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|
; (ld '((include-book "defsys-utilities") . "defsys.lisp") :ld-pre-eval-print t)
; (include-book "defsys-utilities")
; (certify-book "defsys" 1)
; Defsys -- a Verifying Mini-Compiler for M1
; J Strother Moore
; March, 2012
; This file provides the defsys utility. It takes a list of ``modules,''
; compiles them into M1 code, defines the appropriate clocks and semantic
; functions, and proves that the code is correct. Here is an example that
; illustrates what a ``module'' is and how the code is described in a
; high-level source language akin to ACL2 except using IFEQ.
; Every system is configured so that when starting from 0 it calls the MAIN
; module using the arguments on the stack. It then halts. Note that a module
; may return multiple values (see MOD2-FLOOR2) and note how that module is
; called in the :code for MAIN: It is passed to RECOMBINE which treats
; MOD2-FLOOR2 as having supplied 2 of its arguments. (RECOMBINE needs 3 args
; but is given 2 actual expressions in MAIN.)
; Defsys also supports ``ghost variables.'' These are variables need to insure
; termination of the corresponding ACL2 functions. The provisions for ghost
; variables are very hackish, designed with one example in mind: the situation
; when the top level routine in a system doesn't always terminate and MAIN
; calls it. Ghost variables allow the additional keywords :ghost-formals,
; :ghost-base-test, :ghost-base-value and :ghost-decr. These are,
; respectively, a list of variables, a test leading to forced termination, the
; result in the case of forced termination, and a list of ``decrement''
; expressions to be appended to every recursive call of fn. We assume that
; (nth 0 ghost-base-value) is 0 when forced termination occurs.
; Basically a function like
; (defun fn (vars)
; body)
; with those additional keyword specifiers becomes:
; (defun fn (vars ,@ghost-formals)
; (if ,ghost-base-test
; ,ghost-base-value
; body'))
; where body' is body with all calls of fn given the additional final arguments
; listed in ghost-decr. For a relatively simple example of a use of ghost
; variables, see low-seven.lisp.
#|
(defsys t
(mod2-floor2 :formals (x a)
:input (and (natp x) (natp a))
:output (mv (mod x 2) (+ a (floor x 2)))
:code (ifeq x (mv 0 a) (ifeq (- x 1) (mv 1 a) (mod2-floor2 (- x 2) (+ a 1))))
:post-events nil)
(recombine :formals (m q y)
:input (and (natp m)(natp q)(natp y))
:output (+ m (* y q))
:code (+ m (* y q)))
(lessp :formals (x y)
:input (and (natp x)
(natp y))
:output (if (< x y) 1 0)
:code (ifeq y
0
(ifeq x
1
(lessp (- x 1) (- y 1)))))
(mod :formals (x y)
:input (and (natp x)
(natp y)
(not (equal y 0)))
:output (mod x y)
:code (ifeq (lessp x y)
(mod (- x y) y)
x))
(floor :formals (x y a)
:input (and (natp x)
(natp y)
(not (equal y 0))
(natp a))
:output (+ a (floor x y))
:code (ifeq (lessp x y)
(floor (- x y) y (+ a 1))
a))
(main :formals (x y a)
:input (and (natp x)
(natp y)
(not (equal y 0))
(natp a))
:output (+ (* 10000 (+ (mod x y) (* y (floor x y)))) a)
:code (+ (* 10000 (+ (mod x y) (* y (floor x y 0))))
(recombine (mod2-floor2 a 0) 2))))
(acl2::pe 'm1-psi)
(defthm m1-psi-thm
(implies (and (natp x)
(natp y)
(not (equal y 0))
(natp a))
(let ((sf (m1-psi x y a)))
(and (equal (next-inst sf) '(HALT))
(equal (top (stack sf)) (+ (* 10000 x) a))))))
(clk+ 2 (main-clock nil 231 7 456))
(next-inst (m1-psi 231 7 456))
; = (HALT)
(top (stack (m1-psi 231 7 456)))
; = 2310456
QED!
|#
(in-package "M1")
(acl2::program)
; -----------------------------------------------------------------
(defun pack (lst)
(declare (xargs :mode :program))
(intern-in-package-of-symbol
(coerce (acl2::packn1 lst)
'string)
'm1))
; (defmacro trace$ (&rest args) `(acl2::trace$ ,@args))
; (defmacro untrace$ (&rest args) `(acl2::untrace$ ,@args))
; -----------------------------------------------------------------
(acl2::set-irrelevant-formals-ok t)
(defun rev1 (x a)
(if (endp x)
a
(rev1 (cdr x) (cons (car x) a))))
(defun all-but-last (x)
(declare (xargs :mode :logic))
(if (endp x)
nil
(if (endp (cdr x))
nil
(cons (car x) (all-but-last (cdr x))))))
(defun nv (fn var vars)
(let ((temp (member-equal var vars)))
(cond (temp
; if a-reg were not 0, we'd have to add it to this number:
(- (len vars) (len temp)))
(t (er hard 'defsys
"While compiling ~x0 we encountered an undeclared variable ~
~x1. The locals of ~x0 are ~x2."
fn var vars)))))
; When we ILOAD a series of regs, we go from base up. When we ISTORE a
; series of regs, we go down to base.
(defun ILOAD-series (base n)
; (ILOAD-series 7 2) ==> ((ILOAD 7) (ILOAD 8))
(cond ((zp n) nil)
(t (cons `(ILOAD ,base)
(ILOAD-series (+ 1 base) (- n 1))))))
(defun ISTORE-series (base n)
(cond ((zp n) nil)
(t (cons `(ISTORE ,(+ base n -1))
(ISTORE-series base (- n 1))))))
(defun save-regs (n max-a-regs)
`((ISTORE ,(* 2 max-a-regs))
,@(ISTORE-series max-a-regs n)
,@(ILOAD-series 0 n)
(ILOAD ,(* 2 max-a-regs))
,@(ILOAD-series max-a-regs n)
,@(ISTORE-series 0 n)))
; Let mvn below be the ;output-arity of the module. We save the mvn results
; temporarily into the B regs while we restore the pushed A regs. We know that
; at the end of this the ret pc is in the return pc register 2max-a-regs.
(defun restore-regs (mvn n max-a-regs)
`(,@(ISTORE-series max-a-regs mvn)
(ISTORE ,(* 2 max-a-regs))
,@(ISTORE-series 0 n)
,@(ILOAD-series max-a-regs mvn)))
(defun icount (acode)
; Given a segment of acode generated by compiler-expr count how many
; instructions will be in it after it is assembled and linked. We know the
; compiler does not lay down labels and it doesn't generate RETs. So the only
; pseudo-instructions in acode are CALLs.
(cond ((endp acode) 0)
((and (consp (car acode))
(eq (op-code (car acode)) 'CALL))
(+ 2 (icount (cdr acode))))
((and (consp (car acode))
(member (op-code (car acode))
'(iload istore iconst iadd isub imul ifeq goto call)))
(+ (if (eq (op-code (car acode)) 'CALL)
2
1)
(icount (cdr acode))))
(t
(er hard 'icount
"Acode encountered an illegal instruction, label, or pseudo-instruction, ~x0."
(car acode)))))
; We are about to implement a compiler from simple recursive functions to M1.
; We will then implement a clock compiler to produce the corresponding
; clock function. To implement the clock compiler we must know the
; return pc to which which each CALL returns. That return pc affects the
; clock for the CALL since the amount of time taken in the RET from that
; call is a function of that return pc.
; But the clock compiler is not looking at the compiled code where the CALL
; really is. It is looking at the high level language expression that was
; compiled. So how can the clock compiler determine the return pc for each
; call? We solve this problem by ``annotating'' the input definitions before
; we begin compiling. The annotation changes every function call (fn a1
; ... an) into (fn id a1' ... an'), where id is a unique object associated with
; this occurrence of this expression and the ai' are the recursively annotated
; subexpressions.
; The compiler generates annotated call statements, (CALL FOO id).
; Add-return-labels, the function that adds return pc labels after each CALL,
; builds a table associating the ids with the labels generated. The linker
; then builds a table associating labels with pcs. So when the clock
; compiler crawls over the annotated expressions to create the clocks it can
; look at the id of the expression, get the corresponding label, and then the
; corresponding return pc.
