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; Copyright (C) 2018 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: Sol Swords <sswords@centtech.com>
(in-package "STR")
(include-book "std/basic/defs" :dir :system)
(local (include-book "std/basic/arith-equivs" :dir :system))
(local (defthm character-listp-of-make-character-list
(character-listp (make-character-list x))))
(local (defthm coerce-inverse-better
(equal (coerce (coerce x 'string) 'list)
(make-character-list x))
:hints (("goal" :use ((:instance acl2::completion-of-coerce
(x x) (y 'string)))))))
(local (defthm equal-of-coerce-string
(equal (equal (coerce x 'string) (coerce y 'string))
(equal (make-character-list x)
(make-character-list y)))
:hints (("goal" :use ((:instance coerce-inverse-better
(x (make-character-list x)))
(:instance coerce-inverse-better
(x (make-character-list y)))
(:instance acl2::completion-of-coerce
(x x) (y 'string))
(:instance acl2::completion-of-coerce
(x y) (y 'string)))
:in-theory (disable coerce-inverse-better)
:do-not-induct t))
:otf-flg t))
(local (defthm coerce-of-str-fix
(equal (coerce (str-fix x) 'list)
(coerce x 'list))
:hints(("Goal" :in-theory (enable str-fix)
:use ((:instance acl2::completion-of-coerce
(y 'list)))))))
(defsection strrange-equiv
(defund strrange-equiv (len x xidx y yidx)
(declare (xargs :guard (and (stringp x)
(stringp y)
(natp xidx)
(natp yidx)
(natp len)
(<= (+ len xidx) (length x))
(<= (+ len yidx) (length y)))
:measure (nfix len)))
(if (zp len)
t
(and (eql (mbe :logic (char-fix (char x xidx)) :exec (char x xidx))
(mbe :logic (char-fix (char y yidx)) :exec (char y yidx)))
(strrange-equiv (1- len)
x (+ 1 (lnfix xidx))
y (+ 1 (lnfix yidx))))))
(local (in-theory (enable strrange-equiv)))
(local (include-book "std/lists/take" :dir :system))
(local (include-book "std/lists/nthcdr" :dir :system))
(local (in-theory (disable nth nthcdr acl2::take
acl2::take-of-len-free nfix)))
(local (defthm make-character-list-redef
(equal (make-character-list x)
(if (atom x)
nil
(cons (char-fix (car x))
(make-character-list (cdr x)))))
:rule-classes ((:definition :controller-alist ((make-character-list t))))))
(defthmd strrange-equiv-equals-charlist-subseqs-equal
(equal (strrange-equiv len x xidx y yidx)
(equal (make-character-list (take len (nthcdr xidx (coerce x 'list))))
(make-character-list (take len (nthcdr yidx (coerce y 'list))))))
:hints (("goal" :induct (strrange-equiv len x xidx y yidx)
:expand ((:free (x) (take len x))
(:free (x) (nth xidx x))
(:free (x) (nth yidx x))
(:free (x y) (nthcdr (+ 1 x) y)))
:do-not-induct t)))
(defthmd strrange-equiv-equals-subseqs-equal
(equal (strrange-equiv len x xidx y yidx)
(equal (subseq (str-fix x) (nfix xidx) (+ (nfix len) (nfix xidx)))
(subseq (str-fix y) (nfix yidx) (+ (nfix len) (nfix yidx)))))
:hints(("Goal" :in-theory (enable strrange-equiv-equals-charlist-subseqs-equal
subseq)
:do-not-induct t))))
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