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|
; ACL2 String Library
; 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/
;
; 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.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "STR")
(include-book "coerce")
(include-book "std/lists/equiv" :dir :system)
(include-book "std/lists/rev" :dir :system)
(include-book "centaur/fty/fixtype" :dir :system)
(include-book "centaur/fty/basetypes" :dir :system)
(local (include-book "arithmetic"))
(in-theory (disable char<))
(defsection char<-order-thms
:parents (char<)
:short "Basic ordering facts about @('char<')."
(local (in-theory (enable char< char-fix)))
(defthm char<-irreflexive
(equal (char< x x)
nil))
(defthm char<-antisymmetric
(implies (char< x y)
(not (char< y x))))
(defthm char<-transitive
(implies (and (char< x y)
(char< y z))
(char< x z)))
(defthm char<-trichotomy-weak
(implies (and (not (char< x y))
(not (char< y x)))
(equal (chareqv x y)
t))
:hints(("Goal" :in-theory (enable chareqv))))
(defthm char<-trichotomy-strong
(equal (char< x y)
(and (not (chareqv x y))
(not (char< y x))))
:rule-classes ((:rewrite :loop-stopper ((x y))))))
(define character-list-fix ((x character-listp))
:parents (character-listp make-character-list)
:short "Inline fixing function for character lists."
:long "<p>This is identical to @(see make-character-list) except that the
guard requires that @('x') is already a @(see character-listp) so that, via
@(see mbe), we can just return @('x') without fixing it. We leave this
function enabled and never expect to reason about it.</p>"
:inline t
:enabled t
(mbe :logic (make-character-list x)
:exec x))
(define charlisteqv ((x character-listp)
(y character-listp))
:returns equivp
:parents (equivalences)
:inline t
:short "Case-sensitive character-list equivalence test."
:long "<p>@(call charlisteqv) determines if @('x') and @('y') are equivalent
when interpreted as character lists. That is, @('x') and @('y') must have the
same length and their elements must be @(see chareqv) to one another.</p>
<p>See also @(see icharlisteqv) for a case-insensitive alternative.</p>"
(mbe :logic
(equal (make-character-list x)
(make-character-list y))
:exec
(equal x y))
///
(defequiv charlisteqv)
(local (defun ind (x y)
(if (or (atom x) (atom y))
(list x y)
(ind (cdr x) (cdr y)))))
(defrefinement list-equiv charlisteqv
:hints(("Goal"
:in-theory (enable list-equiv)
:induct (ind x y))))
(local (in-theory (enable chareqv)))
(defcong charlisteqv chareqv (car x) 1)
(defcong charlisteqv charlisteqv (cdr x) 1)
(defcong chareqv charlisteqv (cons a x) 1)
(defcong charlisteqv charlisteqv (cons a x) 2)
(defcong charlisteqv equal (len x) 1 :hints(("Goal" :induct (ind x x-equiv))))
(defcong charlisteqv charlisteqv (list-fix x) 1)
(defcong charlisteqv chareqv (nth n x) 2)
(defcong charlisteqv charlisteqv (take n x) 2)
(defcong charlisteqv charlisteqv (nthcdr n x) 2)
(defcong charlisteqv charlisteqv (append x y) 1)
(defcong charlisteqv charlisteqv (append x y) 2)
(defcong charlisteqv charlisteqv (rev x) 1)
(defcong charlisteqv charlisteqv (revappend x y) 2)
(defcong charlisteqv charlisteqv (revappend x y) 1)
(defcong charlisteqv equal (make-character-list x) 1)
(defcong charlisteqv equal (implode x) 1
:hints(("Goal"
:in-theory (disable implode-of-make-character-list)
:use ((:instance implode-of-make-character-list (x x))
(:instance implode-of-make-character-list (x x-equiv))))))
(defthm charlisteqv-when-not-consp-left
(implies (not (consp x))
(equal (charlisteqv x y)
(atom y))))
(defthm charlisteqv-when-not-consp-right
(implies (not (consp y))
(equal (charlisteqv x y)
(atom x))))
(defthm charlisteqv-of-cons-right
(equal (charlisteqv x (cons a y))
(and (consp x)
(chareqv (car x) (double-rewrite a))
(charlisteqv (cdr x) (double-rewrite y)))))
(defthm charlisteqv-of-cons-left
(equal (charlisteqv (cons a x) y)
(and (consp y)
(chareqv (double-rewrite a) (car y))
(charlisteqv (double-rewrite x) (cdr y)))))
(defthm charlisteqv-when-not-same-lens
(implies (not (equal (len x) (len y)))
(not (charlisteqv x y)))
:hints(("Goal" :induct (ind x y))))
(defthmd charlisteqv*
;; For compatibility with the old definition
(equal (charlisteqv x y)
(if (consp x)
(and (consp y)
(chareqv (car x) (car y))
(charlisteqv (cdr x) (cdr y)))
(atom y)))
:rule-classes ((:definition :controller-alist ((charlisteqv$inline t nil))))
:hints(("Goal" :induct (ind x y)))))
;; BOZO kind of misplaced
(defcong streqv equal (explode x) 1
:hints(("Goal" :in-theory (enable streqv str-fix))))
(fty::deffixtype character-list
:pred character-listp
:fix make-character-list
:equiv charlisteqv
:topic character-listp)
(define string-list-fix ((x string-listp))
:returns (x-fix string-listp)
(mbe :logic (if (atom x)
nil
(cons (str-fix (car x))
(string-list-fix (cdr x))))
:exec x)
///
(defthm string-list-fix-when-atom
(implies (atom x)
(equal (string-list-fix x)
nil)))
(defthm string-list-fix-of-cons
(equal (string-list-fix (cons a x))
(cons (str-fix a) (string-list-fix x))))
(defthm string-list-fix-when-string-listp
(implies (string-listp x)
(equal (string-list-fix x)
x)))
(defthm consp-of-string-list-fix
(equal (consp (string-list-fix x))
(consp x)))
(defthm len-of-string-list-fix
(equal (len (string-list-fix x))
(len x))))
(defsection string-list-equiv
(local (in-theory (enable string-list-fix)))
(fty::deffixtype string-list
:pred string-listp
:fix string-list-fix
:equiv string-list-equiv
:define t
:forward t
:topic string-listp)
(fty::deffixcong string-list-equiv streqv (car x) x)
(fty::deffixcong string-list-equiv string-list-equiv (cdr x) x)
(fty::deffixcong streqv string-list-equiv (cons x y) x)
(fty::deffixcong string-list-equiv string-list-equiv (cons x y) y))
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