(mutual-recursion
(defun annotate-expr (x id)
(cond ((atom x) x)
((eq (car x) 'quote) x)
(t (cons (car x) (cons id (annotate-expr-lst (cdr x) 0 id))))))
(defun annotate-expr-lst (x i id)
(cond ((endp x) nil)
(t (cons (annotate-expr (car x) (cons i id))
(annotate-expr-lst (cdr x) (+ i 1) id))))))
(mutual-recursion
(defun strip-annotations-expr (x)
(cond ((atom x) x)
((eq (car x) 'quote) x)
(t (cons (car x) (strip-annotations-expr-lst (cdr (cdr x)))))))
(defun strip-annotations-expr-lst (x)
(cond ((endp x) nil)
(t (cons (strip-annotations-expr (car x))
(strip-annotations-expr-lst (cdr x)))))))
; We handle tail recursive functions only. We can properly compile full-blown
; recursions and also properly compile ``sometimes tail-recursive'' functions
; (which, like mc-flatten, contain both full-blown recursion and
; tail-recursion). But our clock compiler and the basic proof strategy do
; not work for such functions.
(mutual-recursion
(defun recursions-okp (mode fn expr)
; We support two modes, :tail and :none. The former checks that the only
; recursions in expr are tail-recursive. The latter checks that there are no
; recursions in expr.
(cond ((atom expr) t)
((eq (car expr) 'quote) t)
((eq (car expr) 'IF)
(er hard 'compile-expr
"The compiler does not support IF. Use IFEQ."))
((eq (car expr) 'IFEQ)
(and (recursions-okp :none fn (nth 1 expr))
(recursions-okp mode fn (nth 2 expr))
(recursions-okp mode fn (nth 3 expr))))
((eq (car expr) fn)
(if (eq mode :none)
nil
(recursions-okp-lst :none fn (cdr expr))))
(t (recursions-okp-lst :none fn (cdr expr)))))
(defun recursions-okp-lst (mode fn lst)
(cond ((endp lst) t)
(t (and (recursions-okp mode fn (car lst))
(recursions-okp-lst mode fn (cdr lst)))))))
(mutual-recursion
(defun chk-input-output-arity (expr amodules)
; Amodules is the list of modules annotated so far. Each module has a :formals
; and an :output-arity field. We confirm that every call of every function in
; the annotated expression has the right number of arguments. If so, we return
; its output arity. If not, we cause a hard error.
(cond
((atom expr) 1)
((eq (car expr) 'quote) 1)
((eq (car expr) 'MV)
(chk-input-output-arity-lst (cddr expr) amodules))
((eq (car expr) 'IFEQ)
(let ((test-output
(chk-input-output-arity (nth 2 expr) amodules))
(then-output
(chk-input-output-arity (nth 3 expr) amodules))
(else-output
(chk-input-output-arity (nth 4 expr) amodules)))
(cond
((not (equal test-output 1))
(er hard 'defsys
"The test of an IFEQ must return 1 result but the test of ~x0 ~
returns ~x1."
expr test-output))
((equal then-output else-output)
then-output)
(t (er hard 'defsys
"Both branches of an IFEQ must return the same number of ~
results, but in ~x0 the THEN branch returns ~x1 and the ELSE ~
branch returns ~x2."
expr then-output else-output)))))
(t
(let ((fn (car expr))
(expected-inputs
(if (member (car expr) '(+ - *))
2
(if (assoc-equal (car expr) amodules)
(len (cadr (assoc-keyword :formals
(cdr (assoc-equal (car expr) amodules)))))
nil)))
(expected-outputs
(if (member (car expr) '(+ - *))
1
(if (assoc-equal (car expr) amodules)
(cadr (assoc-keyword :output-arity
(cdr (assoc-equal (car expr) amodules))))
nil))))
(cond
((equal expected-inputs nil)
(er hard 'defsys "Unknown function ~x0" fn))
(t (let ((actual-inputs
(chk-input-output-arity-lst (cddr expr) amodules)))
(cond ((equal actual-inputs expected-inputs)
expected-outputs)
(t (er hard 'defsys
"The function ~x0 expects ~x1 inputs but is ~
supplied ~x2 inputs in the annotated expression ~
~x3."
fn expected-inputs actual-inputs expr))))))))))
(defun chk-input-output-arity-lst (expr-lst amodules)
(cond ((endp expr-lst) 0)
(t (+ (chk-input-output-arity (car expr-lst) amodules)
(chk-input-output-arity-lst (cdr expr-lst) amodules))))))
; A module is a program name, fn, followed by a keyword alist containing, at
; most, the keys
; :formals -- list of formal parameters
; :dcls -- nil or a DECLARE form to admit recursive fns
; :input -- hypotheses about the formals (essentially a guard)
; :output -- logical expression equal to the value left on the stack [see note]
; :output-arity -- a natp constant, e.g., 1 or 3
; :code -- source code from which we obtain M1 code by compilation
; Note: If :output-arity is not specified and :output begins with MV,
; :output-arity defaults to the number elements described by :output. Things
; should work when :output is an MV expression and :output-arity is omitted.
; But if :output is some other expression, e.g., (my-algorithm x y), then you
; have to tell defsys how many results are laid down by the code. Of course,
; there can be all sorts of discrepancies ... :output may describe 2 values,
; :output-arity may specify 3, and the code may sometimes produce 2, 3, or 4!
; But to verify, they'd all better agree. This system cannot handle varying
; output arities because the restore-regs code has to know how many values to
; save.
(defun annotate-module (module id)
(let ((legal-keys '(:formals :dcls :input :output
:output-arity :code
:ghost-formals
:ghost-base-test :ghost-base-value
:ghost-decr)))
(cond
((and (consp module)
(symbolp (car module))
(acl2::keyword-value-listp (cdr module))
(acl2::subsetp (acl2::evens (cdr module)) legal-keys))
(let* ((fn (car module))
(expr (cadr (assoc-keyword :code (cdr module))))
(output-arity
(if (assoc-keyword :output-arity (cdr module))
(cadr (assoc-keyword :output-arity (cdr module)))
(if (and (consp (cadr (assoc-keyword :output (cdr module))))
(or (eq (car (cadr (assoc-keyword :output (cdr module))))
'MV)
(eq (car (cadr (assoc-keyword :output (cdr module))))
'acl2::MV)))
(len (cdr (cadr (assoc-keyword :output (cdr module)))))
1))))
(cond
((member 's (cadr (assoc-keyword :formals (cdr module))))
(er hard 'defsys
"It is illegal for a module like ~x0 to use S as a formal ~
parameter because that variable name is used in certain of our ~
proof-support functions."
fn))
((not (recursions-okp :tail fn expr))
(er hard 'defsys
"We only support tail-recursion and the module defining ~x0 is ~
not tail-recursive."
fn))
((not (assoc-keyword :formals (cdr module)))
(er hard 'defsys
"You did not provide :FORMALS for ~x0."
fn))
((not (assoc-keyword :code (cdr module)))
(er hard 'defsys
"You did not provide :CODE for ~x0."
fn))
((not (natp output-arity))
(er hard 'defsys
"When an :output-arity is supplied it must be a natural number ~
and the :output-arity for ~x0 is not."
fn))
((and (> output-arity 1)
(not (equal (cadr (assoc-keyword :input (cdr module))) t))
(not (and
(consp (cadr (assoc-keyword :ghost-base-value (cdr module))))
(or (equal (car (cadr (assoc-keyword :ghost-base-value (cdr module))))
'mv)
(equal (car (cadr (assoc-keyword :ghost-base-value (cdr module))))
'acl2::mv))
(equal (len (cdr (cadr (assoc-keyword :ghost-base-value (cdr module)))))
output-arity))))
(er hard 'defsys
"When the :output-arity is greater than 1 you must supply a ~
:ghost-base-value, which must be an MV form of the appropriate ~
arity. These rules are violated for ~x0 where the ~
:output-arity is ~x1 but :ghost-base-value is ~x2."
fn output-arity (cadr (assoc-keyword :ghost-base-value (cdr module)))))
((and (or (assoc-keyword :ghost-base-test (cdr module))
(assoc-keyword :ghost-decr (cdr module)))
(not (assoc-keyword :ghost-formals (cdr module))))
(er hard 'defsys
"When you supply either a :ghost-base-test or a :ghost-decr, ~
you must supply :ghost-formals but you did not in ~x0."
fn))
((and (or (assoc-keyword :ghost-base-test (cdr module))
(assoc-keyword :ghost-decr (cdr module)))
(not (and (assoc-keyword :ghost-base-test (cdr module))
(assoc-keyword :ghost-base-value (cdr module))
(assoc-keyword :ghost-decr (cdr module)))))
(er hard 'defsys
"When you supply either a :ghost-base-test or
or a :ghost-decr, you must supply both of them and a ~
:ghost-base-value as well. You did not in ~x0."
