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; Copyright (C) 2014, Regents of the University of Texas
; Contributed by Matt Kaufmann (original date October, 2012)
; based on earlier work by Sol Swords.
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
; (certify-book "meta-extract-simple-test" 0 t :ttags :all)
; This example is based on the first one in
; clause-processors/meta-extract-user.lisp, but is simpler -- in particular, it
; does not include that book.
; For a more interesting tutorial example on meta-extract hypotheses, see
; community book
; /projects/acl2/acl2/books/demos/nth-update-nth-meta-extract.lisp.
(in-package "ACL2")
; The following is only needed for developer builds (using ACL2_DEVEL), which
; put some meta-extract functions in :program mode.
(include-book "system/meta-extract" :dir :system)
(include-book "misc/without-waterfall-parallelism" :dir :system)
(encapsulate
((bar (x) t))
(local (defun bar (x) (declare (ignore x)) 1))
(defthm bar-posp
(posp (bar u))
:rule-classes nil))
(defevaluator nthmeta-ev nthmeta-ev-lst
((typespec-check ts x)
(if a b c)
(equal a b)
(not a)
(iff a b)
(implies a b)
(nth n x)
(car x)
(binary-+ x y)
(fix x)
(posp x)
(bar x)))
; Here is a trivial test of the use of meta-extract-global-fact in
; clause-processor rules.
(defun bar-posp-cl-proc (cl hint state)
(declare (xargs :guard t
:stobjs state)
(ignore hint))
(if (equal (meta-extract-formula 'bar-posp state)
'(POSP (BAR U)))
(value (list (cons '(not (posp (bar u))) cl)))
(value (list cl))))
(defthm correctness-of-bar-posp-cl-proc
(implies (and (pseudo-term-listp cl)
(alistp a)
(nthmeta-ev (meta-extract-global-fact '(:formula bar-posp)
state)
a)
(nthmeta-ev (conjoin-clauses
(clauses-result
(bar-posp-cl-proc cl hint state)))
a))
(nthmeta-ev (disjoin cl) a))
:rule-classes :clause-processor)
(without-waterfall-parallelism
(defthm bar-posp-cl-proc-test
(integerp (bar u))
:hints (("Goal"
:clause-processor
(bar-posp-cl-proc clause nil state)))))
; Our first example for :meta rules is based on one in
; books/clause-processors/meta-extract-user.lisp.
; First we develop a meta rule that implements the following fact. (We do not
; need this event.)
(defthm nth-when-symbolp
(implies (symbolp n)
(equal (nth n x) (car x)))
:rule-classes nil)
(defun nth-symbolp-metafn (term mfc state)
(declare (xargs :stobjs state))
(case-match term
(('nth n x)
(if (equal (mfc-ts n mfc state :forcep nil) *ts-symbol*)
`(car ,x)
(prog2$ (cw "Oops, the typeset of n is ~x0~%"
(mfc-ts n mfc state :forcep nil))
term)))
(& term)))
(defthm nth-symbolp-meta
(implies (nthmeta-ev (meta-extract-contextual-fact
`(:typeset ,(cadr term))
mfc
state)
a)
(equal (nthmeta-ev term a)
(nthmeta-ev (nth-symbolp-metafn term mfc state) a)))
:rule-classes ((:meta :trigger-fns (nth))))
(defstub foo (x) t)
(defthm foo-test
(implies (symbolp (foo x))
(equal (nth (foo x) y)
(car y)))
:hints (("Goal" :in-theory '(nth-symbolp-meta))))
(encapsulate
()
(local (include-book "arithmetic-5/top" :dir :system))
(defun nth-symbolp-metafn-alt (term mfc state)
(declare (xargs :stobjs state))
(case-match term
(('nth n x)
(if (let ((ts-n (mfc-ts n mfc state :forcep nil)))
(and (integerp ts-n) ; for guard verification
(<= *min-type-set* ts-n) ; for guard verification
(<= ts-n *max-type-set*) ; for guard verification
(ts-subsetp ts-n *ts-symbol*)))
`(car ,x)
(prog2$ (cw "Oops, the typeset of n is ~x0~%"
(mfc-ts n mfc state :forcep nil))
term)))
(& term)))
(defthm nth-symbolp-meta-alt
(implies (nthmeta-ev (meta-extract-contextual-fact
`(:typeset ,(cadr term)) mfc state)
a)
(equal (nthmeta-ev term a)
(nthmeta-ev (nth-symbolp-metafn-alt term mfc state) a)))
:rule-classes ((:meta :trigger-fns (nth)))))
(defthm foo-test-alt
(implies (symbolp (foo x))
(equal (nth (foo x) y)
(car y)))
:hints (("Goal" :in-theory '(nth-symbolp-meta-alt))))
; Now, a slight variant involving subtypes, implementing this fact: (We do not
; need this event.)
