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|
; S-Expressions for 4-Valued Logic
; Copyright (C) 2010-2012 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
; compose-sexpr.lisp
; Original author: Sol Swords <sswords@centtech.com>
;
; This is for a theorem about a block that looks like this
;
;
; +================================================+
; \ +====+ \
; \ +---------------------->+ b2ins \ \ out2 \
; \ | |------>\blk2\---->+ \
; --->\--| +====+ | \ \ | \ outs
; ins \ | \ \ b1out +--->+ \ \ |->\------
; \ |ins1 \blk1\------>| +====+ | \
; \ +---->\ \ | | \
; \ \ \ +---------------------->+ \
; \ +====+ \
; +================================================+
;
; Here any fork in the signals allows overlap between the two branches -- e.g.,
; some signals in b1out may be routed to both the blk2 inputs and to the
; output. However, any merge between signals requires that the two incoming
; sets be disjoint -- e.g. because signals form out2 and b1out merge to form
; outs, out2 and b1out may not contain the same signals.
(in-package "ACL2")
(include-book "bitspecs")
(include-book "sexpr-to-faig")
(include-book "sexpr-advanced")
(include-book "centaur/misc/hons-extra" :dir :system)
(defund marker (x) (declare (ignore x)) t)
(in-theory (disable marker (marker) (:type-prescription marker)))
(encapsulate
;; -spec-: alist specs, which describe how to convert a set of "formatted"
;; data (numbers, Booleans, etc) into an alist mapping variables to booleans,
;; and back. Also specifies what kind of inputs these must be and what
;; names must be bound in the alist.
(((cmp4v-spec-ins) => *)
((cmp4v-spec-ins1) => *)
((cmp4v-spec-b1out) => *)
((cmp4v-spec-b2ins) => *)
((cmp4v-spec-out) => *)
((cmp4v-spec-out2) => *)
;; -exprs-: alist mapping names to 4v-sexprs
((cmp4v-exprs-blk1) => *)
((cmp4v-exprs-blk2) => *)
((cmp4v-exprs-whole) => *)
;; -hyp: requirements about the formatted data
;; -prop: goal to be proved about formatted data
((cmp4v-blk1-hyp *) => *)
((cmp4v-blk2-hyp *) => *)
((cmp4v-blk1-prop * *) => *)
((cmp4v-blk2-prop * *) => *)
((cmp4v-whole-hyp *) => *)
((cmp4v-whole-prop * *) => *))
(set-ignore-ok t)
(set-irrelevant-formals-ok t)
(local
(progn
(defun cmp4v-spec-ins () nil)
(defun cmp4v-spec-ins1 () nil)
(defun cmp4v-spec-b1out () nil)
(defun cmp4v-spec-b2ins () nil)
(defun cmp4v-spec-out () nil)
(defun cmp4v-spec-out2 () nil)
(defun cmp4v-exprs-blk1 () nil)
(defun cmp4v-exprs-blk2 () nil)
(defun cmp4v-exprs-whole () nil)
(defun cmp4v-blk1-hyp (ins1) nil)
(defun cmp4v-blk2-hyp (b2ins) nil)
(defun cmp4v-blk1-prop (ins1 b1out) t)
(defun cmp4v-blk2-prop (b2ins out2) t)
(defun cmp4v-whole-hyp (ins) nil)
(defun cmp4v-whole-prop (ins out) t)))
;; These two constraints are likely provable by symbolic simulation:
(defthm cmp4v-blk1-ok
(implies (and
(marker 'blk1-ok)
;; ins1 is a set of formatted inputs fitting the shape specified
;; by -spec-ins
(params-for-4v-bitspecp (cmp4v-spec-ins1) ins1)
;; ins1 satisfy the hyp for blk1
(cmp4v-blk1-hyp ins1))
(b* ( ;; transform ins1 to an alist
(al (params-to-4v-alist (cmp4v-spec-ins1) ins1))
;; evaluate the blk1 SEXPRs using the alist
(ev (4v-sexpr-eval-alist (cmp4v-exprs-blk1) al))
;; transform that alist into formatted data according to
;; -spec-ints
(b1out (4v-alist-to-params (cmp4v-spec-b1out) ev)))
(and
;; The resulting formatted data fits the shape specified by -spec-ints
(params-for-4v-bitspecp (cmp4v-spec-b1out) b1out)
;; The result satisfies the property required of blk1.
