ideal))
; The following produced a hard error in v27, because the second defun was
; declared redundant on the first pass and then installed as
; :commonlispcompliant on the second pass:
; (encapsulate nil
; (local
; (defun foo (x) (declare (xargs :guard t :verifyguards nil)) (car x)))
; (defun foo (x) (declare (xargs :guard t)) (car x)))
; (thm (equal (foo 3) xxx))
; The above example was derived from one sent by Jared Davis, who proved nil in
; an early version of v28 by exploiting this idea to trick ACL2 into
; considering guards verified for a function employing mbe.
; Here, we prevent such promotion of :ideal to :commonlispcompliant.
'verifyguards)
(t 'redundant)))
((and (eq (cadr val) :program)
(eq defunmode :logic))
'reclassifying)
(t
; We disallow redefinition from :logic to :program mode. We once thought
; we should allow it and argued that it should just be redundant, i.e.,
; we should do nothing when processing the new :program mode defun. But
; then we considered an example like this:
; (encapsulate nil
; (local (defun foo (x) x))
; (defun foo (x) (declare (xargs :mode :program)) x) ; redundant?
; (defthm fooisid (equal (foo x) x)))
; We clearly don't want to allow this encapsulation or analogous books.
; This is actually prevented by pass 2 of the encapsulate, when it
; discovers that foo is now :program mode. But we have little confidence
; that we avoid similar traps elsewhere and think it is a bad idea to
; allow :logic to :program.
"redefinition from :logic to :program mode is illegal")))
((and (null (cadr val)) ; optimization
(fetchdclfield :nonexecutable
(butlast (cddr def) 1)))
(cond
((let ((event (cddddr (car wrld1))))
(nonidenticaldefp
def
(case (car event)
(mutualrecursion
(assoceq name (stripcdrs (cdr event))))
(defuns
(assoceq name (cdr event)))
(otherwise
(cdr event)))
chkmeasurep
wrld)))
(t
; Note that :nonexecutable definitions always have mode :logic, we we do not
; have to think about the 'reclassifying case.
'redundant)))
(t nil))))
(t nil)))
(defun redundantorreclassifyingdefunsp1 (defunmode symbolclass
ldskipproofsp deflst wrld ans)
(cond ((null deflst) ans)
(t (let ((x (redundantorreclassifyingdefunp
defunmode symbolclass ldskipproofsp (car deflst)
wrld)))
(cond
((consp x) x) ; a message
((eq ans x)
(redundantorreclassifyingdefunsp1
defunmode symbolclass ldskipproofsp (cdr deflst) wrld
ans))
(t nil))))))
(defun redundantorreclassifyingdefunsp (defunmode symbolclass
ldskipproofsp deflst wrld)
; We return 'redundant if the functions in deflst are already identically
; defined with :mode defunmode and class symbolclass. We return
; 'reclassifying if they are all identically defined :programally and
; defunmode is :logic. We return nil otherwise.
; We answer this question by answering it independently for each def in
; deflst. Thus, every def must be 'redundant or 'reclassifying as
; appropriate. This seems really weak because we do not insist that only one
; cltlcommand tuple is involved. But (defuns def1 ... defn) just adds one
; axiom for each defi and the axiom is entirely determined by the defi. Thus,
; if we have executed a defuns that added the axiom for defi then it is the
; same axiom as would be added if we executed a different defuns that contained
; defi. Furthermore, a cltlcommand of the form (defuns :defunmode ignorep
; def1 ... defn) means (defuns def1 ... defn) was executed in this world with
; the indicated defunmode.
; Note: Our redundancy check for definitions is based on the untranslated
; terms. This is different from, say, theorems, where we compare translated
; terms. The reason is that we do not store the translated versions of
; :program definitions and don't want to go to the cost of translating
; what we did store. We could, I suppose. We handle theorems the way we do
; because we store the translated theorem on the property list, so it is easy.
; Our main concern visavis redundancy is arranging for identical definitions
; not to blow us up when we are loading books that have copied definitions and
; I don't think translation will make an important difference to the utility of
; the feature.
; Note: There is a possible bug lurking here. If the host Common Lisp expands
; macros before storing the symbolfunction, then it is we could recognize as
; "redundant" an identical defun that, if actually passed to the underlying
; Common Lisp, would result in the storage of a different symbolfunction
; because of the earlier redefinition of some macro used in the "redundant"
; definition. This is not a soundness problem, since redefinition is involved.
; But it sure might annoy somebody who didn't notice that his redefinition
; wasn't processed.
(cond
((null deflst) 'redundant)
(t (let ((ans (redundantorreclassifyingdefunp
defunmode symbolclass ldskipproofsp (car deflst) wrld)))
(cond ((consp ans) ans) ; a message
(t (redundantorreclassifyingdefunsp1
defunmode symbolclass ldskipproofsp (cdr deflst) wrld
ans)))))))
(defun collectwhencadreq (sym lst)
(cond ((null lst) nil)
((eq sym (cadr (car lst)))
(cons (car lst) (collectwhencadreq sym (cdr lst))))
(t (collectwhencadreq sym (cdr lst)))))
(defun allprogramp (names wrld)
; Names is a list of function symbols. Return t iff every element of
; names is :program.
(cond ((null names) t)
(t (and (programp (car names) wrld)
(allprogramp (cdr names) wrld)))))
; Essay on the Identification of Irrelevant Formals
; A formal is irrelevant if its value does not affect the value of the
; function. Of course, ignored formals have this property, but we here
; address ourselves to the much more subtle problem of formals that are
; used only in irrelevant ways. For example, y in
; (defun foo (x y) (if (zerop x) 0 (foo (1 x) (cons x y))))
; is irrelevant. Clearly, any formal mentioned outside of a recursive call is
; relevant  provided that no previously introduced function has irrelevant
; arguments and no definition tests constants as in (if t x y). But a
; formal that is never used outside a recursive call may still be
; relevant, as illustrated by y in
; (defun foo (x y) (if (< x 2) x (foo y 0)))
; Observe that (foo 3 1) = 1 and (foo 3 0) = 0, thus, y is relevant. (This
; function can be admitted with the measure (cond ((< x 2) 0) ((< y 2) 1) (t
; 2)).)
; Thus, we have to do a transitive closure computation based on which
; formals appear in which actuals of recursive calls. In the first pass we
; see that x, above, is relevant because it is used outside the recursion.
; In the next pass we see that y is relevant because it is passed into the
; x argument position of a recursive call.
; The whole thing is made somewhat more hairy by mutual recursion, though no
; new intellectual problems are raised. However, to cope with mutual recursion
; we stop talking about "formals" and start talking about "slots." A slot here
; is a triple, (fn n . var), where fn is one of the functions in the mutually
; recursive clique, n is a nonnegative integer less than the arity of fn, and
; var is the nth formal of fn. This is redundant (simply (fn . n) would
; suffice) but allows us to recover the formal conveniently. We say a "slot
; is used" in a term if its formal is used in the term and the term occurs
; in the body of the fn of the slot.
; A "recursive call" here means a call of any function in the clique. We
; generally use the variable cliquealist to mean an alist whose elements are
; each of the form (fn formals guard measure body). Thus, if temp is (assoceq
; fn cliquealist) and is nonnil then
; formals = (nth 1 temp)
; guard = (nth 2 temp)
; measure = (nth 3 temp)
; body = (nth 4 temp).
; We make the convention that any variable occurring in either the guard
; or measure is relevant. We do not discuss guards and measures further.
; A second problem is raised by the presence of lambda expressions. We discuss
; them more below.
; Our algorithm iteratively computes the relevant slots of a clique by
; successively enlarging an initial guess. The initial guess consists of all
; the slots used outside of a recursive call. (In this computation we also
; sweep in any slot whose formal is used in an actual expression in a recursive
; call, provided the actual is in a slot already known to be used outside.)
; Clearly, every slot so collected is relevant. We then iterate, sweeping into
; the set every slot used either outside recursion or in an actual used in a
; relevant slot. When this computation ceases to add any new slots we consider
; the uncollected slots to be irrelevant.
; For example, in (defun foo (x y) (if (zerop x) 0 (foo (1 x) (cons x y)))) we
; intially guess that x is relevant and y is not. The next iteration adds
; nothing, because y is not used in the x slot, so we are done.
; On the other hand, in (defun foo (x y) (if (< x 2) x (foo y 0))) we might
; once again guess that y is irrelevant. (Actually, we don't, because we see
; in the initial scan that it is used in the x slot of a recursion AFTER we
; have spotted x occurring outside of a recursive call. But this could be
; remedied by a defn like (defun bar (z x y) (if (not (< z 2)) (bar (1 z) y 0)
; x)) where we don't know x is relevant at the time we process the call and
; would thus guess that y was irrelevant.) However, the second pass would note
; the occurrence of y in a relevant slot and would sweep it into the set. We
; conclude that there are no irrelevant slots in this definition.
; So far we have not discussed lambda expressions; they are unusual in this
; setting because they may hide recursive calls that we should analyze. We do
; not want to expand the lambdas away, for fear of combinatoric explosions.
; Instead, we expand the cliquealist, by adding, for each lambdaapplication a
; new entry that pairs that lambda expression with the appropriate terms.
; (That is, the "fn" of the new clique member is the lambda expression itself.)
; Thus, we actually use assocequal instead of assoceq when looking in
; cliquealist.
(defun formalposition (var formals i)
(cond ((null formals) i)
((eq var (car formals)) i)
(t (formalposition var (cdr formals) (1+ i)))))
(defun makeslot (fn formals var)
(list* fn (formalposition var formals 0) var))
(defun makeslots (fn formals vars)
(cond ((null vars) nil)
(t (cons (makeslot fn formals (car vars))
(makeslots fn formals (cdr vars))))))
(defun slotmember (fn n lst)
; We ask whether (list* fn n var), for some var, is a memberequal of
; the list of slots, lst.
(cond ((null lst) nil)
((and (equal fn (caar lst))
(= n (cadar lst)))
lst)
(t (slotmember fn n (cdr lst)))))
; We now develop the code to expand the cliquealist for lambda expressions.