fn))
((and (and (assoc-keyword :ghost-formals (cdr module))
(assoc-keyword :ghost-base-value (cdr module)))
(not (and (or (equal (car (cadr (assoc-keyword :ghost-base-value (cdr module)))) 'mv)
(equal (car (cadr (assoc-keyword :ghost-base-value (cdr module)))) 'acl2::mv))
(equal 0 (cadr (cadr (assoc-keyword :ghost-base-value (cdr module))))))))
(er hard 'defsys
"When :ghost-formals and a :ghost-base-value are supplied, the ~
:ghost-base-value must be an MV form with first result 0 but ~
in ~x0 the form is ~x1."
fn
(cadr (assoc-keyword :ghost-base-value (cdr module)))))
(t
(list (car module)
:formals (cadr (assoc-keyword :formals (cdr module)))
:dcls (cadr (assoc-keyword :dcls (cdr module)))
:input (or (cadr (assoc-keyword :input (cdr module))) t)
:output (or (cadr (assoc-keyword :output (cdr module)))
:NONE)
:output-arity output-arity
:code (annotate-expr expr id)
:ghost-formals (cadr (assoc-keyword :ghost-formals (cdr module)))
:ghost-base-test (cadr (assoc-keyword :ghost-base-test (cdr module)))
:ghost-base-value (cadr (assoc-keyword :ghost-base-value (cdr module)))
:ghost-decr (cadr (assoc-keyword :ghost-decr (cdr module))))))))
(t (er hard 'defsys
"Bad DEFSYS syntax for module ~x0. Each element must be of the form (symbol ~
:key1 val1 ... :keyn valn) where the only legal :keyi are ~&1."
(car module)
legal-keys)))))
(defun annotate-modules (modules i id ans max-a-regs)
(cond ((endp modules)
(mv (rev1 ans nil) max-a-regs))
(t (let* ((amod (annotate-module (car modules) (cons i id)))
(ans1 (cons amod ans)))
(acl2::prog2$
(chk-input-output-arity
(cadr (assoc-keyword :code (cdr amod)))
ans1)
(annotate-modules (cdr modules) (+ 1 i) id
ans1
(max max-a-regs
(max (len (cadr (assoc-keyword :formals (cdr amod))))
(cadr (assoc-keyword :output-arity (cdr amod)))))))))))
(mutual-recursion
(defun compile-expr (fn loop vars expr max-a-regs)
; expr is an annotated code expression: every fn call is of the form (fn id a1
; ... an) instead of (fn a1 ... an). By the way: this compiler handles
; recursions just fine, including ``sometimes tail-recursive'' functions like
; mc-flatten with some tail-recursive calls and some full-blown recursive
; calls. However, the clock compiler doesn't handle sometimes tail-recursive
; functions properly.
(cond ((atom expr)
(cond ((symbolp expr)
`((ILOAD ,(nv fn expr vars))))
(t `((ICONST ,expr)))))
((eq (car expr) 'quote)
`((ICONST ,(cadr expr))))
((member (car expr) '(+ - *))
`(,@(compile-expr nil nil vars (nth 2 expr) max-a-regs)
,@(compile-expr nil nil vars (nth 3 expr) max-a-regs)
,(case (car expr)
(+ '(IADD))
(- '(ISUB))
(otherwise '(IMUL)))))
((eq (car expr) 'MV)
(compile-expr-lst nil loop vars (cdr (cdr expr)) max-a-regs))
((eq (car expr) 'IF)
(er hard 'compile-expr
"The compiler does not support IF. Use IFEQ."))
((eq (car expr) 'IFEQ)
(let ((a (nth 2 expr))
(b (nth 3 expr))
(c (nth 4 expr)))
(let* ((test (compile-expr nil nil vars a max-a-regs))
(then (compile-expr fn loop vars b max-a-regs))
(else (compile-expr fn loop vars c max-a-regs))
(last-else-inst (car (last else))))
(if (and (consp last-else-inst)
(eq (car last-else-inst) 'GOTO))
`(,@test
(IFEQ ,(+ (icount else) 1))
,@else
,@then)
`(,@test
(IFEQ ,(+ (icount else) 2))
,@else
(GOTO ,(+ (icount then) 1))
,@then)))))
(t (append
(compile-expr-lst nil loop vars (cdr (cdr expr)) max-a-regs)
(if (eq (car expr) fn)
(append (ISTORE-series 0 (len vars))
`((GOTO ,loop)))
`((CALL ,(car expr) ,(cadr expr))))))))
(defun compile-expr-lst (fn loop vars expr-lst max-a-regs)
(declare (xargs :mode :program))
(cond ((endp expr-lst) nil)
(t (append (compile-expr fn loop vars (car expr-lst) max-a-regs)
(compile-expr-lst fn loop vars (cdr expr-lst) max-a-regs))))))
(defun compile-module (module max-a-regs)
(let* ((fn (car module))
(vars (cadr (assoc-keyword :formals (cdr module))))
(n (len vars))
(body (cadr (assoc-keyword :code (cdr module))))
(fn-loop (pack (list fn "-LOOP")))
(fn-exit (pack (list fn "-EXIT"))))
`(,fn
,@(save-regs n max-a-regs)
,fn-loop
,@(compile-expr fn fn-loop vars body max-a-regs)
,fn-exit
,@(restore-regs (cadr (assoc-keyword :output-arity (cdr module)))
n max-a-regs)
(RET ,fn))))
(defun algorithm-name (fn)
(pack (list '! fn)))
(defun nth-series (n base max)
(cond ((>= n max) nil)
(t (cons `(nth ,n ,base)
(nth-series (+ 1 n) base max)))))
(defun mv-nth-series (n base max)
(cond ((>= n max) nil)
(t (cons `(mv-nth ,n (mv-list ,max ,base))
(mv-nth-series (+ 1 n) base max)))))
(mutual-recursion
(defun algorithm-expr (fn expr amodule-lst)
; Expr is an annotated expression and we strip the annotations out as we also
; change the names of all the non-primitives from names such as FLOOR and MOD
; to !FLOOR and !MOD, and convert the IFEQs to IFs. Fn is either nil or a
; function name. When non-nil, fn is the name of a function we are defining
; and expr was (originally) its body. In the case that fn is non-nil and has
; ghostly attributes, we put them into calls of fn. Note that we don't know
; how to make sense of calls of functions with ghostly attributes except at the
; very top-level. If, for example, foo has a ghost formal k and foo is called
; in bar, which has no ghost formal, then what do we use for the x argument in
; the call of foo from bar? We simply return an ill-formed term in which foo
; is called with an insufficient nubmer of arguments.
(cond ((atom expr) expr)
((eq (car expr) 'IFEQ)
`(IF (EQUAL ,(algorithm-expr fn (nth 2 expr) amodule-lst)
0)
,(algorithm-expr fn (nth 3 expr) amodule-lst)
,(algorithm-expr fn (nth 4 expr) amodule-lst)))
(t
(let ((ghost-formals
(cadr
(assoc-keyword :ghost-formals
(cdr (assoc-equal (car expr)
amodule-lst)))))
(ghost-decr
(if (equal (car expr) fn) ; if fn is nil this fails
(cadr
(assoc-keyword :ghost-decr
(cdr (assoc-equal fn
amodule-lst))))
nil))
(!fn (if (member (car expr) '(+ - * mv acl2::mv))
(car expr)
(algorithm-name (car expr))))
(args (algorithm-expr-lst fn (cdr (cdr expr)) amodule-lst)))
(cons !fn
(cond
((and (eq (car expr) fn) ghost-decr)
(append args ghost-decr))
(ghost-formals
(append args ghost-formals))
(t args)))))))
(defun algorithm-expr-lst (fn expr-lst amodule-lst)
(cond
((endp expr-lst) nil)
(t (let* ((x (car expr-lst))
(arg (algorithm-expr fn x amodule-lst))
(output-arity
(cond ((and (consp x)
(not (eq (car x) 'quote))
(assoc-equal (car x) amodule-lst))
(cadr (assoc-keyword :output-arity
(cdr (assoc-equal (car x)
amodule-lst)))))
(t 1)))
(rest (algorithm-expr-lst fn (cdr expr-lst) amodule-lst)))
(cond
((equal output-arity 1)
(cons arg rest))
(t (append (mv-nth-series 0 arg output-arity) rest))))))))
(defun add-return-labels (code i rcode id-to-label-table)
; Every CALL must be followed by a label. In addition, every call is currently
; annotated with a unique id that associates it with the corresponding function
; call in the original high-level expression. We add a unique label after each
; CALL and we build a table associating the unique ids of each call to the
; label generated. We do all this in a second pass, rather than as part of
; compilation, because it is easier to guarantee that all the labels are
; distinct.