(defthm plus-identity
(implies (and (acl2-numberp n)
(not (acl2-numberp x)))
(equal (+ n x)
n))
:rule-classes nil)
(encapsulate
()
(local (include-book "arithmetic-5/top" :dir :system))
(defun plus-identity-metafn (term mfc state)
(declare (xargs :stobjs state))
(case-match term
(('binary-+ n x)
(let ((ts-n (mfc-ts n mfc state :forcep nil))
(ts-x (mfc-ts x mfc state :forcep nil)))
(if (and (integerp ts-n) ; for guard verification
(integerp ts-x) ; for guard verification
(<= *min-type-set* ts-n) ; for guard verification
(<= *min-type-set* ts-x) ; for guard verification
(<= ts-n *max-type-set*) ; for guard verification
(<= ts-x *max-type-set*) ; for guard verification
(ts= ts-n *ts-positive-integer*)
(ts= ts-x *ts-character*))
n
(prog2$ (cw "Oops, the typesets of n and x are ~x0 and ~x1~%"
(mfc-ts n mfc state :forcep nil)
(mfc-ts x mfc state :forcep nil))
term))))
(& term))))
(defthm plus-identity-meta
(implies (and (nthmeta-ev (meta-extract-contextual-fact
`(:typeset ,(cadr term)) mfc state)
a)
(nthmeta-ev (meta-extract-contextual-fact
`(:typeset ,(caddr term)) mfc state)
a))
(equal (nthmeta-ev term a)
(nthmeta-ev (plus-identity-metafn term mfc state) a)))
:rule-classes ((:meta :trigger-fns (binary-+))))
(defthm plus-identity-test
(implies (and (posp (foo x))
(characterp (foo y)))
(equal (+ (foo x) (foo y))
(foo x)))
:hints (("Goal" :in-theory '(posp plus-identity-meta))))
(encapsulate
()
(local (include-book "arithmetic-5/top" :dir :system))
(defun plus-identity-2-metafn (term mfc state)
(declare (xargs :stobjs state))
(case-match term
(('binary-+ ('bar n) y)
(cond
((equal (meta-extract-formula 'bar-posp state)
'(POSP (BAR U)))
(let ((ts-y (mfc-ts y mfc state :forcep nil)))
(if (and (integerp ts-y) ; for guard verification
(<= *min-type-set* ts-y) ; for guard verification
(<= ts-y *max-type-set*) ; for guard verification
(ts= ts-y *ts-character*))
(cadr term)
(prog2$ (cw "Oops, the typesets of n and y are ~x0 and ~x1~%"
(mfc-ts n mfc state :forcep nil)
(mfc-ts y mfc state :forcep nil))
term))))
(t term)))
(& term))))
(defthm plus-identity-2-meta
(implies (and (nthmeta-ev (meta-extract-global-fact '(:formula bar-posp)
state)
(list (cons 'u
(nthmeta-ev (cadr (cadr term))
a))))
(nthmeta-ev (meta-extract-contextual-fact
`(:typeset ,(caddr term)) mfc state)
a))
(equal (nthmeta-ev term a)
(nthmeta-ev (plus-identity-2-metafn term mfc state) a)))
:rule-classes ((:meta :trigger-fns (binary-+))))
(defthm plus-identity-2-test
(implies (and (posp (bar x))
(characterp (foo y)))
(equal (+ (bar x) (foo y))
(bar x)))
:hints (("Goal" :in-theory '(plus-identity-2-meta))))
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