(mutualrecursion
(defun expandcliquealistterm (term cliquealist)
(cond ((variablep term) cliquealist)
((fquotep term) cliquealist)
(t (let ((cliquealist
(expandcliquealisttermlst (fargs term)
cliquealist))
(fn (ffnsymb term)))
(cond
((flambdap fn)
(cond ((assocequal fn cliquealist) cliquealist)
(t (expandcliquealistterm
(lambdabody fn)
(cons
(list fn
(lambdaformals fn)
*t*
*0*
(lambdabody fn))
cliquealist)))))
(t cliquealist))))))
(defun expandcliquealisttermlst (lst cliquealist)
(cond ((null lst) cliquealist)
(t (expandcliquealisttermlst
(cdr lst)
(expandcliquealistterm (car lst) cliquealist)))))
)
(defun expandcliquealist1 (alist cliquealist)
(cond ((null alist) cliquealist)
(t (expandcliquealist1 (cdr alist)
(expandcliquealistterm
(nth 4 (car alist))
cliquealist)))))
(defun expandcliquealist (cliquealist)
(expandcliquealist1 cliquealist cliquealist))
(defun makecliquealist1 (fns formals guards measures bodies)
(cond ((null fns) nil)
(t (cons (list (car fns)
(car formals)
(car guards)
(car measures)
(car bodies))
(makecliquealist1 (cdr fns)
(cdr formals)
(cdr guards)
(cdr measures)
(cdr bodies))))))
(defun makecliquealist (fns formals guards measures bodies)
; This function converts from the data structures used in defunsfn0 to our
; expanded cliquealist. Each element of cliquealist is of the form (fn
; formals guard measure body), where fn is either a function symbol or lambda
; expression.
(expandcliquealist
(makecliquealist1 fns formals guards measures bodies)))
(mutualrecursion
(defun relevantslotsterm (fn formals term cliquealist ans)
; Term is a term occurring in the body of fn which has formals formals. We
; collect a slot into ans if it is used outside a recursive call (or in an
; already known relevant actual to a recursive call).
(cond
((variablep term)
(addtosetequal (makeslot fn formals term) ans))
((fquotep term) ans)
((assocequal (ffnsymb term) cliquealist)
(relevantslotscall fn formals (ffnsymb term) (fargs term) 0
cliquealist ans))
(t
(relevantslotstermlst fn formals (fargs term) cliquealist ans))))
(defun relevantslotstermlst (fn formals lst cliquealist ans)
(cond ((null lst) ans)
(t (relevantslotstermlst
fn formals (cdr lst) cliquealist
(relevantslotsterm fn formals (car lst)
cliquealist ans)))))
(defun relevantslotscall
(fn formals calledfn actuals i cliquealist ans)
; Calledfn is the name of some function in the clique. Actuals is (a tail of)
; the list of actuals in a call of calledfn occurring in the body of fn (which
; has formals formals). Initially, i is 0 and in general is the position in
; the argument list of the first element of actuals. Ans is a list of slots
; which are known to be relevant. We extend ans by adding new, relevant slots
; to it, by seeing which slots are used in the actuals in the relevant slots of
; calledfn.
(cond
((null actuals) ans)
(t
(relevantslotscall
fn formals calledfn (cdr actuals) (1+ i) cliquealist
(if (slotmember calledfn i ans)
(relevantslotsterm fn formals (car actuals)
cliquealist ans)
ans)))))
)
(defun relevantslotsdef
(fn formals guard measure body cliquealist ans)
; Returns all obviously relevant slots in a definition. A slot is obviously
; relevant if it is mentioned in the guard or measure of the definition or is
; mentioned outside of all calls of functions in the clique or it is mentioned
; in some known relevant argument position of a function in the clique.
(let ((vars (allvars1 guard (allvars measure))))
(cond
((subsetpeq formals vars)
(unionequal (makeslots fn formals formals) ans))
(t (relevantslotsterm
fn formals body cliquealist
(unionequal (makeslots fn formals vars) ans))))))
(defun relevantslotsclique1 (alist cliquealist ans)
(cond
((null alist) ans)
(t (relevantslotsclique1
(cdr alist) cliquealist
(relevantslotsdef (nth 0 (car alist))
(nth 1 (car alist))
(nth 2 (car alist))
(nth 3 (car alist))
(nth 4 (car alist))
cliquealist
ans)))))
(defun relevantslotsclique (cliquealist ans)
; We compute the relevant slots in an expanded clique alist (one in which the
; lambda expressions have been elevated to clique membership). The list of
; relevant slots includes the relevant lambda slots. We do it by iteratively
; enlarging ans until it is closed.
(let ((ans1 (relevantslotsclique1 cliquealist cliquealist ans)))
(cond ((equal ans1 ans) ans)
(t (relevantslotsclique cliquealist ans1)))))
(defun allnonlambdaslotsclique (cliquealist)
; We return all the slots in a clique except those for lambda expressions.
(cond ((null cliquealist) nil)
((symbolp (caar cliquealist))
(append (makeslots (caar cliquealist) (cadar cliquealist) (cadar cliquealist))
(allnonlambdaslotsclique (cdr cliquealist))))
(t (allnonlambdaslotsclique (cdr cliquealist)))))
(defun ignored/ignorableslots (fns arglists ignores ignorables)
; Ignored formals are considered not to be irrelevant. Should we do similarly
; for ignorable formals?
;  If yes (ignorables are not irrelevant), then we may miss some irrelevant
; formals. Of course, it is always OK to miss some irrelevant formals, but
; we would prefer not to miss them needlessly.
;  If no (ignorables are irrelevant), then we may report an ignorable variable
; as irrelevant, which might annoy the user even though it really is
; irrelevant, if "ignorable" not only means "could be ignored" but also means
; "could be irrelevant".
; We choose "yes". If the user has gone through the trouble to label a
; variable as irrelevant, then the chance that irrelevance is due to a typo are
; dwarfed by the chance that irrelevance is due to being an ignorable var.
(cond ((null fns) nil)
(t (append (makeslots (car fns) (car arglists) (car ignores))
(makeslots (car fns) (car arglists) (car ignorables))
(ignored/ignorableslots (cdr fns)
(cdr arglists)
(cdr ignores)
(cdr ignorables))))))
(defun irrelevantnonlambdaslotsclique (fns arglists guards measures ignores
ignorables bodies)
; Let cliquealist be an expanded clique alist (one in which lambda expressions have
; been elevated to clique membership). Return all the irrelevant slots for the nonlambda
; members of the clique.
; A "slot" is a triple of the form (fn n . var), where fn is a function symbol,
; n is some nonnegative integer less than the arity of fn, and var is the nth
; formal of fn. If (fn n . var) is in the list returned by this function, then
; the nth formal of fn, namely var, is irrelevant to the value computed by fn.
(let ((cliquealist (makecliquealist fns arglists guards measures bodies)))
(setdifferenceequal (allnonlambdaslotsclique cliquealist)
(append (relevantslotsclique cliquealist nil)
(ignored/ignorableslots
fns arglists ignores ignorables)))))
(defun tilde*irrelevantformalsmsg1 (slots)
(cond ((null slots) nil)
(t (cons (cons "~n0 formal of ~x1, ~x2,"
(list (cons #\0 (list (1+ (cadar slots))))
(cons #\1 (caar slots))
(cons #\2 (cddar slots))))
(tilde*irrelevantformalsmsg1 (cdr slots))))))
(defun tilde*irrelevantformalsmsg (slots)
(list "" "~@*" "~@* and the " "~@* the " (tilde*irrelevantformalsmsg1 slots)))
(defun chkirrelevantformals
(fns arglists guards measures ignores ignorables bodies ctx state)
(let ((irrelevantformalsok
(cdr (assoceq :irrelevantformalsok
(tablealist 'acl2defaultstable (w state))))))
(cond
((or (eq irrelevantformalsok t)
(and (eq irrelevantformalsok :warn)
(warningdisabledp "Irrelevantformals")))
(value nil))
(t
(let ((irrelevantslots
(irrelevantnonlambdaslotsclique
fns arglists guards measures ignores ignorables bodies)))
(cond
((null irrelevantslots) (value nil))
((eq irrelevantformalsok :warn)
(pprogn
(warning$ ctx ("Irrelevantformals")
"The ~*0 ~#1~[is~/are~] irrelevant. See :DOC ~
irrelevantformals."
(tilde*irrelevantformalsmsg irrelevantslots)
(if (cdr irrelevantslots) 1 0))
(value nil)))
(t (er soft ctx
"The ~*0 ~#1~[is~/are~] irrelevant. See :DOC ~
irrelevantformals."
(tilde*irrelevantformalsmsg irrelevantslots)
(if (cdr irrelevantslots) 1 0)))))))))
(deflabel irrelevantformals
:doc
":DocSection ACL2::Programming
formals that are used but only insignificantly~/
Let ~c[fn] be a function of ~c[n] arguments. Let ~c[x] be the ~c[i]th formal of ~c[fn].
We say ~c[x] is ``irrelevant in ~c[fn]'' if ~c[x] is not involved in either the
~il[guard] or the measure for ~c[fn], ~c[x] is used in the body, but the value of
~c[(fn a1...ai...an)] is independent of ~c[ai].~/
The easiest way to define a function with an irrelevant formal is
simply not to use the formal in the body of the
function. Such formals are said to be ``ignored'' by Common Lisp
and a special declaration is provided to allow ignored formals.
ACL2 makes a distinction between ignored and irrelevant formals. Note
however that if a variable is ~ilc[declare]d ~c[ignore]d or ~c[ignorable],
then it will not be reported as irrelevant.
An example of an irrelevant formal is ~c[x] in the definition of ~c[fact]
below.
~bv[]
(defun fact (i x)
(declare (xargs :guard (and (integerp i) (<= 0 i))))
(if (zerop i) 0 (* i (fact (1 i) (cons i x))))).
~ev[]
Observe that ~c[x] is only used in recursive calls of ~c[fact]; it never
``gets out'' into the result. ACL2 can detect some irrelevant
formals by a closure analysis on how the formals are used. For
example, if the ~c[i]th formal is only used in the ~c[i]th argument position
of recursive calls, then it is irrelevant. This is how ~c[x] is used
above.
It is possible for a formal to appear only in recursive calls but
still be relevant. For example, ~c[x] is ~st[not] irrelevant below, even
though it only appears in the recursive call.
~bv[]
(defun fn (i x) (if (zerop i) 0 (fn x (1 i))))
~ev[]
The key observation above is that while ~c[x] only appears in a
recursive call, it appears in an argument position, namely ~c[i]'s, that
is relevant. (The function above can be admitted with a ~c[:]~ilc[guard]
requiring both arguments to be nonnegative integers and the ~c[:measure]
~c[(+ i x)].)
Establishing that a formal is irrelevant, in the sense defined
above, can be an arbitrarily hard problem because it requires
theorem proving. For example, is ~c[x] irrelevant below?
~bv[]
(defun test (i j k x) (if (p i j k) x 0))
~ev[]
Note that the value of ~c[(test i j k x)] is independent of ~c[x] ~[] thus
making ~c[x] irrelevant ~[] precisely if ~c[(p i j k)] is a theorem.