(cond ((endp code)
(mv (rev1 rcode nil)
id-to-label-table))
((and (consp (car code))
(eq (op-code (car code)) 'CALL))
(let ((id (nth 2 (car code)))
(label (pack (list 'ret-pc- i '-from-call- (arg1 (car code))))))
(add-return-labels (cdr code)
(+ 1 i)
(rev1 `(,(car code)
,label)
rcode)
(cons (cons id label) id-to-label-table))))
(t (add-return-labels (cdr code)
i
(cons (car code) rcode)
id-to-label-table))))
(defun compile-module-lst (lst rcode max-a-regs)
(cond ((endp lst)
(add-return-labels (rev1 rcode '(NON-TERMINATING
(GOTO NON-TERMINATING)
ILLEGAL-FINAL-PC
(GOTO ILLEGAL-FINAL-PC)))
0
nil
nil))
(t (compile-module-lst (cdr lst)
(rev1 (compile-module (car lst) max-a-regs)
rcode)
max-a-regs))))
(defun compile-system (top-level-code module-lst max-a-regs)
; module-lst is annotated.
(compile-module-lst module-lst
(rev1 top-level-code nil)
max-a-regs))
(defun expand-CALL (inst ret-label rcode)
(rev1 `((ICONST ,ret-label)
(GOTO ,(arg1 inst)))
rcode))
(defun expand-ret-lst (targets rcode max-a-regs)
(cond ((endp targets)
(rev1 '((GOTO NON-TERMINATING))
rcode))
((endp (cdr targets))
(rev1 `((GOTO ,(car targets)))
rcode))
(t (expand-ret-lst
(cdr targets)
(rev1 `((ILOAD ,(* 2 max-a-regs))
(ICONST ,(car targets))
(ISUB)
(IFEQ ,(car targets)))
rcode)
max-a-regs))))
(defun expand-RET (inst alist rcode max-a-regs)
(expand-ret-lst (cdr (assoc (arg1 inst) alist))
rcode
max-a-regs))
; The alist below maps subrs to the return labels from all their callers.
(defun assemble (code alist rcode max-a-regs)
(cond ((endp code)
(rev1 rcode nil))
((atom (car code))
(assemble (cdr code)
alist
(cons (car code) rcode)
max-a-regs))
((eq (op-code (car code)) 'CALL)
(assemble (cdr code)
alist
(expand-CALL (car code) (cadr code) rcode)
max-a-regs))
((eq (op-code (car code)) 'RET)
(assemble (cdr code)
alist
(expand-RET (car code) alist rcode max-a-regs)
max-a-regs))
(t (assemble (cdr code)
alist
(cons (car code) rcode)
max-a-regs))))
(defun label-table (code pc alist)
(cond ((endp code) alist)
((atom (car code))
(label-table (cdr code)
pc
(cons (cons (car code) pc) alist)))
(t (label-table (cdr code)
(+ 1 pc)
alist))))
(defun assoc-or-report (instr tablename key alist)
(let ((ans (assoc key alist)))
(if ans
ans
(er hard 'link
"While linking the instruction ~x0 no entry was found in ~x1 for ~x2. The ~
value of ~x1 is ~X34."
instr tablename key alist nil))))
(defun link (code pc label-table rcode)
(cond ((endp code)
(rev1 rcode nil))
((atom (car code))
(link (cdr code) pc label-table rcode))
((eq (op-code (car code)) 'ICONST)
; We permit an ICONST instruction to use a label as data and replace the
; label by the corresponding pc.
(link (cdr code)
(+ 1 pc)
label-table
(cons (if (integerp (arg1 (car code)))
(car code)
(list 'ICONST
(cdr (assoc-or-report (car code)
'label-table
(arg1 (car code))
label-table))))
rcode)))
((member (op-code (car code)) '(GOTO IFEQ))
; We permit GOTO and IFEQ to use label names and replace them with the correct
; relative jump distances. However, if the arg given is a number, we leave it
; in place.
(link (cdr code)
(+ 1 pc)
label-table
(cons (if (integerp (arg1 (car code)))
(car code)
(list (op-code (car code))
(- (cdr (assoc-or-report (car code)
'label-table
(arg1 (car code))
label-table))
pc)))
rcode)))
((member (op-code (car code)) '(ILOAD ISTORE IADD ISUB IMUL HALT))
; All other M1 instructions are left as-is.
(link (cdr code)
(+ 1 pc)
label-table
(cons (car code) rcode)))
(t (er hard 'link
"Unrecognized instruction or pseudo-instruction, ~x0."
(car code)))))
(defun defconst-lst (alist)
(cond ((endp alist) nil)
(t (cons `(defconst ,(pack (list '* (caar alist) '*))
,(cdr (car alist)))
(defconst-lst (cdr alist))))))
(defun switch-table (code alist)
(cond ((endp code) alist)
((and (consp (car code))
(eq (op-code (car code)) 'CALL))
(let* ((subr (arg1 (car code)))
(ret-label (cadr code))
(temp (assoc subr alist))
(new-targets (add-to-set-equal ret-label (cdr temp))))
(switch-table (cdr code)
(put-assoc-equal subr new-targets alist))))
(t (switch-table (cdr code) alist))))
; Now we develop a compiler for clock functions. The worst aspect of this
; process is a hack I call the :STOP hack. Recall that the then branch of an
; IF is generally followed by a GOTO that skips over the else branch. So the
; clock for a then branch is generated by getting the clock for the code
; and adding one TICK after it. But this tick is not added if the last
; instruction in the then branch is a GOTO. However, now consider the code for
; (if a (if b c d) e) and suppose c is a tail-recursive call compiled to a
; GOTO. Then the clock for c is correctly handled (no extra TICK) but the
; clock for (if b c d) is not because we would add a TICK -- but that TICK
; is not needed on every path through the code, just some paths. We handle
; this by putting the keyword :STOP into the clock when we see a
; tail-recursive GOTO. Then, we generate clocks like (clk+ (clk+
; 11 (clk+ (foo-clock x) :STOP)) 1) like: (clk+ 11
; (clk+ (foo-clock x) (clk+ :STOP 1))) which we just truncate at the
; :STOP. Thus, the extra TICK is added only on those branches not ending in a
; tail-recursive GOTO. But to make this work we have to normalize ifs and
; associate the clk+s.
(defun normalize-clk+-ifs (x)
(cond ((atom x) x)
((eq (car x) 'quote) x)
((eq (car x) 'IF)
`(IF ,(nth 1 x)
,(normalize-clk+-ifs (nth 2 x))
,(normalize-clk+-ifs (nth 3 x))))
((eq (car x) 'clk+)
(let ((x1 (normalize-clk+-ifs (nth 1 x)))
(x2 (normalize-clk+-ifs (nth 2 x))))
(cond
((and (consp x1)
(eq (car x1) 'IF))
`(IF ,(nth 1 x1)
,(normalize-clk+-ifs `(clk+ ,(nth 2 x1) ,x2))
,(normalize-clk+-ifs `(clk+ ,(nth 3 x1) ,x2))))
((and (consp x2)
(eq (car x2) 'IF))
`(IF ,(nth 1 x2)
,(normalize-clk+-ifs `(clk+ ,x1 ,(nth 2 x2)))
,(normalize-clk+-ifs `(clk+ ,x1 ,(nth 3 x2)))))
(t `(clk+ ,x1 ,x2)))))
(t x)))
(defun flatten-clk+-expr (x)
(cond ((and (consp x)
(eq (car x) 'clk+))
(append (flatten-clk+-expr (nth 1 x))
(flatten-clk+-expr (nth 2 x))))
(t (list x))))
(defun truncate-to-stop (x)
(cond ((endp x) nil)
((eq (car x) :STOP) nil)
(t (cons (car x) (truncate-to-stop (cdr x))))))
(defun combine-adjacent-natp-clocks (lst)
(cond ((endp lst) nil)
((endp (cdr lst)) lst)
(t (let ((x1 (car lst))
(lst1 (combine-adjacent-natp-clocks (cdr lst))))
(cond
((and (natp x1)
(natp (car lst1)))
(cons (+ x1 (car lst1))
(cdr lst1)))
(t (cons x1 lst1)))))))
(defun make-clk+-nest (lst)
(if (endp lst)
0
(if (endp (cdr lst))
(car lst)
`(clk+ ,(car lst)
,(make-clk+-nest (cdr lst))))))
(defun associate-clk+s (x)
(cond ((atom x) x)
((eq (car x) 'quote) x)
((eq (car x) 'clk+)
(make-clk+-nest
(combine-adjacent-natp-clocks
(truncate-to-stop (flatten-clk+-expr x)))))
((eq (car x) 'if)
`(if ,(nth 1 x)
,(associate-clk+s (nth 2 x))
,(associate-clk+s (nth 3 x))))
(t x)))
(defun combine-clocks (lst1 lst2)
; Each of the args is a list of clock expressions that will ultimately be
; combined. For example, lst1 might be '((foo-clock x) 5) and lst2 might be
; '(3). We ``concatentate'', combining explicit clocks (if any) on the last
; element of lst1 and first of lst2. So we combine the two examples above to
; '((foo-clock x) 8). Eventually we'll build a right-associated clk+ nest from
; this list.
