/usr/share/acl2-6.3/books/str/coerce.lisp is in acl2-books-source 6.3-5.
This file is owned by root:root, with mode 0o644.
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; Copyright (C) 2009-2013 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: Jared Davis <jared@centtech.com>
;
; Additional copyright notice for coerce.lisp:
;
; This file is adapted from the Unicode library, Copyright (C) 2005-2013 by
; Jared Davis, which was also released under the GPL.
(in-package "STR")
(include-book "make-character-list")
(defsection str/coerce
:parents (coercion coerce)
:short "Lemmas about @(see coerce) available in the @(see str) library."
:long "<p>We typically do not want to ever reason about coerce. Instead, we
rewrite it away into @(see explode) or @(see implode).</p>"
(local (defthm coerce-string-lemma
(implies (and (character-listp x)
(character-listp y)
(not (equal x y)))
(not (equal (coerce x 'string)
(coerce y 'string))))
:hints(("Goal" :use ((:instance coerce-inverse-1 (x x))
(:instance coerce-inverse-1 (x y)))))))
(defthm equal-of-coerce-strings
(implies (and (character-listp x)
(character-listp y))
(equal (equal (coerce x 'string)
(coerce y 'string))
(equal x y))))
(local (defthm coerce-list-lemma
(implies (and (stringp x)
(stringp y)
(not (equal x y)))
(not (equal (coerce x 'list)
(coerce y 'list))))
:hints(("Goal" :use ((:instance coerce-inverse-2 (x x))
(:instance coerce-inverse-2 (x y)))))))
(defthm equal-of-coerce-lists
(implies (and (stringp x)
(stringp y))
(equal (equal (coerce x 'list)
(coerce y 'list))
(equal x y))))
;; Redundant with built-in ACL2 rule character-listp-coerce
;; (defthm character-listp-of-coerce-list
;; (character-listp (coerce x 'list)))
(defthm coerce-list-under-iff
(iff (coerce string 'list)
(and (stringp string)
(not (equal "" string))))
:hints(("Goal"
:in-theory (disable equal-of-coerce-lists)
:use ((:instance equal-of-coerce-lists
(x string)
(y ""))))))
(defthm length-of-coerce
;; Wow, coerce is sort of awful in that (coerce "foo" 'string) returns ""
;; and (coerce '(1 2 3) 'list) returns nil. This leads to a weird length
;; theorem. We normally just leave length enabled, so this rule won't have
;; many uses.
(equal (length (coerce x y))
(cond ((equal y 'list)
(if (stringp x)
(length x)
0))
(t
(if (stringp x)
0
(len x)))))
:hints(("Goal"
:use ((:instance completion-of-coerce
(x x)
(y y))))))
(defthm len-of-coerce-to-string
(equal (len (coerce x 'string))
0))
(defthm coerce-inverse-1-better
(equal (coerce (coerce x 'string) 'list)
(if (stringp x)
nil
(make-character-list x)))
:hints(("Goal"
:use ((:instance acl2::completion-of-coerce
(acl2::x x)
(acl2::y 'string))))))
(defthm coerce-inverse-2-better
(equal (coerce (coerce x 'list) 'string)
(if (stringp x)
x
"")))
(in-theory (disable coerce-inverse-1 coerce-inverse-2))
(defthm coerce-to-list-of-make-character-list
(equal (coerce (make-character-list x) 'string)
(coerce x 'string))
:hints(("Goal"
:use ((:instance acl2::completion-of-coerce
(acl2::x x)
(acl2::y 'string)))))))
(defsection explode
:parents (coercion coerce)
:short "Convert a string to a character list."
:long "<p>@(call explode) is logically nothing more than @('(coerce x
'list)').</p>
<p>Even though @(see coerce) is built into ACL2, we prefer to use @('explode') as
our normal form. We rewrite all uses of @('(coerce x 'list)') into
@('(str::explode x')') with the following rule:</p>
@(def coerce-to-list-removal)
<p>The basic rationale for this is that @('coerce')'s extra @(''list') argument
means we can't write, e.g., congruence relations about @('(coerce x 'list)'),
whereas this is no problem for @('(explode x)').</p>
<p>We do the same thing for @('(coerce x 'string)') — see @(see
implode).</p>
<p><b>BOZO</b> consider using misc/fast-coerce here.</p>"
(definlined explode (x)
(declare (type string x))
(coerce x 'list))
(in-theory (disable (:t explode)))
(local (in-theory (enable explode)))
(defthm true-listp-of-explode
(true-listp (explode x))
:rule-classes :type-prescription)
(defthm character-listp-of-explode
(character-listp (explode x)))
(defthm explode-when-not-stringp
(implies (not (stringp x))
(equal (explode x)
nil)))
(defthm equal-of-explodes
(implies (and (stringp x)
(stringp y))
(equal (equal (explode x)
(explode y))
(equal x y))))
(defthm explode-under-iff
(iff (explode string)
(and (stringp string)
(not (equal "" string)))))
(local (defthm l0
(implies (true-listp x)
(iff (consp x)
x))))
(defthm consp-of-explode
(equal (consp (explode string))
(and (stringp string)
(not (equal "" string)))))
(defthm coerce-to-list-removal
(equal (coerce x 'list)
(explode x)))
(local (in-theory (disable acl2::explode)))
(theory-invariant (incompatible (:definition acl2::explode$inline)
(:rewrite coerce-to-list-removal))))
(defsection implode
:parents (coercion coerce)
:short "Convert a character list into a string."
:long "<p>@(call implode) is logically nothing more than @('(coerce x
'string)').</p>
<p>Even though @(see coerce) is built into ACL2, we prefer to use @('implode')
as our normal form. We rewrite all uses of @('(coerce x 'string)') into
@('(str::implode x')') with the following rule:</p>
@(def coerce-to-string-removal)
<p>The basic rationale for this is that @('coerce')'s extra @(''string')
argument means we can't write, e.g., congruence relations about @('(coerce x
'string)'), whereas this is no problem for @('(implode x)').</p>
<p>We do the same thing for @('(coerce x 'list)') — see @(see
explode).</p>"
(definlined implode (x)
(declare (xargs :guard (character-listp x)))
(coerce x 'string))
(in-theory (disable (:t implode)))
(local (in-theory (enable implode)))
(defthm stringp-of-implode
(stringp (implode x))
:rule-classes :type-prescription)
(defthm equal-of-implodes
(implies (and (character-listp x)
(character-listp y))
(equal (equal (implode x)
(implode y))
(equal x y))))
(defthm implode-of-make-character-list
(equal (implode (make-character-list x))
(implode x)))
(local (defthm l0
(equal (equal (len x) 0)
(atom x))))
(defthm equal-of-implode-with-empty-string
(equal (equal "" (implode x))
(atom x))
:hints(("Goal"
:in-theory (disable length-of-coerce)
:use ((:instance length-of-coerce
(x x)
(y 'string))))))
(defthm coerce-to-string-removal
(equal (coerce x 'string)
(implode x)))
(local (in-theory (disable acl2::implode$inline)))
(theory-invariant (incompatible (:definition acl2::implode$inline)
(:rewrite coerce-to-string-removal))))
(defsection implode-explode-inversion
:parents (implode explode)
:short "Inversion theorems for @(see implode) and @(see explode)."
(local (in-theory (e/d (implode explode)
(coerce-to-string-removal
coerce-to-list-removal))))
(defthm explode-of-implode
(equal (explode (implode x))
(if (stringp x)
nil
(make-character-list x))))
(defthm implode-of-explode
(equal (implode (explode x))
(if (stringp x)
x
""))))
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