ACL2's syntactic analysis of a definition does not guarantee to
notice all irrelevant formals.
We regard the presence of irrelevant formals as an indication that
something is wrong with the definition. We cause an error on such
definitions and suggest that you recode the definition so as to
eliminate the irrelevant formals. If you must have an irrelevant
formal, one way to ``trick'' ACL2 into accepting the definition,
without slowing down the execution of your function, is to use the
formal in an irrelevant way in the ~il[guard]. For example, to admit
fact, above, with its irrelevant ~c[x] one might use
~bv[]
(defun fact (i x)
(declare (xargs :guard (and (integerp i) (<= 0 i) (equal x x))))
(if (zerop i) 0 (* i (fact (1 i) (cons i x)))))
~ev[]
For those who really want to turn off this feature, we have
provided a way to use the ~ilc[acl2defaultstable] for this purpose;
~pl[setirrelevantformalsok].
If you need to introduce a function with an irrelevant formal,
please explain to the authors why this should be allowed.")
(defun chklogicsubfunctions (names0 names terms wrld str ctx state)
; Assume we are defining names in terms of terms (1:1 correspondence). Assume
; also that the definitions are to be :logic. Then we insist that every
; function used in terms be :logic. Str is a string used in our error
; message and is either "guard" or "body".
(cond ((null names) (value nil))
(t (let ((bad (collectprograms
(setdifferenceeq (allfnnames (car terms))
names0)
wrld)))
(cond
(bad
(er soft ctx
"The ~@0 for ~x1 calls the :program function~#2~[ ~
~&2~/s ~&2~]. We require that :logic definitions be ~
defined entirely in terms of :logically defined ~
functions. See :DOC defunmode."
str (car names) bad))
(t (chklogicsubfunctions names0 (cdr names) (cdr terms)
wrld str ctx state)))))))
;; RAG  This function strips out the functions which are
;; nonclassical in a chkacceptabledefuns "fives" structure.
#+:nonstandardanalysis
(defun getnonclassicalfnsfromlist (names wrld fnssofar)
(cond ((null names) fnssofar)
(t (let ((fns (if (or (not (symbolp (car names)))
(classicalp (car names) wrld))
fnssofar
(cons (car names) fnssofar))))
(getnonclassicalfnsfromlist (cdr names) wrld fns)))))
;; RAG  This function takes in a list of terms and returns any
;; nonclassical functions referenced in the terms.
#+:nonstandardanalysis
(defmacro getnonclassicalfns (lst wrld)
`(getnonclassicalfnsaux ,lst ,wrld nil))
#+:nonstandardanalysis
(defun getnonclassicalfnsaux (lst wrld fnssofar)
(cond ((null lst) fnssofar)
(t (getnonclassicalfnsaux
(cdr lst)
wrld
(getnonclassicalfnsfromlist
(allfnnames (car lst)) wrld fnssofar)))))
;; RAG  this function checks that the measures used to accept the definition
;; are classical. Note, *0* is a signal that the default measure is being used
;; (see getmeasures1)  and in that case, we know it's classical, since it's
;; just the acl2count of some tuple consisting of variables in the defun.
#+:nonstandardanalysis
(defun stripzeromeasures (lst accum)
(if (consp lst)
(if (equal (car lst) *0*)
(stripzeromeasures (cdr lst) accum)
(stripzeromeasures (cdr lst) (cons (car lst) accum)))
accum))
#+:nonstandardanalysis
(defun chkclassicalmeasures (measures names ctx wrld state)
(let ((nonclassicalfns (getnonclassicalfns
(stripzeromeasures measures nil)
wrld)))
(cond ((null nonclassicalfns)
(value nil))
(t
(er soft ctx
"It is illegal to use nonclassical measures to justify a ~
recursive definition. However, there has been an ~
attempt to recursively define ~*0 using the ~
nonclassical functions ~*1 in the measure."
`("<MissingFunction>" "~x*," "~x* and " "~x*, " ,names)
`("<MissingFunction>" "~x*," "~x* and " "~x*, "
,nonclassicalfns))))))
;; RAG  This function checks that nonclassical functions only appear
;; on nonrecursive functions.
#+:nonstandardanalysis
(defun chknorecursivenonclassical (nonclassicalfns names mp rel
measures
bodies ctx
wrld state)
(cond ((and (int= (length names) 1)
(not (ffnnamepmodmbe (car names) (car bodies))))
; Then there is definitely no recursion (see analogous computation in
; putproprecursiveplst). Note that with :bogusmutualrecursionok, a clique
; of size greater than 1 might not actually have any recursion. But then it
; will be up to the user in this case to eliminate the appearance of possible
; recursion.
(value nil))
((not (null nonclassicalfns))
(er soft ctx
"It is illegal to use nonclassical functions in a ~
recursive definition. However, there has been an ~
attempt to recursively define ~*0 using the ~
nonclassical function ~*1."
`("<MissingFunction>" "~x*," "~x* and " "~x*, " ,names)
`("<MissingFunction>" "~x*," "~x* and " "~x*, "
,nonclassicalfns)))
((not (and (classicalp mp wrld)
(classicalp rel wrld)))
(er soft ctx
"It is illegal to use a nonclassical function as a ~
wellordering or wellordered domain in a recursive ~
definition. However, there has been an ~
attempt to recursively define ~*0 using the ~
wellordering function ~x* and domain ~x*."
`("<MissingFunction>" "~x*," "~x* and " "~x*, " ,names)
mp
rel))
(t
(chkclassicalmeasures measures names ctx wrld state))))
(defun unioncollectnonx (x lst)
(cond ((endp lst) nil)
(t (unionequal (collectnonx x (car lst))
(unioncollectnonx x (cdr lst))))))
(defun translatemeasures (terms ctx wrld state)
; WARNING: Keep this in sync with translatetermlst. Here we allow (:? var1
; ... vark), where the vari are distinct variables.
(cond ((null terms) (value nil))
(t (erlet*
((term
(cond ((and (consp (car terms))
(eq (car (car terms)) :?))
(cond ((arglistp (cdr (car terms)))
(value (car terms)))
(t (er soft ctx
"A measure whose car is :? must be of the ~
form (:? v1 ... vk), where (v1 ... vk) is ~
a list of distinct variables. The measure ~
~x0 is thus illegal."
(car terms)))))
(t
(translate (car terms) t t t ctx wrld state))))
(rst (translatemeasures (cdr terms) ctx wrld state)))
(value (cons term rst))))))
;; RAG  I modified the function below to check for recursive
;; definitions using nonclassical predicates.
(defun chkacceptabledefuns (lst ctx wrld state #+:nonstandardanalysis stdp)
; Rockwell Addition: We now also return the nonexecutable flag.
; This function does all of the syntactic checking associated with
; defuns. It causes an error if it doesn't like what it sees. It
; returns the traditional 3 values of an errorproducing,
; outputproducing function. However, the "real" value of the
; function is a list of 18 items extracted from lst during the
; checking. These items are:
; names  the names of the fns in the clique
; arglists  their formals
; docs  their documentation strings
; pairs  the (sectionsymbol . citations) pairs parsed from docs
; guards  their translated guards
; measures  their translated measure terms
; mp  the domain predicate (e.g., op) for wellfoundedness
; rel  the wellfounded relation (e.g., o<)
; hints  their translated hints, to be used during the proofs of
; the measure conjectures, all flattened into a single list
; of hints of the form ((clid . settings) ...).
; guardhints
;  like hints but to be used for the guard conjectures
; stdhints (always returned, but only of interest when
; #+:nonstandardanalysis)
;  like hints but to be used for the stdp conjectures
; otfflg  t or nil, used as "Onward Thru the Fog" arg for prove
; bodies  their translated bodies
; symbolclass
;  :program, :ideal, or :commonlispcompliant
; normalizeps
;  list of Booleans, used to determine for each fn in the clique
; whether its body is to be normalized
; reclassifyingp
;  t or nil, t if this is a reclassifying from :program
; with identical defs.
; wrld  a modified wrld in which the following properties
; may have been stored for each fn in names:
; 'formals, 'stobjsin and 'stobjsout
; nonexecutablep  t or nil according to whether these defuns are to
; nonexecutable. Nonexecutable defuns may violate the
; translate conventions on stobjs.
(erlet*
((fives (chkdefunstuples lst ctx wrld state)))
; Fives is a list in 1:1 correspondence with lst. Each element of
; fives is a 5tuple of the form (name args doc edcls body). Consider the
; element of fives that corresponds to
; (name args (DECLARE ...) "Doc" (DECLARE ...) body)
; in lst. Then that element of fives is (name args "Doc" (...) body),
; where the ... is the cdrs of the DECLARE forms appended together.
; No translation has yet been applied to them. The newness of name
; has not been checked yet either, though we know it is all but new,
; i.e., is a symbol in the right package. We do know that the args
; are all legal.
(erprogn
(chknoduplicatedefuns (stripcars fives) ctx state)
(chkxargskeywords fives
'(:nonexecutable
:guard :measure :stobjs :wellfoundedrelation
:hints
:guardhints
#+:nonstandardanalysis :stdhints
:mode :verifyguards
:otfflg :normalize)
ctx state)
(let* ((names (stripcars fives))
(arglists (stripcadrs fives))
(ignores (getignores fives))
(ignorables (getignorables fives))
(assumep (or (eq (ldskipproofsp state) 'includebook)
(eq (ldskipproofsp state) 'includebookwithlocals)))
(donottranslatehints
(or assumep
(eq (ldskipproofsp state) 'initializeacl2)))
(docs (getdocs fives)))
(erlet*
((stobjsinlst (getstobjsinlst fives ctx wrld state))
(guards (translatetermlst (getguards fives wrld)
; Stobjsout: Each guard returns one, nonstobj result. This arg
; is used for each guard.
'(nil)
; Logicmodep: Since guards have nothing to do with the logic, and
; since they may legitimately have mode :program, we set logicmodep
; to nil here. This arg is used for each guard.
nil
; Knownstobjslst:
; Here is a slight abuse. Translatetermlst is expecting, in this
; argument, a list in 1:1 correspondence with its first argument,
; specifying the knownstobjs for the translation of corresponding
; terms. But we are supplying the stobjsin for the term, not the
; knownstobjs. The former is a list of stobj flags and the latter is
; a list of stobj names, i.e., the list we supply may contain a NIL
; element where it should have no element at all. This is allowed by
; stobjsp. Technically we ought to map over the stobjsinlst and
; change each element to its collectnonx nil.
stobjsinlst
ctx wrld state))
; By using stobjsout '(nil) we enable the thorough checking of the
; use of state. Thus, the above call ensures that guards do not
; modify (or return) state. We are taking the conservative position
; because intuitively there is a confusion over the question of
; whether, when, and how often guards are run. By prohibiting them
; from modifying state we don't have to answer the questions about
; when they run.
