; 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 "strprefixp")
(local (include-book "std/lists/nthcdr" :dir :system))
(local (include-book "misc/assert" :dir :system))
(local (include-book "arithmetic/top" :dir :system))
(local (in-theory (disable acl2::prefixp-when-equal-lengths)))

(local (defthm crock
         (implies (and (equal (len x) (len y))
                       (true-listp x)
                       (true-listp y))
                  (equal (prefixp x y)
                         (equal x y)))
         :hints(("Goal" :in-theory (enable prefixp)))))

(defsection strsuffixp
  :parents (substrings)
  :short "Case-sensitive string suffix test."

  :long "<p>@(call strsuffixp) determines if the string @('x') is a suffix of
the string @('y'), in a case-sensitive manner.</p>

<p>Logically, we ask whether @('|x| < |y|'), and whether</p>

@({
  (equal (nthcdr (- |y| |x|) (explode x))
         (explode y))
})

<p>But we use a more efficient implementation that avoids coercing the strings
into lists; basically we ask if the last @('|x|') characters of @('y') are
equal to @('x').</p>

<p>Corner case: we regard the empty string as a suffix of every other string.
That is, @('(strsuffixp \"\" x)') is always true.</p>"

  (definlined strsuffixp (x y)
    (declare (type string x y))
    (mbe :logic
         (let* ((xchars (explode x))
                (ychars (explode y))
                ;; note that using, e.g., (len (explode x)) instead of (length
                ;; x)) gives better congruence behavior
                (xlen   (len xchars))
                (ylen   (len ychars)))
           (and (<= xlen ylen)
                (equal (nthcdr (- ylen xlen) (explode y))
                       (explode x))))
         :exec
         (let* ((xlen (length x))
                (ylen (length y)))
           (and (<= xlen ylen)
                (strprefixp-impl x y 0 (- ylen xlen) xlen ylen)))))

  (local (in-theory (enable strsuffixp)))

  (local (defthm c0
           (implies (and (natp n)
                         (<= (len x) n)
                         (true-listp x))
                    (equal (nthcdr n x) nil))))

  (local (defthm c1
           (implies (true-listp x)
                    (not (nthcdr (len x) x)))))

  (defthm strsuffixp-of-empty
    (strsuffixp "" y))

  (local
   (progn
     (assert! (strsuffixp "" ""))
     (assert! (strsuffixp "" "foo"))
     (assert! (strsuffixp "o" "foo"))
     (assert! (strsuffixp "oo" "foo"))
     (assert! (not (strsuffixp "ooo" "foo")))
     (assert! (not (strsuffixp "fo" "foo")))
     (assert! (strsuffixp "foo" "foo"))))

  (defcong streqv equal (strsuffixp x y) 1)
  (defcong streqv equal (strsuffixp x y) 2))