(let ((x1 (car (last lst1)))
(x2 (car lst2)))
(cond
((and (natp x1)
(natp x2))
(append (all-but-last lst1)
(cons (+ x1 x2)
(cdr lst2))))
(t (append lst1 lst2)))))
(mutual-recursion
(defun compile-clock-expr (fn loop vars expr amodule-lst)
; Expr is an annotated expression.
(cond ((atom expr)
'(1)) ; ILOAD or ICONST
((eq (car expr) 'quote)
'(1)) ; ICONST
((member (car expr) '(+ - *))
(combine-clocks
(compile-clock-expr nil nil vars (nth 2 expr) amodule-lst)
(combine-clocks
(compile-clock-expr nil nil vars (nth 3 expr) amodule-lst)
'(1)))) ; IADD, ISUB, IMUL
((eq (car expr) 'MV)
(compile-clock-expr-lst nil loop vars (cdr (cdr expr)) amodule-lst))
((eq (car expr) 'IF)
(er hard 'compile-clock-expr
"The clock compiler does not support IF. Use IFEQ."))
((eq (car expr) 'IFEQ)
(let ((a (nth 2 expr))
(b (nth 3 expr))
(c (nth 4 expr)))
(let* ((test-clock (compile-clock-expr nil nil vars a amodule-lst))
(then-clock (compile-clock-expr fn loop vars b amodule-lst))
(else-clock (compile-clock-expr fn loop vars c amodule-lst)))
; I have debated whether the first arg to algorithm-expr below should be fn or
; nil. I will supply nil and that means that we won't supply ghost args if we
; see a call of fn. But I don't expect a call of fn in the test of a tail
; recursive definition of fn!
`((IF (EQUAL ,(algorithm-expr nil a amodule-lst) 0)
,(make-clk+-nest
(combine-clocks
test-clock
(combine-clocks
'(1) ; IFEQ
then-clock)))
,(make-clk+-nest
(combine-clocks
test-clock
(combine-clocks
'(1) ; IFEQ
(if (and (consp c)
(eq (car c) fn))
else-clock
(combine-clocks
else-clock
'(1))))))))))) ; (GOTO skip-around-then)
(t (combine-clocks
(compile-clock-expr-lst nil loop vars (cdr (cdr expr)) amodule-lst)
(cond
((eq (car expr) fn)
`(,(+ 1 (len (ISTORE-series 0 (len vars))))
(,(pack (list loop '-CLOCK))
,@(algorithm-expr-lst nil (cdr (cdr expr)) amodule-lst)
,@(cadr (assoc-keyword :ghost-decr
(cdr (assoc-equal fn amodule-lst)))))
; Note the :STOP hack marker, indicating that the preceding is a tail-recursive jump.
; This prevents any subsequent clock from being appended to this branch.
:STOP))
(t
`(2
(,(pack (list (car expr) '-CLOCK))
',(cadr expr) ; id
,@(algorithm-expr-lst fn (cdr (cdr expr)) amodule-lst)
,@(cadr (assoc-keyword :ghost-formals
(cdr (assoc-equal (car expr) amodule-lst))))))))))))
(defun compile-clock-expr-lst (fn loop vars expr-lst amodule-lst)
(declare (xargs :mode :program))
(cond ((endp expr-lst) nil)
(t (combine-clocks
(compile-clock-expr fn loop vars (car expr-lst) amodule-lst)
(compile-clock-expr-lst fn loop vars (cdr expr-lst) amodule-lst))))))
; Now we develop the code to extract from a recursive clock function the
; part of the clock that drives the code once around the loop.
(mutual-recursion
(defun calledp (fn x)
(cond ((atom x) nil)
((eq (car x) 'quote) nil)
((eq fn (car x)) t)
(t (calledp-lst fn (cdr x)))))
(defun calledp-lst (fn lst)
(cond ((endp lst) nil)
(t (or (calledp fn (car lst))
(calledp-lst fn (cdr lst)))))))
(defun generate-induction-hint-expr (fn hfn vars expr a)
; Fn is the name of a recursive clock function, like FACT-LOOP-CLOCK, and
; expr is its body. We dive through expr and gut it, replacing all base-case
; exits by (list ,@vars s) and all clk+ nests containing calls of fn, e.g., (clk+ a
; (clk+ b (clk+ c (fn ...)))) by (hfn ... (m1 s (clk+ a (clk+ b c)))). We assume (and
; check later) that every call of fn is the last argument of some clk+ nest
; output. We check that by only looking for and replacing such calls and then
; finally confirm that the result has no calls of fn.
(cond ((atom expr) `(list ,@vars s))
((eq (car expr) 'quote) `(list ,@vars s))
((eq (car expr) 'IF)
`(IF ,(nth 1 expr)
,(generate-induction-hint-expr fn hfn vars (nth 2 expr) a)
,(generate-induction-hint-expr fn hfn vars (nth 3 expr) a)))
((eq (car expr) fn)
`(,hfn ,@(cdr expr) ,(if a
`(m1 s ,(make-clk+-nest (rev1 a nil)))
's)))
((eq (car expr) 'clk+)
(generate-induction-hint-expr fn hfn vars (nth 2 expr)
(cons (nth 1 expr) a)))
((calledp fn expr)
(er hard 'defsys
"It was thought impossible for a clock function, specifically ~
~x0, to be called recursively in its body except as the deepest ~
argument of CLK+ nests in output branches of top-level IFs, but ~
it is called in ~x1."
fn expr))
(t `(list ,@vars s))))
(defun make-push-nest (lst stack)
(cond ((endp lst) stack)
(t (make-push-nest (cdr lst) `(push ,(car lst) ,stack)))))
(defun make-acl2-body (ghost-base-test ghost-base-value hyps body)
(let ((body1 (if (eq hyps t)
body
`(if ,hyps ,body ,ghost-base-value))))
(if ghost-base-test
`(if ,ghost-base-test
,ghost-base-value
,body1)
body1)))
; The following function generates two or three functions depending on whether
; the module is iterative. If it has a loop in it, we generate three
; functions: the loop clock, the top-level clock (including entry and
; exit costs), and the induction hint. If it does not have a loop, we just
; generate the ``loop'' clock (even though it is not a loop, it is the core
; of the module) and the top-level clock.
(defun repeat (e n)
(if (zp n)
nil
(cons e (repeat e (- n 1)))))
(defun defun-clock-and-hint-fns (module max-a-regs amodule-lst)
(let* ((fn (car module))
(loop (pack (list fn '-loop)))
(vars (cadr (assoc-keyword :formals (cdr module))))
(ghost-formals (cadr (assoc-keyword :ghost-formals (cdr module))))
(vars-and-ghosts (append vars ghost-formals))
(ghost-base-test (cadr (assoc-keyword :ghost-base-test (cdr module))))
(dcls (cadr (assoc-keyword :dcls (cdr module))))
(hyps (cadr (assoc-keyword :input (cdr module))))
(output-arity (cadr (assoc-keyword :output-arity (cdr module))))
(expr (cadr (assoc-keyword :code (cdr module))))
(loop-clock-list (compile-clock-expr fn loop vars expr amodule-lst))
(loop-clock (pack (list loop '-clock)))
(loop-clock-body
(associate-clk+s
(normalize-clk+-ifs
(make-clk+-nest loop-clock-list))))
(clock (pack (list fn '-clock)))
(clock-body (if ghost-formals
`(if (equal (mv-nth 0 (mv-list ,output-arity
(,(algorithm-name fn) ,@vars-and-ghosts)))
0)
(clk+ ,(len (save-regs (len vars) max-a-regs))
(,loop-clock ,@vars-and-ghosts))
(clk+ ,(len (save-regs (len vars) max-a-regs))
(clk+ (,loop-clock ,@vars-and-ghosts)
(clk+ ,(len (restore-regs output-arity
(len vars)
max-a-regs))
(exit-clock ',fn ret-pc)))))
`(clk+ ,(len (save-regs (len vars) max-a-regs))
(clk+ (,loop-clock ,@vars-and-ghosts)
(clk+ ,(len (restore-regs output-arity
(len vars)
max-a-regs))
(exit-clock ',fn ret-pc))))))
(hint (pack (list loop '-induction-hint)))
(hint-body (if (calledp loop-clock loop-clock-body)
(generate-induction-hint-expr loop-clock hint vars loop-clock-body nil)
:NON-RECURSIVE)))
(cond ((and (not (eq hint-body :NON-RECURSIVE))
(calledp loop-clock hint-body))
(er hard 'defsys
"In the process of defining the hint function ~x0 we gutted ~
the body of the corresponding clock function, ~x1, and ~
replaced all the recursive calls at the end of output CLK+ ~
nests by recursive calls of the ~x0. But the original ~
clock function name, ~x0, still occurs in the purported ~
induction hint function body, ~x1, contrary to what we ~
thought was possible!"
hint fn hint-body))
(t
`(
(defun ,loop-clock ,vars-and-ghosts
,@dcls
; Clock fns return nil on forced termination, so I ignore ghost-base-value below.