(nonexecutablep
(getunambiguousxargsflg :NONEXECUTABLE
fives
nil ctx state))
(defunmode (getunambiguousxargsflg :MODE
fives
(defaultdefunmode wrld)
ctx state))
(verifyguards (getunambiguousxargsflg :VERIFYGUARDS
fives
'(unspecified)
ctx state)))
(erprogn
(chkdefunmode defunmode names ctx state)
(cond ((not (or (eq nonexecutablep t)
(eq nonexecutablep nil)))
(er soft ctx
"The :NONEXECUTABLE flag must be T or NIL, but ~
~x0 is neither."
nonexecutablep))
((and nonexecutablep
(eq defunmode :program))
(er soft ctx
":NONEXECUTABLE functions must be defined in :LOGIC ~
mode."))
((and nonexecutablep
(unioncollectnonx nil stobjsinlst))
(er soft ctx
":NONEXECUTABLE functions may not declare any ~
singlethreaded objects, but you used ~&0."
(unioncollectnonx nil stobjsinlst)))
(t (value nil)))
(cond ((consp verifyguards)
; This means that the user did not specify a :verifyguards. We will default
; it appropriately.
(value nil))
((eq defunmode :program)
(if (eq verifyguards nil)
(value nil)
(er soft ctx
"When the :MODE is :program, the only legal ~
:VERIFYGUARDS setting is NIL. ~x0 is illegal."
verifyguards)))
((or (eq verifyguards nil)
(eq verifyguards t))
(value nil))
(t (er soft ctx
"The legal :VERIFYGUARD settings are NIL and T. ~x0 is ~
illegal."
verifyguards)))
(let* ((symbolclass (cond ((eq defunmode :program) :program)
((consp verifyguards)
(cond
((= (defaultverifyguardseagerness wrld)
0)
:ideal)
((= (defaultverifyguardseagerness wrld)
1)
(if (getguardsp fives wrld)
:commonlispcompliant
:ideal))
(t :commonlispcompliant)))
(verifyguards :commonlispcompliant)
(t :ideal)))
(rc (redundantorreclassifyingdefunsp
defunmode symbolclass (ldskipproofsp state) lst wrld)))
(cond
((eq rc 'redundant)
(value 'redundant))
((eq rc 'verifyguards)
; We avoid needless complication by simply causing a polite error in this
; case. If that proves to be too inconvenient for users, we could look into
; arranging for a call of verifyguards here.
(let ((includebookpath
(globalval 'includebookpath wrld)))
(mvlet
(erp evwrldandcmdwrld state)
(stategloballet*
((inhibitoutputlst
(cons 'error (fgetglobal 'inhibitoutputlst state))))
; Keep the following in sync with pefn.
(let ((wrld (w state)))
(erlet*
((evwrld (erdecodelogicalname (car names) wrld :pe state))
(cmdwrld (superiorcommandworld evwrld wrld :pe
state)))
(value (cons evwrld cmdwrld)))))
(mvlet (erp1 val1 state)
(er soft ctx
"The definition of ~x0~#1~[~/ (along with the ~
others in its mutualrecursion clique)~]~@2 ~
demands guard verification, but there is already ~
a corresponding existing definition without its ~
guard verified. ~@3Use verifyguards instead; ~
see :DOC verifyguards. ~#4~[Here is the existing ~
definition of ~x0:~/The existing definition of ~
~x0 appears to precede this one in the same ~
toplevel command.~]"
(car names)
names
(cond
(includebookpath
(cons " in the book ~xa"
(list (cons #\a (car includebookpath)))))
(t ""))
(cond
((cddr includebookpath)
(cons "Note: The above book is included under ~
the following sequence of included books ~
from outside to inside, i.e., toplevel ~
included book first:~~&b.~"
(list (cons #\b (reverse
(cdr includebookpath))))))
((cdr includebookpath)
(cons "Note: The above book is included inside ~
the book ~xb. "
(list (cons #\b (cadr includebookpath)))))
(t ""))
(if erp 1 0))
(pprogn (if erp
state
(pefn1 wrld (standardco state)
(car evwrldandcmdwrld)
(cdr evwrldandcmdwrld)
state))
(mv erp1 val1 state))))))
(t
(erlet*
((wrld0 (chkjustnewnames names 'function rc ctx wrld state))
(docpairs (translatedoclst names docs ctx state))
(untranslatedmeasures
; If the defunmode is :program, or equivalently, the symbolclass is :program,
; then we don't need the measures. But we do need "measures" that pass the
; tests below, such as the call of chkfreeandignoredvarslsts. So, we
; simply pretend that no measures were supplied, which is clearly reasonable if
; we are defining the functions to have symbolclass :program.
(getmeasures symbolclass fives ctx state))
(measures (translatemeasures untranslatedmeasures ctx wrld0
state))
; We originally used stobjsout '(nil) above, again, because we felt
; uneasy about measures changing state. But we know no logical
; justification for this feeling, nor do we ever expect to execute the
; measures in Common Lisp. In fact we find it useful to be able to
; pass state into a measure even when its argument position isn't
; "state"; consider for example the function bigclockentry.
(rel (getunambiguousxargsflg
:WELLFOUNDEDRELATION
fives
(defaultwellfoundedrelation wrld)
ctx state))
(hints (if (or donottranslatehints
(eq defunmode :program))
(value nil)
(let ((hints (gethints fives)))
(if hints
(translatehints
(cons "Measure Lemma for" (car names))
(append hints (defaulthints wrld))
ctx wrld0 state)
(value nil)))))
(guardhints (if (or donottranslatehints
(eq defunmode :program))
(value nil)
(let ((guardhints
(getguardhints fives)))
(if guardhints
(translatehints
(cons "Guard for" (car names))
(append guardhints
(defaulthints wrld))
ctx wrld0 state)
(value nil)))))
(stdhints #+:nonstandardanalysis
(cond
((and stdp (not assumep))
(translatehints
(cons "Stdp for" (car names))
(append (getstdhints fives)
(defaulthints wrld))
ctx wrld0 state))
(t (value nil)))
#:nonstandardanalysis
(value nil))
(otfflg (if donottranslatehints
(value nil)
(getunambiguousxargsflg :OTFFLG
fives t ctx state)))
(normalizeps (getnormalizeps fives nil ctx state)))
(erprogn
(cond
((not (and (symbolp rel)
(assoceq
rel
(globalval 'wellfoundedrelationalist
wrld))))
(er soft ctx
"The :WELLFOUNDEDRELATION specified by XARGS must be a ~
symbol which has previously been shown to be a ~
wellfounded relation. ~x0 has not been. See :DOC ~
wellfoundedrelation."
rel))
(t (value nil)))
(let ((mp (cadr (assoceq
rel
(globalval 'wellfoundedrelationalist
wrld))))
(bigmutrec (bigmutrec names)))
(erlet*
((wrld1 (updatew bigmutrec
(putpropxlst2 names 'formals
arglists wrld0)))
(wrld2 (updatew bigmutrec
(storestobjsins names stobjsinlst
wrld1)))
(bodiesandbindings
(translatebodies nonexecutablep
names
(getbodies fives)
; Slight abuse here, see guards translation above:
stobjsinlst
ctx wrld2 state)))
(let* ((bodies (car bodiesandbindings))
(bindings
(superdefunwartbindings
(cdr bodiesandbindings)))
#+:nonstandardanalysis
(nonclassicalfns
(getnonclassicalfns bodies wrld)))
(erprogn
(if assumep
(value nil)
(erprogn
(chkstobjsoutbound names bindings ctx state)
#+:nonstandardanalysis
(chknorecursivenonclassical
nonclassicalfns
names mp rel measures bodies ctx wrld state)))
(let* ((wrld30 (storesuperdefunwartsstobjsin
names wrld2))
(wrld3 #+:nonstandardanalysis
(if (or stdp
(null nonclassicalfns))
wrld30
(putpropxlst1 names 'classicalp
nil wrld30))
#:nonstandardanalysis
wrld30))
(erprogn
(if (eq defunmode :logic)
; Although translate checks for inappropriate calls of :program functions,
; translate11 and translate1 do not.
(erprogn
(chklogicsubfunctions names names
guards wrld3 "guard"
ctx state)
(chklogicsubfunctions names names bodies
wrld3 "body"
ctx state))
(value nil))
(if (eq symbolclass :commonlispcompliant)
(erprogn
(chkcommonlispcompliantsubfunctions
names names guards wrld3 "guard" ctx state)
(chkcommonlispcompliantsubfunctions
names names bodies wrld3 "body" ctx state))
(value nil))
(mvlet
(erp val state)
; This mvlet is just an aside that lets us conditionally check a bunch of
; conditions we needn't do in assumep mode.
(cond
(assumep (mv nil nil state))
(t
(erprogn
(chkfreeandignoredvarslsts names
arglists
guards
measures
ignores
ignorables
bodies
ctx state)
(chkirrelevantformals names arglists
guards
measures
ignores
ignorables
bodies ctx state)
(chkmutualrecursion names bodies ctx
state))))
(cond
(erp (mv erp val state))
(t (value (list 'chkacceptabledefuns
names
arglists
docs
docpairs
guards
measures
mp
rel
hints
guardhints
stdhints ;nil for nonstd
otfflg
bodies
symbolclass
normalizeps
(and (eq rc 'reclassifying)
(allprogramp names wrld))
(storestobjsout
names
bindings
wrld3)
nonexecutablep
))))))))))))))))))))))
(deflabel XARGS
:doc
":DocSection Miscellaneous
giving ~il[hints] to ~ilc[defun]~/
Common Lisp's ~ilc[defun] function does not easily allow one to pass extra
arguments such as ``~il[hints]''. ACL2 therefore supports a peculiar new
declaration (~pl[declare]) designed explicitly for passing
additional arguments to ~ilc[defun] via a keywordlike syntax.
The following declaration is nonsensical but does illustrate all of
the ~ilc[xargs] keywords:
~bv[]
(declare (xargs :guard (symbolp x)
:guardhints ((\"Goal\" :intheory (theory batch1)))
:hints ((\"Goal\" :intheory (theory batch1)))
:measure ( i j)
:mode :logic
:nonexecutable t
:normalize nil
:otfflg t
:stobjs ($s)
:verifyguards t
:wellfoundedrelation mywfr))~/
General Form:
(xargs :key1 val1 ... :keyn valn)
~ev[]
where the keywords and their respective values are as shown below.