(cmp4v-blk1-prop ins1 b1out)))))
(defthm cmp4v-blk2-ok
(implies (and
(marker 'blk2-ok)
;; ins2 and ints are sets of formatted inputs fitting the shapes
;; specified by -spec-ins2 and -spec-ints, resp.
(params-for-4v-bitspecp (cmp4v-spec-b2ins) b2ins)
;; ins2 and ints together satisfy the hyp for blk2
(cmp4v-blk2-hyp b2ins))
(b* ( ;; transform ints and ins2 to an alist
(al (params-to-4v-alist (cmp4v-spec-b2ins) b2ins))
;; evaluate the blk2 SEXPRs using the alist
(ev (4v-sexpr-eval-alist (cmp4v-exprs-blk2) al))
;; transform that alist into formatted data according to
;; -spec-out2.
(out2 (4v-alist-to-params (cmp4v-spec-out2) ev)))
(and
;; The resulting formatted data fits the shape specified by -spec-out2
(params-for-4v-bitspecp (cmp4v-spec-out2) out2)
;; The result satisfies the property required of blk2.
(cmp4v-blk2-prop b2ins out2)))))
;; These three might need some theorem proving:
(defthm cmp4v-whole-hyp-impl-blk1-hyp
;; If the inputs are well-formed and the hyp for the whole block is
;; satisfied, then the hyp for blk1 is satisfied by the extraction of the
;; blk1 inputs.
(implies (and (marker 'hyp-implies-blk1-hyp)
(cmp4v-whole-hyp ins)
(params-for-4v-bitspecp (cmp4v-spec-ins) ins))
(cmp4v-blk1-hyp
(4v-alist-to-params
(cmp4v-spec-ins1)
(params-to-4v-alist
(cmp4v-spec-ins) ins)))))
(defthm cmp4v-blk1-prop-implies-blk2-hyp
;; If the hyp for the whole thing and for blk1 are both satisfied and the
;; inputs and cut signals are of the right shape, then the blk2 hyp is
;; satisfied.
(implies
(marker 'prop1-implies-blk2-hyp)
(let* ((ins1 (4v-alist-to-params
(cmp4v-spec-ins1)
(params-to-4v-alist
(cmp4v-spec-ins) ins)))
(b2ins (4v-alist-to-params
(cmp4v-spec-b2ins)
(append (params-to-4v-alist (cmp4v-spec-b1out) b1out)
(params-to-4v-alist (cmp4v-spec-ins) ins)))))
(implies (and (cmp4v-whole-hyp ins)
(cmp4v-blk1-prop ins1 b1out)
(params-for-4v-bitspecp (cmp4v-spec-ins) ins)
(params-for-4v-bitspecp (cmp4v-spec-b1out) b1out))
(cmp4v-blk2-hyp b2ins)))))
(defthm cmp4v-blk1-and-blk2-props-imply-whole
;; If the blk1 and blk2 props are satisfied, all the data is of the right
;; shapes, and the hyp for the whole thing is satisfied, then the goal
;; property is satisfied.
(implies
(marker 'props-imply-whole)
(let* ((ins1 (4v-alist-to-params
(cmp4v-spec-ins1)
(params-to-4v-alist
(cmp4v-spec-ins) ins)))
(b2ins (4v-alist-to-params
(cmp4v-spec-b2ins)
(append (params-to-4v-alist (cmp4v-spec-b1out) b1out)
(params-to-4v-alist (cmp4v-spec-ins) ins))))
(outs (4v-alist-to-params
(cmp4v-spec-out)
(append (params-to-4v-alist
(cmp4v-spec-b1out) b1out)
(params-to-4v-alist
(cmp4v-spec-out2) out2)))))
(implies (and (params-for-4v-bitspecp (cmp4v-spec-ins) ins)
(params-for-4v-bitspecp (cmp4v-spec-b1out) b1out)
(params-for-4v-bitspecp (cmp4v-spec-out2) out2)
(cmp4v-whole-hyp ins)
(cmp4v-blk1-prop ins1 b1out)
(cmp4v-blk2-prop b2ins out2))
(cmp4v-whole-prop ins outs)))))
(defthm cmp4v-sexprs-whole-are-composition
;; SEXPR composition of blk1 and blk2 gives the whole block
(implies (marker 'sexprs-are-composition)
(4v-sexpr-alist-equiv
(cmp4v-exprs-whole)
(make-fast-alist
(4v-sexpr-alist-extract
(alist-keys (cmp4v-exprs-whole))
(make-fast-alist
(append (cmp4v-exprs-blk1)
(4v-sexpr-restrict-alist
(cmp4v-exprs-blk2)
(make-fast-alist (cmp4v-exprs-blk1))))))))))
(defthm cmp4v-misc-reqs
(implies (marker 'misc-reqs)
(and
;; The input variables used in the blk1 SEXPRs are a subset of the variables
;; mentioned in -spec-ins1
(hons-subset (4v-sexpr-vars-list (alist-vals (cmp4v-exprs-blk1)))
(4v-bitspec-vars (cmp4v-spec-ins1)))
;; The input variables used in the blk2 SEXPRs are a subset of
;; the variables mentioned in b2ins.