,(make-acl2-body ghost-base-test 0 hyps loop-clock-body))
(defun ,clock (ret-pc ,@vars-and-ghosts)
,clock-body)
,@(if (eq fn 'MAIN)
`((defun m1-psi (,@vars-and-ghosts)
(m1 (make-state 0
',(repeat 0 (+ (* 2 max-a-regs) 1))
,(make-push-nest vars nil)
(psi))
(clk+ 2
(main-clock nil ,@vars-and-ghosts)))))
nil)
,@(cond ((not (eq hint-body :NON-RECURSIVE))
`((defun ,hint (,@vars-and-ghosts s)
,@dcls
; Hint functions return nil on forced termination, so I ignore ghost-base-value below.
,(make-acl2-body ghost-base-test nil hyps hint-body))))
(t nil)))))))
(defun defun-algorithm (module amodule-lst)
(let* ((fn (car module))
(ghost-formals (cadr (assoc-keyword :ghost-formals (cdr module))))
(ghost-base-test (cadr (assoc-keyword :ghost-base-test (cdr module))))
(ghost-base-value (cadr (assoc-keyword :ghost-base-value (cdr module))))
(vars-and-ghosts
(append (cadr (assoc-keyword :formals (cdr module)))
ghost-formals))
(dcls (cadr (assoc-keyword :dcls (cdr module))))
(hyps (cadr (assoc-keyword :input (cdr module))))
(body (cadr (assoc-keyword :code (cdr module))))
(!fn (algorithm-name fn))
(!body (algorithm-expr fn body amodule-lst)))
(mv `(defun ,!fn ,vars-and-ghosts ,@dcls
,(make-acl2-body ghost-base-test ghost-base-value hyps !body))
(calledp !fn !body))))
(defun make-equal-var-top-pop-stack (vars stack)
(cond ((endp vars) nil)
(t (cons `(equal ,(car vars) (top ,stack))
(make-equal-var-top-pop-stack (cdr vars) `(pop ,stack))))))
(defun nth-i-locals-lst (n max-a-regs)
(nth-series n '(locals s) max-a-regs))
(defun push-lst (nthfn n expr stack)
(cond ((zp n) stack)
(t `(push (,nthfn ,(- n 1) ,expr)
,(push-lst nthfn (- n 1) expr stack)))))
(mutual-recursion
(defun ghost-calls (expr amodule-lst)
; We return the list of all modules with ghost formals that are called in expr.
(cond ((atom expr) nil)
((eq (car expr) 'quote) nil)
((cadr (assoc-keyword :ghost-formals
(cdr (assoc-equal (car expr) amodule-lst))))
(cons (car expr)
(ghost-calls-lst (cddr expr) amodule-lst)))
(t (ghost-calls-lst (cddr expr) amodule-lst))))
(defun ghost-calls-lst (lst amodule-lst)
(cond ((endp lst) nil)
(t (append (ghost-calls (car lst) amodule-lst)
(ghost-calls-lst (cdr lst) amodule-lst))))))
(defun verification-events-for-module (module ans max-a-regs amodule-lst)
(let* ((fn (car module))
(vars (cadr (assoc-keyword :formals (cdr module))))
(ghost-formals (cadr (assoc-keyword :ghost-formals (cdr module))))
(vars-and-ghosts (append vars ghost-formals))
(hyps (cadr (assoc-keyword :input (cdr module))))
(rhs (cadr (assoc-keyword :output (cdr module))))
(output-arity (cadr (assoc-keyword :output-arity (cdr module))))
(expr (cadr (assoc-keyword :code (cdr module))))
(ghost-calls (ghost-calls expr amodule-lst))
(ghost-call (car ghost-calls)))
; If module contains a ghost call (a call to a module with ghost formals) then
; either the only ghost calls are to the module itself (i.e., this is the
; module introducing nontermination), or else the module should be MAIN, there
; is only one ghost call, and MAIN has the same ghost formals as the ghost
; calling module.
(acl2::prog2$
(if
(or (not ghost-calls)
(acl2::subsetp ghost-calls (list fn))
(and (equal fn 'MAIN)
(equal ghost-calls (list ghost-call))
(equal
(cadr
(assoc-keyword :ghost-formals (cdr module)))
(cadr
(assoc-keyword :ghost-formals
(cdr (assoc-equal ghost-call
amodule-lst)))))))
nil
(acl2::cw
"The module named ~x0 calls ~x1 and the called module has ghost ~
formals. (Presumably ~x1 does not necessarily terminate and thus ~
thus ~x0 won't either.) How are the ghost formals for ~x1 passed ~
down to its clock function in the clock function for ~x0? I ~
have a really draconian convention: I allow this only if the calling ~
module is MAIN, the only ghostly call MAIN makes is to ~x1, and MAIN ~
has identical ghost formals. Under these circumstances I pass MAIN's ~
ghosts down to ~x1. However, these draconian restrictions are not ~
met in this system. I wasn't motivated to figure out what is really ~
needed in such general cases as this. I suspect this defsys will ~
fail! However, if you :TRANS1 it and replay the workable part to get ~
to the first nonsensical event, perhaps you can see how to patch up ~
the remaining events."
fn ghost-call))
(mv-let
(alg-def recursivep)
(defun-algorithm module amodule-lst)
(rev1
`(,alg-def
,@(defun-clock-and-hint-fns module max-a-regs amodule-lst)
(defun ,(pack (list fn '-loop-final-locals)) (,@vars-and-ghosts s)
(locals (m1 s (,(pack (list fn '-loop-clock)) ,@vars-and-ghosts))))
; (defthm ,(pack (list 'true-listp- fn '-loop-final-locals))
; (implies (acl2::true-listp (locals s))
; (acl2::true-listp (,(pack (list fn '-loop-final-locals)) ,@vars-and-ghosts s))))
(defthm ,(pack (list 'len- fn '-loop-final-locals))
(<= (len (locals s))
(len (,(pack (list fn '-loop-final-locals)) ,@vars-and-ghosts s)))
:rule-classes :linear)
,@(if (and (eq fn 'MAIN)
ghost-calls)
; Given our draconian restriction that MAIN is the only module that can call a
; module with ghost formals, we know that ghost-call is the name of the called
; module, that ghost-call's correctness theorem splits on whether ghost-call
; terminates and that in the event that it does not, m1 hangs at
; ghost-call's loop. In this case, we handle MAIN differently than for normal
; always-terminating MAINs. In particular, we splice in a definition for MAIN's
; final (still non-terminal) stack and then use it in the correcness results.
`((defun main-loop-final-stack (,@vars-and-ghosts s)
(stack (m1 s (main-loop-clock ,@vars-and-ghosts)))))
nil)
(defthm ,(pack (list fn '-loop-is- (algorithm-name fn)))
(implies
(and (ready-at ,(pack (list '* fn '-loop*)) (list ,@vars) 0 s)
,@(if (equal hyps t) nil (list hyps)))
(equal
(m1 s (,(pack (list fn '-loop-clock)) ,@vars-and-ghosts))
,(let ((terminal-state
`(make-state
,(pack (list '* fn '-exit*))
,(if (equal (len vars) max-a-regs)
`(,(pack (list fn '-loop-final-locals)) ,@vars-and-ghosts s)
`(update-nth* ,(len vars)
(list ,@(nth-i-locals-lst (len vars) max-a-regs))
(,(pack (list fn '-loop-final-locals))
,@vars-and-ghosts s)))
,(if (equal output-arity 1)
`(push (,(algorithm-name fn) ,@vars-and-ghosts) (stack s))
(push-lst 'mv-nth
output-arity
`(,(algorithm-name fn) ,@vars-and-ghosts)
'(stack s)))
(psi))))
(if ghost-formals
(if (and (eq fn 'MAIN)
ghost-calls)
`(if (equal (mv-nth 0 (mv-list ,output-arity (!MAIN ,@vars-and-ghosts))) 0)
; Note that if MAIN hangs, it hangs at ghost-call's loop, not *MAIN-LOOP*.