Note that once ``inside'' the xargs form, the ``extra arguments'' to
~ilc[defun] are passed exactly as though they were keyword arguments.
~c[:]~ilc[GUARD]~nl[]
~c[Value] is a term involving only the formals of the function being
defined. The actual ~il[guard] used for the definition is the
conjunction of all the ~il[guard]s and types (~pl[declare]) ~il[declare]d.
~c[:GUARDHINTS]~nl[]
~c[Value]: hints (~pl[hints]), to be used during the ~il[guard]
verification proofs as opposed to the termination proofs of the
~ilc[defun].
~c[:]~ilc[HINTS]~nl[]
Value: hints (~pl[hints]), to be used during the termination
proofs as opposed to the ~il[guard] verification proofs of the ~ilc[defun].
~c[:MEASURE]~nl[]
~c[Value] is a term involving only the formals of the function being
defined. This term is indicates what is getting smaller in the
recursion. The wellfounded relation with which successive measures
are compared is ~ilc[o<]. Also allowed is a special case,
~c[(:? v1 ... vk)], where ~c[(v1 ... vk)] enumerates a subset of the
formal parameters such that some valid measure involves only those
formal parameters. However, this special case is only allowed for
definitions that are redundant (~pl[redundantevents]) or are
executed when skipping proofs (~pl[skipproofs]).
~c[:MODE]~nl[]
~c[Value] is ~c[:]~ilc[program] or ~c[:]~ilc[logic], indicating the ~ilc[defun] mode of the
function introduced. ~l[defunmode]. If unspecified, the
~ilc[defun] mode defaults to the default ~ilc[defun] mode of the current ~il[world].
To convert a function from ~c[:]~ilc[program] mode to ~c[:]~ilc[logic] mode,
~pl[verifytermination].
~c[:NONEXECUTABLE]~nl[]
~c[Value] is ~c[t] or ~c[nil] (the default). If ~c[t], the function has no
executable counterpart and is permitted to use singlethreaded object names
and functions arbitrarily, as in theorems rather than as in executable
definitions. Such functions are not permitted to declare any names to be
~c[:]~ilc[stobj]s but accessors, etc., may be used, just as in theorems.
Since the default is ~c[nil], the value supplied is only of interest when it
is ~c[t].
~c[:NORMALIZE]~nl[]
Value is a flag telling ~ilc[defun] whether to propagate ~ilc[if] tests
upward. Since the default is to do so, the value supplied is only of
interest when it is ~c[nil].
(~l[defun]).
~c[:]~ilc[OTFFLG]~nl[]
Value is a flag indicating ``onward through the fog''
(~pl[otfflg]).
~c[:STOBJS]~nl[]
~c[Value] is either a single ~ilc[stobj] name or a true list of stobj names.
Every stobj name among the formals of the function must be listed, if the
corresponding actual is to be treated as a stobj. That is, if a function
uses a stobj name as a formal parameter but the name is not declared among
the ~c[:stobjs] then the corresponding argument is treated as ordinary.
The only exception to this rule is ~ilc[state]: whether you include it
or not, ~c[state] is always treated as a singlethreaded object. This
declaration has two effects. One is to enforce the syntactic restrictions
on singlethreaded objects. The other is to strengthen the ~ilc[guard] of
the function being defined so that it includes conjuncts specifying that
each declared singlethreaded object argument satisfies the recognizer for
the corresponding singlethreaded object.
~c[:]~ilc[VERIFYGUARDS]~nl[]
~c[Value] is ~c[t] or ~c[nil], indicating whether or not ~il[guard]s are to be
verified upon completion of the termination proof. This flag should
only be ~c[t] if the ~c[:mode] is unspecified but the default ~ilc[defun] mode is
~c[:]~ilc[logic], or else the ~c[:mode] is ~c[:]~ilc[logic].
~c[:]~ilc[WELLFOUNDEDRELATION]~nl[]
~c[Value] is a function symbol that is known to be a wellfounded
relation in the sense that a rule of class ~c[:]~ilc[wellfoundedrelation]
has been proved about it. ~l[wellfoundedrelation].~/")
(defmacro linkdoctokeyword (name parent see)
`(defdoc ,name
,(concatenate
'string
":DocSection "
(symbolname parent)
"
"
(stringdowncase (symbolname see))
" keyword ~c[:" (symbolname name) "]~/
~l["
(stringdowncase (symbolname see))
"].~/~/")))
(defmacro linkdocto (name parent see)
`(defdoc ,name
,(concatenate
'string
":DocSection "
(symbolpackagename parent)
"::"
(symbolname parent)
"
~l["
(stringdowncase (symbolname see))
"].~/~/~/")))
(linkdoctokeyword guardhints miscellaneous xargs)
(linkdoctokeyword measure miscellaneous xargs)
(linkdoctokeyword mode miscellaneous xargs)
(linkdoctokeyword nonexecutable miscellaneous xargs)
(linkdoctokeyword normalize miscellaneous xargs)
(linkdoctokeyword stobjs miscellaneous xargs)
(linkdoctokeyword donotinduct miscellaneous hints)
(linkdoctokeyword donot miscellaneous hints)
(linkdoctokeyword expand miscellaneous hints)
(linkdoctokeyword restrict miscellaneous hints)
(linkdoctokeyword handsoff miscellaneous hints)
(linkdoctokeyword induct miscellaneous hints)
(linkdoctokeyword use miscellaneous hints)
(linkdoctokeyword cases miscellaneous hints)
(linkdoctokeyword by miscellaneous hints)
(linkdoctokeyword nonlinearp miscellaneous hints)
(linkdocto readbyte$ programming io)
(linkdocto openinputchannel programming io)
(linkdocto openinputchannelp programming io)
(linkdocto closeinputchannel programming io)
(linkdocto readchar$ programming io)
(linkdocto peekchar$ programming io)
(linkdocto readobject programming io)
(linkdocto openoutputchannel programming io)
(linkdocto openoutputchannelp programming io)
(linkdocto closeoutputchannel programming io)
(linkdocto writebyte$ programming io)
(linkdocto printobject$ programming io)
(linkdocto lambda miscellaneous term)
(linkdocto untranslate miscellaneous userdefinedfunctionstable)
(linkdocto setldskipproofsp other ldskipproofsp)
(linkdocto setldredefinitionaction other ldredefinitionaction)
#+:nonstandardanalysis
(defun buildvalidstdusageclause (arglist body)
(cond ((null arglist)
(list (mconsterm* 'standardnumberp body)))
(t (cons (mconsterm* 'not
(mconsterm* 'standardnumberp (car arglist)))
(buildvalidstdusageclause (cdr arglist) body)))))
#+:nonstandardanalysis
(defun verifyvalidstdusage (names arglists bodies hints otfflg
ttree0 ctx ens wrld state)
(cond
((null (cdr names))
(let* ((name (car names))
(arglist (car arglists))
(body (car bodies)))
(mvlet
(clset clsetttree)
(cleanupclauseset
(list (buildvalidstdusageclause arglist body))
ens
wrld ttree0 state)
(pprogn
(incrementtimer 'othertime state)
(let ((displayedgoal (prettyifyclauseset
clset
(let*abstractionp state)
wrld)))
(pprogn
(cond ((null clset)
(io? event nil state
(name)
(fms "~%The admission of ~x0 as a classical function ~
is trivial."
(list (cons #\0 name))
(proofsco state)
state
nil)))
(t
(io? event nil state
(displayedgoal name)
(fms "~%The admission of ~x0 as a classical function ~
with nonclassical body requires that it return ~
standard values for standard arguments. That ~
is, we must prove~%~%Goal~%~q1."
(list (cons #\0 name)
(cons #\1 displayedgoal))
(proofsco state)
state
nil))))
(incrementtimer 'printtime state)
(cond
((null clset)
(value clsetttree))
(t
(mvlet (erp ttree state)
(prove (termifyclauseset clset)
(makepspv ens
wrld
:displayedgoal displayedgoal
:otfflg otfflg)
hints ens wrld ctx state)
(cond (erp (mv t nil state))
(t
(pprogn
(io? event nil state
(name)
(fms "That completes the proof that ~x0 ~
returns standard values for standard ~
arguments."
(list (cons #\0 name))
(proofsco state)
state
nil))
(incrementtimer 'printtime state)
(value (constagtrees
clsetttree
ttree))))))))))))))
(t (er soft ctx
"It is not permitted to use MUTUALRECURSION to define nonstandard ~
predicates. Use MUTUALRECURSION to define standard versions of ~
these predicates, then use DEFUNSTD to generalize them, if that's ~
what you mean."))))
(defun defunsfn0
; WARNING: This function installs a world. That is safe at the time of this
; writing because this function is only called by defunsfn, where that call is
; protected by a revertworldonerror.
(names arglists docs pairs guards measures mp rel hints guardhints
stdhints
otfflg bodies symbolclass normalizeps nonexecutablep
#+:nonstandardanalysis stdp
ctx wrld state)
#:nonstandardanalysis
(declare (ignore stdhints))
(cond
((eq symbolclass :program)
(defunsfnshortcut names docs pairs guards bodies wrld state))
(t
(let ((ens (ens state))
(bigmutrec (bigmutrec names)))
(erlet*
((trip (putinductioninfo names arglists
measures
bodies
mp rel
hints
otfflg
bigmutrec
ctx ens wrld state)))
(let ((col (car trip)))
(erlet*
((wrld1 (updatew bigmutrec (cadr trip)))
(wrld2 (updatew bigmutrec
(putpropdefunrunicmappingpairs names t wrld1)))
(wrld3 (updatew bigmutrec
(putpropxlst2unless names 'guard guards *t*
wrld2)))
; There is no wrld4.
; Rockwell Addition: To save time, the nurewriter doesn't look at
; functions unless they contain nurewrite targets, as defined in
; rewrite.lisp. Here is where I store the property that says whether a
; function is a target.
(wrld5 (updatew
bigmutrec
(cond ((eq (car names) 'NTH)
(putprop 'nth 'nthupdaterewritertargetp
t wrld3))
((getprop (car names) 'recursivep nil
'currentacl2world wrld3)
; Nthupdaterewriter does not go into recursive functions. We could consider
; redoing this computation when installing a new definition rule, as well as
; the putprop below, but that's a heuristic decision that doesn't seem to be so
; important.
wrld3)
((nthupdaterewritertargetp (car bodies) wrld3)
; This precomputation of whether the body of the function is a
; potential target for nthupdaterewriter is insensitive to whether
; the functions being seen are disabled. If the function being
; defined calls a nonrecursive function that uses NTH, then this
; function is marked as being a target. If later that subroutine is
; disabled, then nthupdaterewriter will not go into it and this
; function may no longer really be a potential target. But if we do
; not ``memoize'' the computation this way then it may be
; exponentially slow, going repeatedly into large bodies called
; more than one time in a function.