(hons-subset (4v-sexpr-vars-list (alist-vals (cmp4v-exprs-blk2)))
(4v-bitspec-vars (cmp4v-spec-b2ins)))
;; The variables of b1out are a subset of the keys of exprs-blk1
(hons-subset (4v-bitspec-vars (cmp4v-spec-b1out))
(alist-keys (cmp4v-exprs-blk1)))
;; The variables of out2 are a subset of the keys of exprs-blk2
(hons-subset (4v-bitspec-vars (cmp4v-spec-out2))
(alist-keys (cmp4v-exprs-blk2)))
;; The keys of exprs-whole are a superset of the vars of spec-out.
(hons-subset (4v-bitspec-vars (cmp4v-spec-out))
(alist-keys (cmp4v-exprs-whole)))
;; No duplicate signals between the inputs and the outputs of blk1
(not (hons-intersect-p (alist-keys (cmp4v-exprs-blk1))
(4v-bitspec-vars (cmp4v-spec-ins))))
;; No duplicate signals between the outputs of blk1 and the
;; outputs of blk2
(not (hons-intersect-p (alist-keys (cmp4v-exprs-blk1))
(alist-keys (cmp4v-exprs-blk2))))
;; No duplicate signals between the inputs and the outputs of blk2
(not (hons-intersect-p (alist-keys (cmp4v-exprs-blk2))
(4v-bitspec-vars (cmp4v-spec-ins))))
;; The input bitspec for block1 is a subset of the full
;; input bitspec
(hons-subset (hons-copy (cmp4v-spec-ins1))
(hons-copy (cmp4v-spec-ins)))
;; The block2 input bitspec is a subset of the union of the ins
;; and b1out bitspecs
(hons-subset (hons-copy (cmp4v-spec-b2ins))
(hons-copy (append (cmp4v-spec-ins)
(cmp4v-spec-b1out))))
;; The output bitspec is a subset of the union of the outputs
;; from the two blocks.
(hons-subset (hons-copy (cmp4v-spec-out))
(hons-copy (append (cmp4v-spec-b1out)
(cmp4v-spec-out2))))
;; No duplicate names in the internal signals or inputs
(not (hons-dups-p (4v-bitspec-vars (cmp4v-spec-ins))))
(not (hons-dups-p (4v-bitspec-vars (cmp4v-spec-ins1))))
(not (hons-dups-p (4v-bitspec-vars (cmp4v-spec-out))))
(not (hons-dups-p (4v-bitspec-vars (cmp4v-spec-out2))))
(not (hons-dups-p (4v-bitspec-vars (cmp4v-spec-b1out))))
(not (hons-dups-p (4v-bitspec-vars (cmp4v-spec-b2ins))))
;; All alist-specs are well-formed
(4v-bitspecp (cmp4v-spec-ins))
(4v-bitspecp (cmp4v-spec-ins1))
(4v-bitspecp (cmp4v-spec-out))
(4v-bitspecp (cmp4v-spec-out2))
(4v-bitspecp (cmp4v-spec-b1out))
(4v-bitspecp (cmp4v-spec-b2ins))))))
(local
(progn
(in-theory (enable 4v-alists-agree-to-4v-env-equiv))
(defthm 4v-alists-agree-for-new-append-extract-lemma
(implies (and (subsetp-equal keys (append xkeys (alist-keys b)))
(subsetp-equal xkeys (alist-keys a))
(not (intersectp-equal (alist-keys a) (alist-keys b))))
(4v-alists-agree keys (append (4v-alist-extract xkeys a) b)
(append a b)))
:hints (("goal" :do-not-induct t
:in-theory (e/d ()
(4v-env-equiv-to-key-and-env-equiv
4v-fix)))
(witness :ruleset 4v-env-equiv-witnessing)
(and stable-under-simplificationp
'(:in-theory (e/d (hons-assoc-equal-iff-member-alist-keys
alists-compatible-hons-assoc-equal)
(alist-keys-member-hons-assoc-equal
4v-fix))))
(set-reasoning)))
(defthm 4v-sexpr-eval-alist-new-append-extract-lemma
(implies (and (subsetp-equal (4v-sexpr-vars-list (alist-vals x))
(append xkeys (alist-keys b)))