; Note also that we disavow any knowledge of the stack at that point, although
; with some care we could reconstruct it: it is (stack s) with MAIN's locals
; and return pc popped off, then (len vars) of (LOCALS s) pushed, then the
; return pc pushed, then k locals of that state pushed, where k is the number
; of vars of ghost-calls, and then the return pc back to MAIN. But I do not
; think we care about the stack of an infinitely looping state, since we'll
; never pop back into it.
(make-state ,(pack (list '* ghost-call '-loop*))
(main-loop-final-locals ,@vars-and-ghosts s)
(main-loop-final-stack ,@vars-and-ghosts s)
(psi))
,terminal-state)
`(if (equal (mv-nth 0 (mv-list ,output-arity
(,(algorithm-name fn) ,@vars-and-ghosts)))
0)
(make-state ,(pack (list '* fn '-loop*))
(,(pack (list fn '-loop-final-locals)) ,@vars-and-ghosts s)
(stack s)
(psi))
,terminal-state))
terminal-state))))
:hints (("Goal"
,@(if recursivep
`(:induct (,(pack (list fn '-loop-induction-hint)) ,@vars-and-ghosts s))
`(:do-not-induct t)))))
(in-theory (disable ,(pack (list fn '-loop-clock))
,(pack (list fn '-loop-final-locals))
,@(if (and (eq fn 'MAIN)
ghost-calls)
'(MAIN-LOOP-FINAL-STACK)
nil)))
(defun ,(pack (list fn '-final-locals)) (call-id ,@vars-and-ghosts s)
(locals (m1 s (,(pack (list fn '-clock)) call-id ,@vars-and-ghosts))))
; (defthm ,(pack (list 'true-listp- fn '-final-locals))
; (implies (acl2::true-listp (locals s))
; (acl2::true-listp (,(pack (list fn '-final-locals)) call-id ,@vars-and-ghosts s))))
(defthm ,(pack (list 'len- fn '-final-locals))
(<= (len (locals s))
(len (,(pack (list fn '-final-locals)) call-id ,@vars-and-ghosts s)))
:rule-classes :linear)
; We do an analogous treatment for the top-level MAIN theorem if it has a ghost call in it.
,@(if (and (eq fn 'MAIN)
ghost-calls)
`((defun main-final-stack (call-id ,@vars-and-ghosts s)
(stack (m1 s (main-clock call-id ,@vars-and-ghosts)))))
nil)
; We force the READY-AT and the requirements on call-id. The idea is that if
; the theorem fails to apply at a place where the fn code is clocked, it is
; because of elementary programming mistakes having to do with pushing the
; right arguments.
(defthm ,(pack (list fn '-is- (algorithm-name fn)))
(implies
(and (acl2::force
(ready-at ,(pack (list '* fn '*))
(locals s)
,(+ 1 (len vars))
s))
(acl2::force
(member (cdr (assoc call-id *id-to-label-table*))
(cdr (assoc ',fn *switch-table*))))
(acl2::force
(equal (top (stack s)) (final-pc ',fn call-id)))
,@(make-equal-var-top-pop-stack (rev1 vars nil) '(pop (stack s)))
,@(if (equal hyps t) nil `(,hyps)))
(equal
(m1 s (,(pack (list fn '-clock)) call-id ,@vars-and-ghosts))
,(let ((terminal-state
`(make-state (top (stack s))
(update-nth* 0
(list ,@(nth-i-locals-lst 0 max-a-regs))
(,(pack (list fn '-final-locals))
call-id ,@vars-and-ghosts s))
,(if (equal output-arity 1)
`(push (,(algorithm-name fn) ,@vars-and-ghosts)
(popn ,(+ 1 (len vars)) (stack s)))
(push-lst 'mv-nth
output-arity
`(,(algorithm-name fn) ,@vars-and-ghosts)
`(popn ,(+ 1 (len vars)) (stack s))))
(psi))))
(if ghost-formals
(if (and (eq fn 'main)
ghost-calls)
`(if (equal (mv-nth 0 (mv-list ,output-arity
(!MAIN ,@vars-and-ghosts)))
0)
(make-state ,(pack (list '* ghost-call '-loop*))
(,(pack (list fn '-final-locals)) call-id ,@vars-and-ghosts s)
(main-final-stack call-id ,@vars-and-ghosts s)
(psi))
,terminal-state)
`(if (equal (mv-nth 0 (mv-list ,output-arity
(,(algorithm-name fn) ,@vars-and-ghosts)))
0)
(make-state ,(pack (list '* fn '-loop*))
(,(pack (list fn '-final-locals)) call-id ,@vars-and-ghosts s)
(push (final-pc ',fn call-id)
,(push-lst 'nth
(len vars)
'(locals s)
`(popn ,(+ 1 (len vars)) (stack s))))
(psi))
,terminal-state))
terminal-state))))
:hints (("Goal" :do-not-induct t)))
(in-theory (disable ,(pack (list fn '-clock))
,(pack (list fn '-final-locals))
,@(if (and (eq fn 'MAIN)
ghost-calls)
`(main-final-stack)
nil)))
,@(if (eq rhs :NONE)
nil
`((defthm ,(pack (list (algorithm-name fn) '-spec))
,(let ((concl `(equal (,(pack (list (algorithm-name fn))) ,@vars-and-ghosts)
,rhs)))
(if (equal hyps t)
concl
`(implies ,hyps ,concl)))))))
ans)))))
(defun verification-events-for-modules (amod-lst ans max-a-regs amodule-lst)
; amod-lst is a tail of amodule-lst, the full list of annotated modules.
(cond ((endp amod-lst) (rev1 ans nil))
(t (verification-events-for-modules
(cdr amod-lst)
(verification-events-for-module (car amod-lst) ans max-a-regs amodule-lst)
max-a-regs amodule-lst))))
; Before we execute the events created by defsys we give the user a chance to
; elaborate them.
; We develop a utility that allows us to edit a list of events ``off line.''
; The utility takes a list of events and a list of commands and carries out the
; commands. We do not expand macros in the event list, nor do we look inside
; of encapsulates. Each edit command is of the form (ev-type ev-name place x),
; where
; ev-type = DEFTHM, place = :before, :after, :hints, or :rule-classes
; ev-type = DEFUN, place = :before, :after, or :xargs
; When place is :before or :after, x is assumed to be a list of events and is
; spliced in before or after the one identified.
; When place is :hints, :xargs, or :rule-classes, x is a legal value for that
; and replaces the value given (or is added as the value if none is present).
; Errors are caused if a command is not used.
#|
(edit-event-lst
'((defun foo (x) (+ 1 x))
(defun bar (x y) (declare (ignore x)) (declare (type integerp y)) (+ 1 y))
(defun mum1 (x y) (declare (ignore x)) (declare (xargs :measure (m x))) (declare (type integerp y)) (+ 1 y))
(defun mum2 (x y) (declare (ignore x) (xargs :measure (m x)) (type integerp y)) (+ 1 y))
(defthm lem1 (equal rhs lhs))
(defthm lem2 (equal rhs lhs) :rule-classes :rewrite)
(defthm lem3 (equal rhs lhs) :rule-classes :rewrite :hints (("Goal" :do-not-induct t)))
(defthm lem4 (equal rhs lhs) :hints (("Goal" :do-not-induct t)) :rule-classes :rewrite :otf-flg t))
'((defthm lem1 :before (a b c))
(defthm lem1 :before (d e f))
(defthm lem3 :hints (("Goal" a b c)))
(defthm lem1 :after (u v w))
(defthm lem1 :after (x y z))
(defun mum2 :xargs (u v w))
;(defun mum2 :guard-hints (a b c)) ; <--- illegal edit command
))
|#
(defun relevant-edit-commands (ev-type ev-name commands relevant-cmds leftover-cmds)
; We return (mv relevant-cmds leftover-cmds), where relevant-cmds are all the
; commands in commands that identify the event with the given type and name and
; leftover-commands are the other commands.