(putprop (car names)
'nthupdaterewritertargetp
t wrld3))
(t wrld3))))
#+:nonstandardanalysis
(assumep
(value (or (eq (ldskipproofsp state) 'includebook)
(eq (ldskipproofsp state)
'includebookwithlocals))))
(ttree1 #+:nonstandardanalysis
(if (and stdp (not assumep))
(verifyvalidstdusage names arglists bodies
stdhints otfflg
(caddr trip)
ctx ens wrld state)
(value (caddr trip)))
#:nonstandardanalysis
(value (caddr trip))))
(mvlet
(wrld6 ttree2)
(putpropbodylst names arglists bodies normalizeps
(getprop (car names) 'recursivep nil
'currentacl2world wrld5)
(makecontrolleralist names wrld5)
#+:nonstandardanalysis stdp
ens wrld5 wrld5 nil)
(erprogn
(updatew bigmutrec wrld6)
(mvlet
(wrld7 ttree2 state)
(putproptypeprescriptionlst names
(fnrunenume (car names)
t nil wrld6)
ens wrld6 ttree2 state)
(erprogn
(updatew bigmutrec wrld7)
(erlet*
((wrld8 (updatew bigmutrec
(putproplevelnolst names wrld7)))
(wrld9 (updatew bigmutrec
(putpropprimitiverecursivedefunplst
names wrld8)))
(wrld10 (updatew bigmutrec
(updatedocdatabaselst names docs pairs
wrld9)))
(wrld11 (updatew bigmutrec
(putpropxlst1 names 'congruences nil wrld10)))
(wrld11a (updatew bigmutrec
(putpropxlst1 names 'coarsenings nil
wrld11)))
(wrld11b (updatew bigmutrec
(if nonexecutablep
(putpropxlst1 names 'nonexecutablep
t
wrld11a)
wrld11a))))
(let ((wrld12
#+:nonstandardanalysis
(if stdp
(putpropxlst1
names 'unnormalizedbody nil
(putpropxlst1 names 'defbodies nil wrld11b))
wrld11b)
#:nonstandardanalysis
wrld11b))
(pprogn
(printdefunmsg names ttree2 wrld12 col state)
(setw 'extension wrld12 state)
(cond
((eq symbolclass :commonlispcompliant)
(erlet*
((guardhints
(if guardhints
(value guardhints)
(let ((defaulthints (defaulthints wrld12)))
(if defaulthints ; then we haven't yet translated
(translatehints
(cons "Guard for" (car names))
defaulthints
ctx wrld12 state)
(value nil)))))
(pair (verifyguardsfn1 names guardhints otfflg
ctx state)))
; Pair is of the form (wrld . ttree3) and we return a pair of the same
; form, but we must combine this ttree with the ones produced by the
; termination proofs and typeprescriptions.
(value
(cons (car pair)
(constagtrees ttree1
(constagtrees
ttree2
(cdr pair)))))))
(t (value
(cons wrld12
(constagtrees ttree1
ttree2)))))))))))))))))))
(defun stripnonhiddenpackagenames (knownpackagealist)
(if (endp knownpackagealist)
nil
(let ((packageentry (car knownpackagealist)))
(cond ((packageentryhiddenp packageentry)
(stripnonhiddenpackagenames (cdr knownpackagealist)))
(t (cons (packageentryname packageentry)
(stripnonhiddenpackagenames (cdr knownpackagealist))))))))
(defun inpackagefn (str state)
; Important Note: Don't change the formals of this function without
; reading the *initialeventdefmacros* discussion in axioms.lisp.
(cond ((not (stringp str))
(er soft 'inpackage
"The argument to INPACKAGE must be a string, but ~
~x0 is not."
str))
((not (findnonhiddenpackageentry str (knownpackagealist state)))
(er soft 'inpackage
"The argument to INPACKAGE must be a known package ~
name, but ~x0 is not. The known packages are ~*1"
str
(tilde*&vstrings
'&
(stripnonhiddenpackagenames (knownpackagealist state))
#\.)))
(t (let ((state (fputglobal 'currentpackage str state)))
(value str)))))
(defun defstobjfunctionsp (names embeddedeventlst)
; This function determines whether all the names in names are being
; defined as part of a defstobj event. If so, it returns the
; name of the stobj; otherwise, nil.
; Explanation of the context: Defstobj uses defun to define the recognizers,
; accessors and updaters. But defstobj must install its own versions of the
; raw lisp code for these functions, to take advantage of the
; singlethreadedness of their use. So what happens when defstobj executes
; (defun name ...), where name is say an updater? Defunsfn is run on the
; singleton list '(name) and the axiomatic def of name. At the end of the
; normal processing, defunsfn computes a CLTLCOMMAND for name. When this
; command is installed by addtrip, it sets the symbolfunction of name to the
; given body. Addtrip also installs a *1*name definition by oneifying the
; given body. But in the case of a defstobj function we do not want the first
; thing to happen: defstobj will compute a special body for the name and
; install it with its own CLTLCOMMAND. So to handle defstobj, defunsfn tells
; addtrip not to set the symbolfunction. This is done by setting the ignorep
; flag in the defun CLTLCOMMAND. So the question arises: how does defun know
; that the name it is defining is being introduced by defstobj? This function
; answers that question.
; Note that *1*name should still be defined as the oneified axiomatic body, as
; with any defun. Before v29 we introduced the *1* function at defun time.
; (We still do so if the function is being reclassified with an identical body,
; from :program mode to :logic mode, since there is no need to redefine its
; symbolfunction   indeed its installed symbolfunction might be
; handcoded as part of these sources  but addtrip must generate a *1*
; body.) Because stobj functions can be inlined as macros (via the :inline
; keyword of defstobj), we need to defer definition of the *1* function until
; after the raw Lisp def (which may be a macro) has been added. We failed to
; do this in v28, which caused an error in openMCL as reported by John
; Matthews:
; (defstobj tinystate
; (progc :type (unsignedbyte 10) :initially 0)
; :inline t)
;
; (updateprogc 3 tinystate)
; Note: At the moment, defstobj does not introduce any mutually
; recursive functions. So every name is handled separately by
; defunsfns. Hence, names, here, is always a singleton, though we do
; not exploit that. Also, embeddedeventlst is always a list
; eeentries, each being a cons with the name of some superevent like
; ENCAPSULATE, INCLUDEBOOK, or DEFSTOBJ, in the car. The eeentry
; for the most immediate superevent is the first on the list. At the
; moment, defstobj does not use encapsulate or other structuring
; mechanisms. Thus, the defstobj eeentry will be first on the list.
; But we look up the list, just in case. The eeentry for a defstobj
; is of the form (defstobj name names) where name is the name of the
; stobj and names is the list of recognizers, accessors and updaters
; and their helpers.
(let ((temp (assoceq 'defstobj embeddedeventlst)))
(cond ((and temp
(subsetpequal names (caddr temp)))
(cadr temp))
(t nil))))
; The following definition only supports nonstandard analysis, but it seems
; reasonable to allow it in the standard version too.
; #+:nonstandardanalysis
(defun indexofnonnumber (lst)
(cond
((endp lst) nil)
((acl2numberp (car lst))
(let ((temp (indexofnonnumber (cdr lst))))
(and temp (1+ temp))))
(t 0)))
#+:nonstandardanalysis
(defun nonstderror (fn index formals actuals)
(er hard fn
"Function ~x0 was called with the ~n1 formal parameter, ~x2, bound to ~
actual parameter ~x3, which is not a (standard) number. This is illegal, ~
because the arguments of a function defined with defunstd must all be ~
(standard) numbers."
fn (list index) (nth index formals) (nth index actuals)))
#+:nonstandardanalysis
(defun nonstdbody (name formals body)
; The body below is a bit inefficient in the case that we get an error.
; However, we do not expect to get errors very often, and the alternative is to
; bind a variable that we have to check is not in formals.
`(if (indexofnonnumber (list ,@formals))
(nonstderror ',name
(indexofnonnumber ',formals)
',formals
(list ,@formals))
,body))
#+:nonstandardanalysis
(defun nonstddeflst (deflst)
(if (and (consp deflst) (null (cdr deflst)))
(let* ((def (car deflst))
(fn (car def))
(formals (cadr def))
(body (car (last def))))
`((,@(butlast def 1)
,(nonstdbody fn formals body))))
(er hard 'nonstddeflst
"Unexpected call; please contact ACL2 implementors.")))
; Rockwell Addition: To support nonexecutable fns we have to be able,
; at defun time, to introduce an undefined function. So this stuff is
; moved up from otherevents.lisp.
(defun makeudfinsigs (names wrld)
(cond
((endp names) nil)
(t (cons (list (car names)
(formals (car names) wrld)
(stobjsin (car names) wrld)
(stobjsout (car names) wrld))
(makeudfinsigs (cdr names) wrld)))))
(defun introudf (insig wrld)
(casematch
insig
((fn formals stobjsin stobjsout)
(putprop
fn 'coarsenings nil
(putprop
fn 'congruences nil
(putprop
fn 'constrainedp t
; We could do a (putpropunless fn 'guard *t* *t* &) here but it would
; be silly.
; We could do a (putpropunless fn 'constraintlst nil nil &) here but
; it would be silly. The corresponding putprop isn't necessary
; either; we will put all the constraintlst properties with
; putpropconstraints.
(putprop
fn 'symbolclass :commonlispcompliant
(putpropunless
fn 'stobjsout stobjsout nil
(putpropunless
fn 'stobjsin stobjsin nil
(putprop
fn 'formals formals wrld))))))))
(& (er hard 'storesignature "Unrecognized signature!" insig))))
(defun introudflst1 (insigs wrld)
(cond ((null insigs) wrld)
(t (introudflst1 (cdr insigs)
(introudf (car insigs) wrld)))))
(defun introudflst2 (insigs)
; Insigs is a list of internal form signatures, e.g., ((fn1 formals1
; stobjsin1 stobjsout1) ...), and we convert it to a "deflst"
; suitable for giving the Common Lisp version of defuns, ((fn1
; formals1 body1) ...), where each bodyi is just a throw to
; 'rawevfncall with the signal that says there is no body. Note
; that the body we build (in this ACL2 code) is a Common Lisp body but
; not an ACL2 expression!