(subsetp-equal xkeys (alist-keys a))
(not (intersectp-equal (alist-keys a) (alist-keys b))))
(equal (4v-sexpr-eval-alist x (append (4v-alist-extract xkeys a) b))
(4v-sexpr-eval-alist x (append a b))))
:hints(("Goal" :in-theory (disable 4v-sexpr-eval))))
(defthm 4v-alist-to-params-new-append-extract-lemma
(implies (and (subsetp-equal (4v-bitspec-vars spec)
(append xkeys (alist-keys b)))
(subsetp-equal xkeys (alist-keys a))
(not (intersectp-equal (alist-keys a) (alist-keys b))))
(equal (4v-alist-to-params spec (append (4v-alist-extract xkeys a) b))
(4v-alist-to-params spec (append a b))))
:hints(("Goal" :in-theory (e/d
(4v-alist-to-params-when-4v-alists-agree-rw)
(4v-alist-to-params)))))
(defthm 4v-alists-agree-4v-alist-extract
(implies (subsetp-equal keys1 keys)
(4v-alists-agree keys1 (4v-alist-extract keys a) a))
:hints (("goal" :do-not-induct t
:in-theory (disable 4v-env-equiv-to-key-and-env-equiv
4v-fix))
(witness :ruleset 4v-env-equiv-witnessing)
(and stable-under-simplificationp
'(:in-theory (e/d (hons-assoc-equal-iff-member-alist-keys)
(alist-keys-member-hons-assoc-equal
4v-fix))))
(set-reasoning)
(and stable-under-simplificationp
'(:in-theory (e/d (alist-keys-member-hons-assoc-equal)
(hons-assoc-equal-iff-member-alist-keys
4v-fix))))))
(defthm 4v-sexpr-eval-alist-4v-alist-extract
(implies (subsetp-equal (4v-sexpr-vars-list (alist-vals x))
keys)
(equal (4v-sexpr-eval-alist x (4v-alist-extract keys a))
(4v-sexpr-eval-alist x a)))
:hints(("Goal" :in-theory (disable 4v-sexpr-eval))))
(defthm 4v-alist-to-params-4v-alist-extract
(implies (subsetp-equal (4v-bitspec-vars spec) keys)
(equal (4v-alist-to-params spec (4v-alist-extract keys a))
(4v-alist-to-params spec a)))
:hints (("goal" :in-theory (e/d (4v-alist-to-params-when-4v-alists-agree-rw)
(4v-alists-agree-to-4v-env-equiv)))))
(defthm 4v-alist-for-bitspecp-4v-alist-extract
(implies (subsetp-equal (4v-bitspec-vars spec) keys)
(equal (4v-alist-for-bitspecp spec (4v-alist-extract keys a))
(4v-alist-for-bitspecp spec a)))
:hints (("goal" :in-theory (e/d (4v-alist-for-bitspecp-when-4v-alists-agree-rw)
(4v-alists-agree-to-4v-env-equiv)))))
(defthm 4v-sexpr-eval-alist-4v-sexpr-alist-extract
(equal (4v-sexpr-eval-alist (4v-sexpr-alist-extract keys al) env)
(4v-alist-extract keys (4v-sexpr-eval-alist al env))))
(defthm 4v-alist-for-bitspec-entryp-when-member2
(implies (and (member-equal x spec)
(4v-alist-for-bitspecp spec alist))
(4v-alist-for-bitspec-entryp x alist))
:hints(("Goal" :in-theory (e/d (member-equal)
(4v-alist-for-bitspec-entryp)))))
(defthm 4v-alist-for-bitspecp-when-subset
(implies (and (subsetp-equal spec1 spec)
(4v-alist-for-bitspecp spec alist))
(4v-alist-for-bitspecp spec1 alist))
:hints(("Goal" :in-theory (e/d (subsetp-equal)
(4v-alist-for-bitspec-entryp)))))
(defthm 4v-alists-agree-append-extract-second
(implies (subsetp-equal keys
(append (alist-keys al1) keys2))
(4v-alists-agree keys (append al1 (4v-alist-extract keys2 al2))
(append al1 al2)))
:hints (("goal" :in-theory (e/d (hons-assoc-equal-iff-member-alist-keys