(cond
((endp commands)
(mv (rev1 relevant-cmds nil) (rev1 leftover-cmds nil)))
((and (eq ev-type (nth 0 (car commands)))
(eq ev-name (nth 1 (car commands))))
(relevant-edit-commands ev-type ev-name (cdr commands)
(cons (car commands) relevant-cmds)
leftover-cmds))
(t
(relevant-edit-commands ev-type ev-name (cdr commands)
relevant-cmds
(cons (car commands) leftover-cmds)))))
(defun replace-keyword-arg (key val lst)
(cond ((endp lst)
(list :key val))
((eq key (car lst))
(list* key val (cdr (cdr lst))))
(t (list* (car lst) (car (cdr lst))
(replace-keyword-arg key val (cdr (cdr lst)))))))
(defun edit-hints (event x)
(let ((name (nth 1 event))
(term (nth 2 event))
(alist (cdr (cdr (cdr event)))))
`(DEFTHM ,name ,term
,@(if (assoc-keyword :hints alist)
(replace-keyword-arg :hints x alist)
`(:hints ,x ,@alist)))))
(defun edit-rule-classes (event x)
(let ((name (nth 1 event))
(term (nth 2 event))
(alist (cdr (cdr (cdr event)))))
`(DEFTHM ,name ,term
,@(if (assoc-keyword :rule-classes alist)
(replace-keyword-arg :rule-classes x alist)
`(:rule-classes ,x ,@alist)))))
(defun replace-xargs (dcls x)
(cond ((endp dcls) `((DECLARE (XARGS ,@x))))
((and (eq (car (car dcls)) 'DECLARE)
(assoc 'XARGS (cdr (car dcls))))
(cons (cons 'DECLARE
(put-assoc-equal 'XARGS x (cdr (car dcls))))
(cdr dcls)))
(t (cons (car dcls)
(replace-xargs (cdr dcls) x)))))
(defun edit-xargs (event x)
(let ((name (nth 1 event))
(vars (nth 2 event))
(dcls (all-but-last (cdr (cdr (cdr event)))))
(body (nth (- (len event) 1) event)))
`(DEFUN ,name ,vars
,@(replace-xargs dcls x)
,body)))
(defun do-edit-command (cmd event before-events after-events)
(let ((ev-type (nth 0 cmd))
(place (nth 2 cmd))
(x (nth 3 cmd)))
(case place
(:before
(mv (append before-events x) event after-events))
(:after
(mv before-events event (append after-events x)))
(:hints
(cond
((eq ev-type 'defthm)
(mv before-events (edit-hints event x) after-events))
(t (mv nil
(er hard 'defsys
"The event editor cannot handle a :hints edit command ~
except on DEFTHM events. So ~x0 is an illegal edit ~
command."
cmd)
nil))))
(:rule-classes
(cond
((eq ev-type 'defthm)
(mv before-events (edit-rule-classes event x) after-events))
(t (mv nil
(er hard 'defsys
"The event editor cannot handle a :rule-classes edit ~
command except on DEFTHM events. So ~x0 is an illegal ~
edit command."
cmd)
nil))))
(:xargs
(cond
((eq ev-type 'defun)
(mv before-events (edit-xargs event x) after-events))
(t (mv nil
(er hard 'defsys
"The event editor cannot handle an :xargs edit command ~
except on DEFUN events. So ~x0 is an illegal edit ~
command."
cmd)
nil))))
(otherwise
(mv nil
(er hard 'defsys
"The event editor cannot handle the command ~x0. Legal ~
commands are (DEFTHM name :HINTS x), (DEFTHM name ~
:RULE-CLASSES x), (DEFUN name :XARGS x), (ev-type name ~
:BEFORE x), or (ev-type name :AFTER x)."
cmd)
nil)))))
(defun do-edit-commands (cmds event before-events after-events)
(cond
((endp cmds)
(mv before-events event after-events))
(t (mv-let (new-before-events new-event new-after-events)
(do-edit-command (car cmds) event before-events after-events)
(do-edit-commands (cdr cmds)
new-event new-before-events new-after-events)))))
(defun edit-event-lst (events commands)
(cond
((endp events)
(cond (commands
(er hard 'xdefsys
"The following commands were not used, ~x0."
commands))
(t nil)))
((and (consp (car events))
(consp (cdr (car events)))
(symbolp (cadr (car events))))
(mv-let (relevant-cmds leftover-cmds)
(relevant-edit-commands (car (car events))
(cadr (car events))
commands nil nil)
(mv-let (before-events new-event after-events)
(do-edit-commands relevant-cmds (car events) nil nil)
(append before-events
(cons new-event
(append after-events
(edit-event-lst (cdr events) leftover-cmds)))))))
(t (cons (car events)
(edit-event-lst (cdr events) commands)))))
(defmacro defsys (acl2::&key ld-flg modules edit-commands)
(mv-let
(amodule-lst max-a-regs)
(annotate-modules modules 0 nil nil 0)
(mv-let
(ccode id-to-label-table)
(compile-system '((CALL MAIN) (HALT))
amodule-lst max-a-regs)
; This system will require a total of 2*max-a-regs + 1 locals. The first max-var
; of them, locals 0, ..., max-var-1, are called the ``A registers''. The next
; max-var of them, namely max-var, max-var+1, ..., 2max-var-1, are the ``B
; registers''. The last, 2max-var, is the return-pc register. The A registers
; are used to hold the locals of the active module. The B registers are used
; merely to implement the basic operations of CALL and RET. (To enter a module
; with n locals, we pop n items off the stack and store them in the B
; registers. Then we push the relevant A registers to protect them. Then we
; move the B registers to the A registers for use by the module's code.
; Exiting upon RET is the symmetric operation.)
(let* ((switch-table (switch-table ccode nil))
(acode (assemble ccode switch-table nil max-a-regs))
(label-table (label-table acode 0 nil))
(event-lst
`((defconst *amodule-lst* ',amodule-lst)
(defconst *max-a-regs* ,max-a-regs)
(defconst *ccode* ',ccode)
(defconst *acode* ',acode)
(defconst *psi* ',(link acode 0 label-table nil))
(defun psi () *psi*)
(defthm next-inst-psi
(implies (acl2::syntaxp (acl2::quotep i))
(equal (nth i (psi)) (nth i *psi*))))
(in-theory (disable psi (:executable-counterpart psi)))
(defconst *id-to-label-table* ',id-to-label-table)
(defconst *switch-table* ',switch-table)
(defconst *label-table* ',label-table)
,@(defconst-lst label-table)
; The code above generates the M1 byte code and our tables. Now we work on the
; verification events for each successive module. The following function is
; used in all the top-level clock functions, to compute the time to exit a
; call with a given id. From id we get the corresponding return pc label and
; then compute where that label occurs in list of return targets considered.
; If you look at expand-ret you see that jumpting to the first pc in lst takes
; 4 instructions, the next 8, etc., until you get to the last pc in lst, which
; takes just 1 more instruction than the previous label took.
(defun exit-clock (fn id)
(let* ((exit (cdr (assoc id *id-to-label-table*)))
(lst (cdr (assoc fn *switch-table*)))
(tail (member-equal exit lst)))
(cond ((or (endp tail)
(endp (cdr tail)))
(+ 1 (* 4 (nfix (- (len lst) 1)))))
(t (* 4 (+ 1 (nfix (- (len lst) (len tail)))))))))
; This is used in the code correctness theorems and returns the final pc given
; the called routine and the id of the call.
(defun final-pc (fn id)
(cond ((assoc-equal id *id-to-label-table*)
(let* ((label (cdr (assoc-equal id *id-to-label-table*))))
(cond ((member label (cdr (assoc fn *switch-table*)))
(cdr (assoc label *label-table*)))
(t *illegal-final-pc*))))
(t *illegal-final-pc*)))
(defun ready-at (pc local-names d s)
(and (acl2::true-listp s)
(equal (len s) 4)
(equal (pc s) pc)
;(acl2::true-listp (locals s))
(<= ,(+ (* 2 max-a-regs) 1) (len (locals s)))
(name-locals local-names (locals s) 0)
(<= d (len (stack s)))
(equal (program s) (psi))))
,@(verification-events-for-modules amodule-lst nil
max-a-regs amodule-lst)
))
(elaborated-event-lst
(edit-event-lst event-lst edit-commands))
(final-event-lst
`((defconst *defsys-events*
',event-lst)
(defconst *elaborated-defsys-events*
',elaborated-event-lst)
,@elaborated-event-lst)))
(if ld-flg
`(ld ',final-event-lst :ld-pre-eval-print t)
`(encapsulate nil ,@final-event-lst))))))
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