(cond
((null insigs) nil)
(t (cons `(,(caar insigs)
,(cadar insigs)
(declare (ignore ,@(cadar insigs)))
(throwrawevfncall '(evfncallnullbodyer ,(caar insigs))))
(introudflst2 (cdr insigs))))))
(defun introudflst (insigs wrld)
; Insigs is a list of internal form signatures. We know all the
; function symbols are new in wrld. We declare each of them to have
; the given formals, stobjsin, and stobjsout, symbolclass
; :commonlispcompliant, a guard of t and constrainedp of t. We also
; arrange to execute a defun in the underlying Common Lisp so that
; each function is defined to throw to an error handler if called from
; ACL2.
(if (null insigs)
wrld
(globalset 'cltlcommand
`(defuns nil nil ,@(introudflst2 insigs))
(introudflst1 insigs wrld))))
(defun defunsfn (deflst state eventform #+:nonstandardanalysis stdp)
; Important Note: Don't change the formals of this function without
; reading the *initialeventdefmacros* discussion in axioms.lisp.
; On Guards
; When a function symbol fn is defund the user supplies a guard, g, and a
; body b. Logically speaking, the axiom introduced for fn is
; (fn x1...xn) = b.
; After admitting fn, the guardrelated properties are set as follows:
; prop after defun
; body b*
; guard g
; unnormalizedbody b
; typeprescription computed from b
; symbolclass :ideal
; * We actually normalize the above. During normalization we may expand some
; bootstrap nonrec fns.
; In addition, we magically set the symbolfunction of fn
; symbolfunction b
; and the symbolfunction of *1*fn as a program which computes the logical
; value of (fn x). However, *1*fn is quite fancy because it uses the raw body
; in the symbolfunction of fn if fn is :commonlispcompliant, and may signal
; a guard error if 'guardcheckingon is set to other than nil or :none. See
; oneifycltlcode for the details.
; Observe that the symbolfunction after defun may be a form that
; violates the guards on primitives. Until the guards in fn are
; checked, we cannot let raw Common Lisp evaluate fn.
; Intuitively, we think of the Common Lisp programmer intending to defun (fn
; x1...xn) to be b, and is declaring that the raw fn can be called only on
; arguments satisfying g. The need for guards stems from the fact that there
; are many Common Lisp primitives, such as car and cdr and + and *, whose
; behavior outside of their guarded domains is unspecified. To use these
; functions in the body of fn one must "guard" fn so that it is never called in
; a way that would lead to the violation of the primitive guards. Thus, we
; make a formal precondition on the use of the Common Lisp program fn that the
; guard g, along with the tests along the various paths through body b, imply
; each of the guards for every subroutine in b. We also require that each of
; the guards in g be satisfied. This is what we mean when we say fn is
; :commonlispcompliant.
; It is, however, often impossible to check the guards at defun time. For
; example, if fn calls itself recursively and then gives the result to +, we
; would have to prove that the guard on + is satisfied by fn's recursive
; result, before we admit fn. In general, induction may be necessary to
; establish that the recursive calls satisfy the guards of their masters;
; hence, it is probably also necessary for the user to formulate general lemmas
; about fn to establish those conditions. Furthermore, guard checking is no
; longer logically necessary and hence automatically doing it at defun time may
; be a waste of time.
(withctxsummarized
(if (outputininfixp state)
eventform
(cond ((atom deflst)
(msg "( DEFUNS ~x0)"
deflst))
((atom (car deflst))
(cons 'defuns (car deflst)))
((null (cdr deflst))
#+:nonstandardanalysis
(if stdp
(cons 'defunstd (caar deflst))
(cons 'defun (caar deflst)))
#:nonstandardanalysis
(cons 'defun (caar deflst)))
(t (msg *mutualrecursionctxstring*
(caar deflst)))))
(let ((wrld (w state))
(deflst0
#+:nonstandardanalysis
(if stdp
(nonstddeflst deflst)
deflst)
#:nonstandardanalysis
deflst)
(eventform (or eventform (list 'defuns deflst))))
(revertworldonerror
(erlet*
((tuple (chkacceptabledefuns deflst ctx wrld state
#+:nonstandardanalysis stdp)))
; chkacceptabledefuns puts the 'formals, 'stobjsin and 'stobjsout
; properties (which are necessary for the translation of the bodies).
; All other properties are put by the defunsfn0 call below.
(cond
((eq tuple 'redundant)
(stopredundantevent state))
(t
(enforceredundancy
eventform ctx wrld
(let ((names (nth 1 tuple))
(arglists (nth 2 tuple))
(docs (nth 3 tuple))
(pairs (nth 4 tuple))
(guards (nth 5 tuple))
(measures (nth 6 tuple))
(mp (nth 7 tuple))
(rel (nth 8 tuple))
(hints (nth 9 tuple))
(guardhints (nth 10 tuple))
(stdhints (nth 11 tuple))
(otfflg (nth 12 tuple))
(bodies (nth 13 tuple))
(symbolclass (nth 14 tuple))
(normalizeps (nth 15 tuple))
(reclassifyingp (nth 16 tuple))
(wrld (nth 17 tuple))
(nonexecutablep (nth 18 tuple)))
(erlet*
((pair (defunsfn0
names
arglists
docs
pairs
guards
measures
mp
rel
hints
guardhints
stdhints
otfflg
bodies
symbolclass
normalizeps
nonexecutablep
#+:nonstandardanalysis stdp
ctx
wrld
state)))
; Pair is of the form (wrld . ttree).
(erprogn
(chkassumptionfreettree (cdr pair) ctx state)
(installevent (cond ((null (cdr names)) (car names))
(t names))
eventform
(cond ((null (cdr names)) 'defun)
(t 'defuns))
(cond ((null (cdr names)) (car names))
(t names))
(cdr pair)
(cond
(nonexecutablep
`(defuns nil nil
,@(introudflst2
(makeudfinsigs names wrld))))
(t `(defuns ,(if (eq symbolclass :program)
:program
:logic)
,(if reclassifyingp
'reclassifying
(if (defstobjfunctionsp names
(globalval 'embeddedeventlst
(car pair)))
(cons 'defstobj
; The following expression computes the stobj name, e.g., $S, for
; which this defun is supportive. The STOBJSIN of this function is
; built into the expression created by oneifycltlcode
; namely, in the throwrawevfncall expression (see
; oneifyfailform). We cannot compute the STOBJSIN of the function
; accurately from the world because $S is not yet known to be a stobj!
; This problem is a version of the superdefunwart problem.
(defstobjfunctionsp names
(globalval
'embeddedeventlst
(car pair))))
nil))
,@deflst0)))
t
ctx
(car pair)
state))))))))))))
(defun defunfn (def state eventform #+:nonstandardanalysis stdp)
; Important Note: Don't change the formals of this function without
; reading the *initialeventdefmacros* discussion in axioms.lisp.
; The only reason this function exists is so that the defmacro for
; defun is in the form expected by primordialeventdefmacros.
(defunsfn (list def) state
(or eventform (cons 'defun def))
#+:nonstandardanalysis stdp))
; Here we develop the :args keyword command that will print all that
; we know about a function.
(defun argsfn (name state)
(io? temporary nil (mv erp val state)
(name)
(let ((wrld (w state))
(channel (standardco state)))
(cond
((and (symbolp name)
(functionsymbolp name wrld))
(let* ((formals (formals name wrld))
(stobjsin (stobjsin name wrld))
(stobjsout (stobjsout name wrld))
(docp (accessdocstringdatabase name state))
(guard (untranslate (guard name nil wrld) t wrld))
(tp (findrunedtypeprescription
(list :typeprescription name)
(getprop name 'typeprescriptions nil
'currentacl2world wrld)))
(tpthm (cond (tp (untranslate
(access typeprescription tp :corollary)
t wrld))
(t nil)))
(constraint (mvlet (somename constraintlst)
(constraintinfo name wrld)
(if somename
(untranslate (conjoin constraintlst)
t wrld)
t))))
(pprogn
(fms "Function ~x0~~
Formals: ~y1~~
Signature: ~y2~~
~ => ~y3~~
Guard: ~q4~~
Guards Verified: ~y5~~
DefunMode: ~@6~~
Type: ~#7~[builtin (or unrestricted)~/~q8~]~~
~#9~[~/Constraint: ~qa~~]~
~#d~[~/Documentation available via :DOC~]~%"
(list (cons #\0 name)
(cons #\1 formals)
(cons #\2 (cons name
(prettyifystobjflags stobjsin)))
(cons #\3 (prettyifystobjsout stobjsout))
(cons #\4 guard)
(cons #\5 (eq (symbolclass name wrld)
:commonlispcompliant))
(cons #\6 (defunmodestring (fdefunmode name wrld)))
(cons #\7 (if tpthm 1 0))
(cons #\8 tpthm)
(cons #\9 (if (eq constraint t) 0 1))
(cons #\a constraint)
(cons #\d (if docp 1 0)))
channel state nil)
(value name))))
((and (symbolp name)
(getprop name 'macrobody nil 'currentacl2world wrld))
(let ((args (macroargs name wrld))
(docp (accessdocstringdatabase name state))
(guard (untranslate (guard name nil wrld) t wrld)))
(pprogn
(fms "Macro ~x0~~
Macro Args: ~y1~~
Guard: ~q2~~
~#3~[~/Documentation available via :DOC~]~%"
(list (cons #\0 name)
(cons #\1 args)
(cons #\2 guard)
(cons #\3 (if docp 1 0)))
channel state nil)
(value name))))
((membereq name '(let lambda declare quote))
(pprogn (fms "Special form, basic to the Common Lisp language. ~
See for example CLtL."
nil channel state nil)
(value name)))
(t (er soft :args
"~x0 is neither a function symbol nor a macro name."
name))))))
(defmacro args (name)
":DocSection Documentation
~c[args], ~ilc[guard], ~c[type], ~ilc[constraint], etc., of a function symbol~/
~bv[]
Example:
:args assoceq
~ev[]~/
~c[Args] takes one argument, a symbol which must be the name of a
function or macro, and prints out the formal parameters, the ~il[guard]
expression, the output ~il[signature], the deduced type, the ~il[constraint]
(if any), and whether ~il[documentation] about the symbol is available
via ~c[:]~ilc[doc].~/"
(list 'argsfn name 'state))
; We now develop the code for verifytermination, a macro that is essentially
; a form of defun.
(defun makeverifyterminationdef (olddef newdcls state)
; Olddef is a def tuple that has previously been accepted by defuns. For
; example, if is of the form (fn args ...dcls... body), where dcls is a list of
; at most one doc string and possibly many DECLARE forms. Newdcls is a new
; list of dcls (known to satisfy plausibledclsp). We create a new def tuple
; that uses newdcls instead of ...dcls... but which keeps any member of the
; old dcls not specified by the newdcls except for the :mode (if any), which
; is replaced by :mode :logic.