hons-assoc-equal-when-not-member-alist-keys)
(4v-alists-agree-to-4v-env-equiv
4v-fix
alist-keys-member-hons-assoc-equal))
:do-not-induct t)
(witness :ruleset (4v-alists-agree-witnessing
4v-alists-agree-4v-lookup-ex))
(witness :ruleset set-reasoning-no-consp)))
(defthm 4v-sexpr-eval-alist-append-extract-second
(implies (subsetp-equal (4v-sexpr-vars-list (alist-vals x))
(append (alist-keys al1) keys2))
(equal (4v-sexpr-eval-alist x (append al1 (4v-alist-extract keys2 al2)))
(4v-sexpr-eval-alist x (append al1 al2))))
:hints(("Goal" :in-theory (disable 4v-sexpr-eval))))
(defthm 4v-alist-to-params-append-extract-second
(implies (subsetp-equal (4v-bitspec-vars spec)
(append (alist-keys al1) keys2))
(equal (4v-alist-to-params spec (append al1 (4v-alist-extract keys2 al2)))
(4v-alist-to-params spec (append al1 al2))))
:hints(("Goal" :in-theory (e/d (4v-alist-to-params-when-4v-alists-agree-rw)
(4v-alist-to-params)))))
(defthm 4v-alist-for-bitspecp-append-when-first-covers
(implies (subsetp-equal (4v-bitspec-vars spec)
(alist-keys a))
(equal (4v-alist-for-bitspecp spec (append a b))
(4v-alist-for-bitspecp spec a)))
:hints(("Goal" :in-theory (e/d (4v-alist-for-bitspecp-when-4v-alists-agree-rw)
(4v-alist-for-bitspec-entryp append)))))
(defthm bitspec-member-var-subsets
(implies (member-equal a b)
(subsetp-equal (4v-bitspec-entry-vars a) (4v-bitspec-vars b)))
:hints(("Goal" :in-theory (e/d (subsetp-equal 4v-bitspec-vars)
(4v-bitspec-entry-vars)))))
(defthm bitspec-subsets-vars-subsets
(implies (subsetp-equal a b)
(subsetp-equal (4v-bitspec-vars a) (4v-bitspec-vars b)))
:hints(("Goal" :in-theory (e/d (subsetp-equal 4v-bitspec-vars)
(4v-bitspec-entry-vars)))))
(defthm 4v-bitspec-vars-append
(equal (4v-bitspec-vars (append a b))
(append (4v-bitspec-vars a) (4v-bitspec-vars b)))
:hints(("Goal" :in-theory (disable 4v-bitspec-entry-vars))))
(defthm cmp4v-blk2-vars-subset-of-ints-and-ins2
(subsetp-equal (4v-sexpr-vars-list (alist-vals (cmp4v-exprs-blk2)))
(append (4v-bitspec-vars (cmp4v-spec-b1out))
(4v-bitspec-vars (cmp4v-spec-ins))))
:hints (("goal" :use ((:instance bitspec-subsets-vars-subsets
(a (cmp4v-spec-b2ins))
(b (append (cmp4v-spec-b1out)
(cmp4v-spec-ins))))
cmp4v-misc-reqs)
:in-theory (e/d (marker)
(bitspec-subsets-vars-subsets
cmp4v-misc-reqs)))))
(defthm subsetp-equal-bitspec-vars-append
(implies (subsetp-equal a (append b c))
(subsetp-equal (4v-bitspec-vars a)
(append (4v-bitspec-vars b)
(4v-bitspec-vars c))))
:hints (("goal" :use ((:instance bitspec-subsets-vars-subsets
(b (append b c)))))))
(defthm cmp4v-vars-out-subset-of-b1out-and-out2
(subsetp-equal (4v-bitspec-vars (cmp4v-spec-out))
(append (4v-bitspec-vars (cmp4v-spec-b1out))
(4v-bitspec-vars (cmp4v-spec-out2))))
:hints (("goal" :use cmp4v-misc-reqs
:in-theory (e/d (marker) (cmp4v-misc-reqs)))))
(defthm cmp4v-vars-of-out-subset-of-blk1-out2
(subsetp-equal (4v-bitspec-vars (cmp4v-spec-out))
(append (alist-keys (cmp4v-exprs-blk1))
(4v-bitspec-vars (cmp4v-spec-out2))))
:hints (("goal" :use cmp4v-misc-reqs
