/usr/share/acl2-6.3/books/system/f-put-global.lisp is in acl2-books-source 6.3-5.
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; Copyright (C) 2008-2011 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/
;
; 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Sol Swords <sswords@centtech.com>
(in-package "ACL2")
;; This book proves that F-PUT-GLOBAL preserves STATE-P1, allowing it to be
;; used in guard-verified recursive logic-mode functions.
(local
(progn
(defthm all-boundp-add-pair
(implies (all-boundp al1 al2)
(all-boundp al1 (add-pair kay val al2))))
(in-theory (disable all-boundp add-pair))
(in-theory (disable open-channels-p
ordered-symbol-alistp
plist-worldp
symbol-alistp
timer-alistp
known-package-alistp
true-listp
32-bit-integer-listp
integer-listp
file-clock-p
readable-files-p
written-files-p
read-files-p
writeable-files-p
true-list-listp))))
(defund state-p1-good-worldp (world)
(and (plist-worldp world)
(symbol-alistp
(getprop 'acl2-defaults-table
'table-alist
nil 'current-acl2-world
world))
(known-package-alistp
(getprop 'known-package-alist
'global-value
nil 'current-acl2-world
world))))
(defthm state-p1-put-global
(implies (and (state-p1 state)
(symbolp key)
(cond ((eq key 'current-acl2-world) (state-p1-good-worldp val))
((eq key 'timer-alist) (timer-alistp val))
(t)))
(state-p1 (put-global key val state)))
:hints(("Goal" :in-theory (enable state-p1 state-p1-good-worldp))))
;; [Jared]: disabling the built-in ACL2 rule about assoc of add-pair because it
;; has unnecessary hyps.
(in-theory (disable assoc-add-pair))
(defthm assoc-add-pair-better
(equal (assoc-equal k1 (add-pair k2 v al))
(if (equal k1 k2)
(cons k2 v)
(assoc-equal k1 al)))
:hints(("Goal" :in-theory (enable add-pair))))
(defthm get-global-of-put-global
(equal (get-global k1 (put-global k2 val state))
(if (equal k1 k2)
val
(get-global k1 state))))
(defthm boundp-global1-of-put-global
(equal (boundp-global1 k1 (put-global k2 val state))
(or (equal k1 k2)
(boundp-global1 k1 state))))
(in-theory (disable boundp-global1 get-global put-global))
(defthmd not-in-ordered-symbol-alist-when-not-symbol
(implies (and (ordered-symbol-alistp a)
(not (symbolp k)))
(not (assoc k a)))
:hints(("Goal" :in-theory (enable ordered-symbol-alistp))))
(defthmd not-in-ordered-symbol-alist-when-<-first
(implies (and (ordered-symbol-alistp a)
(symbol-< k (caar a)))
(not (assoc k a)))
:hints (("goal" :induct (ordered-symbol-alistp a)
:in-theory (enable not-in-ordered-symbol-alist-when-not-symbol
ordered-symbol-alistp))))
(defthm add-pair-same
(implies (and (ordered-symbol-alistp a)
(assoc k a))
(equal (add-pair k (cdr (assoc k a)) a)
a))
:hints(("Goal" :in-theory (enable not-in-ordered-symbol-alist-when-<-first
not-in-ordered-symbol-alist-when-not-symbol
ordered-symbol-alistp
add-pair)
:induct t)
(and stable-under-simplificationp
'(:cases ((symbolp k))))))
(local
(defthm update-nth-same
(implies (< (nfix n) (len x))
(equal (update-nth n (nth n x) x)
x))))
(defthm put-global-of-same
(implies (and (state-p1 state)
(boundp-global1 k state))
(equal (put-global k (get-global k state) state)
state))
:hints(("Goal" :in-theory (enable get-global put-global
boundp-global1
state-p1))))
(defconst *basic-well-formed-state*
(list nil ;; open-input-channels
nil ;; open-output-channels
*initial-global-table* ;; global-table
nil ;; t-stack
nil ;; 32-bit-integer-stack
0 ;; big-clock-entry
nil ;; idates
nil ;; acl2-oracle
0 ;; file-clock
nil ;; readable-files
nil ;; written-files
nil ;; read-files
nil ;; writable-files
nil ;; list-all-package-names-lst
nil ;; user-stobj-alist1
))
(local (defthm state-p1-of-basic-well-formed-state
(state-p1 *basic-well-formed-state*)))
;; It might be nice to make this more transparent to the various state
;; accessors so that, e.g.,
;; (get-global x (state-fix state)) = (get-global x state).
;; But that's more complicated since we'd need an appropriate fixing function
;; for each field.
(defund state-fix (state)
(declare (xargs :stobjs state))
(mbe :logic (non-exec (if (state-p state)
state
*basic-well-formed-state*))
:exec state))
(defthm state-p1-of-state-fix
(state-p1 (state-fix state))
:hints(("Goal" :in-theory (enable state-fix))))
(defthm state-fix-when-state-p1
(implies (state-p1 state)
(equal (state-fix state)
state))
:hints(("Goal" :in-theory (enable state-fix))))
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