(let* ((fn (car olddef))
(args (cadr olddef))
(body (car (last (cddr olddef))))
(dcls (butlast (cddr olddef) 1))
(newfields (dclfields newdcls))
(modifiedolddcls (stripdcls
(addtoseteq :mode newfields)
dcls)))
`(,fn ,args
,@newdcls
,@(if (and (not (membereq :mode newfields))
(eq (defaultdefunmode (w state)) :program))
'((declare (xargs :mode :logic)))
nil)
,@modifiedolddcls
,body)))
(defun makeverifyterminationdefslst (defslst lst state)
; Defslst is a list of def tuples as previously accepted by defuns. Lst is
; a list of tuples supplied to verifytermination. Each element of a list is
; of the form (fn . dcls) where dcls satisfies plausibledclsp, i.e., is a list
; of doc strings and/or DECLARE forms. We copy defslst, modifying each member
; by merging in the dcls specified for the fn in lst. If some fn in defslst
; is not mentioned in lst, we don't modify its def tuple except to declare it
; of :mode :logic.
(cond
((null defslst) nil)
(t (let ((temp (assoceq (caar defslst) lst)))
(cons (makeverifyterminationdef (car defslst) (cdr temp) state)
(makeverifyterminationdefslst (cdr defslst) lst state))))))
(defun chkacceptableverifytermination1 (lst clique fn1 ctx wrld state)
; Lst is the input to verifytermination. Clique is a list of function
; symbols, fn1 is a member of clique (and used for error reporting only). Lst
; is putatively of the form ((fn . dcls) ...) where each fn is a member of
; clique and each dcls is a plausibledclsp, as above. That means that each
; dcls is a list containing documentation strings and DECLARE forms mentioning
; only TYPE, IGNORE, and XARGS. We do not check that the dcls are actually
; legal because what we will ultimately do with them in verifyterminationfn
; is just create a modified definition to submit to defuns. Thus, defuns will
; ultimately approve the dcls. By construction, the dcls submitted to
; verifytermination will find their way, whole, into the submitted defuns. We
; return nil or cause an error according to whether lst satisfies the
; restrictions noted above.
(cond ((null lst) (value nil))
((not (and (consp (car lst))
(symbolp (caar lst))
(functionsymbolp (caar lst) wrld)
(plausibledclsp (cdar lst))))
(er soft ctx
"Each argument to verifytermination must be of the form (name ~
dcl ... dcl), where each dcl is either a DECLARE form or a ~
documentation string. The DECLARE forms may contain TYPE, ~
IGNORE, and XARGS entries, where the legal XARGS keys are ~
:GUARD, :MEASURE, :WELLFOUNDEDRELATION, HINTS, :GUARDHINTS, ~
:MODE, :VERIFYGUARDS and :OTFFLG. The argument ~x0 is ~
illegal. See :DOC verifytermination."
(car lst)))
((not (membereq (caar lst) clique))
(er soft ctx
"The functions symbols whose termination is to be verified must ~
all be members of the same clique of mutually recursive ~
functions. ~x0 is not in the clique of ~x1. The clique of ~x1 ~
consists of ~&2. See :DOC verifytermination."
(caar lst) fn1 clique))
(t (chkacceptableverifytermination1 (cdr lst) clique fn1 ctx wrld state))))
(defun uniformdefunmodes (defunmode clique wrld)
; DefunMode should be a defunmode. Clique is a list of fns. If defunmode is
; :program then we return :program if every element of clique is
; :program; else nil. If defunmode is :logic we return :logic if
; every element of clique is :logic; else nil.
(cond ((null clique) defunmode)
((programp (car clique) wrld)
(and (eq defunmode :program)
(uniformdefunmodes defunmode (cdr clique) wrld)))
(t (and (eq defunmode :logic)
(uniformdefunmodes defunmode (cdr clique) wrld)))))
(defun recoverdefslst (fn wrld state)
; Fn is a :program function symbol in wrld. Thus, it was introduced by defun.
; (Constrained and :nonexecutable functions are :logic.) We return the
; defslst that introduced it fn. We recover this from the cltlcommand for
; fn.
(let ((val
(scantocltlcommand
(cdr (lookupworldindex 'event
(getprop fn 'absoluteeventnumber
'(:error "See ~
RECOVERDEFSLST.")
'currentacl2world wrld)
wrld)))))
(cond ((and (consp val)
(eq (car val) 'defuns))
; Val is of the form (defuns defunmodeflg ignorep def1 ... defn). If
; defunmodeflg is nonnil then the parent event was (defuns def1 ... defn)
; and the defunmode was defunmodeflg. If defunmodeflg is nil, the parent
; was an encapsulate or :nonexecutable. In the former case we return (def1
; ... defn); in the latter we return nil.
(cond ((cadr val) (value (cdddr val)))
(t (value nil))))
(t (value
(er hard 'recoverdefslst
"We failed to find the expected CLTLCOMMAND for the ~
introduction of ~x0."
fn))))))
(defun getclique (fn wrld state)
; Fn must be a function symbol. We return the list of mutually recursive fns
; in the clique containing fn, according to their original definitions. If fn
; is :program we have to look for the cltlcommand and recover the clique from
; the defslst. Otherwise, we can use the 'recursivep property.
(cond ((programp fn wrld)
(erlet* ((defs (recoverdefslst fn wrld state)))
(value (stripcars defs))))
(t (let ((recp (getprop fn 'recursivep nil
'currentacl2world wrld)))
(value (cond ((null recp) (list fn))
(t recp)))))))
(defun chkacceptableverifytermination (lst ctx wrld state)
; We check that lst is acceptable input for verifytermination. To be
; acceptable, lst must be of the form ((fn . dcls) ...) where each fn is the
; name of a function, all of which are in the same clique and have the same
; defunmode and each dcls is a plausibledclsp as above. We cause an error or
; return nil
(cond
((and (consp lst)
(consp (car lst))
(symbolp (caar lst)))
(cond
((functionsymbolp (caar lst) wrld)
(erlet* ((clique (getclique (caar lst) wrld state)))
(cond
((not (uniformdefunmodes (fdefunmode (caar lst) wrld)
clique
wrld))
(er soft ctx
"The function ~x0 is ~#1~[:program~/:logic~] but some ~
member of its clique of mutually recursive peers is not. The ~
clique consists of ~&2. Since verifytermination must deal ~
with the entire clique, in the sense that it will either admit ~
into the logic all of the functions in the clique (in which ~
case the clique must be uniformly :program) or none of the ~
functions in the clique (in which case the clique must be ~
uniformly :logic, making verifytermination redundant). ~
The clique containing ~x0 is neither. This can only happen ~
because some members of the clique have been redefined."
(caar lst)
(if (programp (caar lst) wrld) 0 1)
clique))
(t (chkacceptableverifytermination1 lst clique (caar lst) ctx wrld state)))))
(t (er soft ctx
"The symbol ~x0 is not a function symbol in the current ACL2 world."
(caar lst)))))
((atom lst)
(er soft ctx
"Verifytermination requires at least one argument."))
(t (er soft ctx
"The first argument supplied to verifytermination, ~x0, is not of ~
the form (fn dcl ...)."
(car lst)))))
(defun verifyterminationfn (lst state eventform #+:nonstandardanalysis stdp)
(whenlogic
; It is convenient to use whenlogic so that we skip verifytermination during
; pass1 of the bootstrap in axioms.lisp.
"VERIFYTERMINATION"
(let* ((lst (cond ((and (consp lst)
(symbolp (car lst)))
(list lst))
(t lst)))
(ctx
(cond ((null lst) "(VERIFYTERMINATION)")
((and (consp lst)
(consp (car lst)))
(cond
((null (cdr lst))
(cond
((symbolp (caar lst))
(cond
((null (cdr (car lst)))
(msg "( VERIFYTERMINATION ~x0)" (caar lst)))
(t (msg "( VERIFYTERMINATION ~x0 ...)" (caar lst)))))
((null (cdr (car lst)))
(msg "( VERIFYTERMINATION (~x0))" (caar lst)))
(t (msg "( VERIFYTERMINATION (~x0 ...))" (caar lst)))))
((null (cdr (car lst)))
(msg "( VERIFYTERMINATION (~x0) ...)" (caar lst)))
(t (msg "( VERIFYTERMINATION (~x0 ...) ...)" (caar lst)))))
(t (cons 'VERIFYTERMINATION lst))))
(wrld (w state))
(eventform (or eventform
(cons 'VERIFYTERMINATION lst))))
(erprogn
(chkacceptableverifytermination lst ctx wrld state)
(erlet*
((defslst (recoverdefslst (caar lst) wrld state)))
(defunsfn
(makeverifyterminationdefslst defslst lst state)
state
eventform
#+:nonstandardanalysis stdp))))))
; When we defined instantiablep we included the comment that a certain
; invariant holds between it and the axioms. The functions here are
; not used in the system but can be used to check that invariant.
; They were not defined earlier because they use event tuples.
(defun fnsusedinaxioms (lst wrld ans)
; Intended for use only by checkoutinstantiablep.
(cond ((null lst) ans)
((and (eq (caar lst) 'eventlandmark)
(eq (cadar lst) 'globalvalue)
(eq (accesseventtupletype (cddar lst)) 'defaxiom))
; In this case, (car lst) is a tuple of the form
; (eventlandmark globalvalue . tuple)
; where tuple is a defaxiom of some name, namex, and we are interested
; in all the function symbols occurring in the formula named namex.
(fnsusedinaxioms (cdr lst)
wrld
(allffnsymbs (formula
(accesseventtuplenamex
(cddar lst))
nil
wrld)
ans)))
(t (fnsusedinaxioms (cdr lst) wrld ans))))
(defun checkoutinstantiablep1 (fns wrld)
; Intended for use only by checkoutinstantiablep.
(cond ((null fns) nil)
((instantiablep (car fns) wrld)
(cons (car fns) (checkoutinstantiablep1 (cdr fns) wrld)))
(t (checkoutinstantiablep1 (cdr fns) wrld))))
(defun checkoutinstantiablep (wrld)
; See the comment in instantiablep.
(let ((bad (checkoutinstantiablep1 (fnsusedinaxioms wrld wrld nil)
wrld)))
(cond
((null bad) "Everything checks")
(t (er hard 'checkoutinstantiablep
"The following functions are instantiable and shouldn't be:~%~x0"
bad)))))