:in-theory (e/d (marker) (cmp4v-misc-reqs)))))
(defthm out2-vars-not-intersecting-blk1-keys
(not (intersectp-equal (4v-bitspec-vars (cmp4v-spec-out2))
(alist-keys (cmp4v-exprs-blk1))))
:hints (("goal" :use cmp4v-misc-reqs
:in-theory (e/d (marker) (cmp4v-misc-reqs)))
(witness :ruleset set-reasoning-no-consp)))
(defthm cmp4v-b1out-vars-not-intersecting-ins
(not (intersectp-equal (4v-bitspec-vars (cmp4v-spec-b1out))
(4v-bitspec-vars (cmp4v-spec-ins))))
:hints (("goal" :use cmp4v-misc-reqs
:in-theory (e/d ((marker))
(cmp4v-misc-reqs)))
(set-reasoning)))
(in-theory (e/d* ()
(4v-sexpr-eval-alist
set::double-containment
4v-fix 4vp
4v-alist-to-params
4v-bitspec-vars
4v-bitspec-entry-vars
params-to-4v-alist
(:rules-of-class :type-prescription :here)
no-duplicatesp-equal-non-cons
4v-alist-extract not
4v-bitspecp
no-duplicatesp-equal
subsetp-when-atom-left
append 4v-sexpr-alist-extract
subsetp-trans
intersectp-equal-non-cons-1
intersectp-equal-non-cons
4v-sexpr-vars-list
4v-sexpr-restrict-alist
alist-vals-when-atom
alist-keys-when-atom
4v-alist-to-params-append-when-first-does-not-intersect-vars
4v-alist-for-bitspecp
params-for-4v-bitspecp)
((:type-prescription 4v-bitspec-vars))))))
;; BOZO fix up the above thms so that this isnt' necessary
(local (in-theory (disable COMMUTATIVITY-OF-APPEND-UNDER-SET-EQUIV)))
(defthm cmp4v-generic-theorem
(implies (and
;; The formatted input vector, ins, is of the form dictated by
;; cmp4v-spec-ins.
(params-for-4v-bitspecp (cmp4v-spec-ins) ins)
;; ins satisfies the top-level hyp
(cmp4v-whole-hyp ins))
(b* ( ;; Form the input alist for the whole block
(al (params-to-4v-alist (cmp4v-spec-ins) ins))
;; Evaluate the whole block on the inputs
(ev (4v-sexpr-eval-alist (cmp4v-exprs-whole)
al))
;; Transform the result alist to formatted data
(out (4v-alist-to-params (cmp4v-spec-out) ev)))
(and
;; The results are of the format dictated by -spec-out2
(params-for-4v-bitspecp (cmp4v-spec-out) out)
;; The results satisfy the top-level property.
(cmp4v-whole-prop ins out))))
:hints ((b* ((ins1 '(4v-alist-to-params
(cmp4v-spec-ins1)
(params-to-4v-alist (cmp4v-spec-ins) ins)))
(b1out `(b* ((al (params-to-4v-alist (cmp4v-spec-ins1) ,ins1))
(ev (4v-sexpr-eval-alist (cmp4v-exprs-blk1) al)))
(4v-alist-to-params (cmp4v-spec-b1out) ev)))
(b2ins `(4v-alist-to-params
(cmp4v-spec-b2ins)
(append (params-to-4v-alist (cmp4v-spec-b1out) ,b1out)
(params-to-4v-alist (cmp4v-spec-ins) ins))))
(out2 `(b* ((al (params-to-4v-alist (cmp4v-spec-b2ins)
,b2ins))
(ev (4v-sexpr-eval-alist (cmp4v-exprs-blk2) al)))
(4v-alist-to-params (cmp4v-spec-out2) ev))))
`(:use (cmp4v-misc-reqs
(:instance
cmp4v-blk1-and-blk2-props-imply-whole
(out2 ,out2) (b1out ,b1out))
(:instance cmp4v-blk2-ok (b2ins ,b2ins))
(:instance cmp4v-blk1-ok (ins1 ,ins1))
(:instance cmp4v-blk1-prop-implies-blk2-hyp
(b1out ,b1out)))
:in-theory (e/d (marker)
(cmp4v-blk1-and-blk2-props-imply-whole
cmp4v-blk2-ok
cmp4v-blk1-ok
cmp4v-blk1-prop-implies-blk2-hyp
cmp4v-misc-reqs))
:do-not-induct t))))
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