/usr/share/acl2-6.3/books/str/char-case.lisp is in acl2-books-source 6.3-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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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.
; char-case.lisp
;
; Original authors: Jared Davis <jared@centtech.com> and
; Sol Swords <sswords@centtech.com>
(in-package "STR")
(include-book "eqv")
(include-book "tools/bstar" :dir :system)
(local (include-book "arithmetic"))
(defmacro little-a () (char-code #\a))
(defmacro little-z () (char-code #\z))
(defmacro big-a () (char-code #\A))
(defmacro big-z () (char-code #\Z))
(defmacro case-delta () (- (little-a) (big-a)))
(defsection up-alpha-p
:parents (cases acl2::upper-case-p)
:short "Determine if a character is an upper-case letter (A-Z)."
:long "<p>@(call up-alpha-p) determines if @('x') is an upper-case alphabetic
character.</p>
<p>ACL2 has a built-in alternative to this function, @(see acl2::upper-case-p),
but it is irritating to use because it has @(see standard-char-p) guards. In
contrast, @('up-alpha-p') works on arbitrary characters.</p>"
(definlined up-alpha-p (x)
(declare (type character x))
(b* (((the (unsigned-byte 8) code) (char-code x)))
(and (<= (big-a) code)
(<= code (big-z)))))
(local (in-theory (enable up-alpha-p)))
(defcong chareqv equal (up-alpha-p x) 1)
;; Rewrite ACL2's upper-case-p to up-alpha-p. It seems simplest to just do
;; the proof by exhaustive testing.
(local (defund exhaustive-test (n)
(and (let ((x (code-char n)))
(equal (acl2::upper-case-p x)
(and (<= (big-a) (char-code x))
(<= (char-code x) (big-z)))))
(or (zp n)
(exhaustive-test (- n 1))))))
(local (defthm lemma1
(implies (and (natp n)
(<= n 255))
(equal (char-code (code-char n))
n))))
(local (defthm lemma2
(implies (and (natp n)
(natp m)
(exhaustive-test n)
(= x (code-char m))
(<= m n)
(<= n 255))
(equal (acl2::upper-case-p x)
(and (<= (big-a) (char-code x))
(<= (char-code x) (big-z)))))
:hints(("Goal"
:induct (exhaustive-test n)
:in-theory (enable exhaustive-test)))))
(local (defthm lemma3
(implies (characterp x)
(equal (acl2::upper-case-p x)
(and (<= (big-a) (char-code x))
(<= (char-code x) (big-z)))))
:hints(("Goal"
:in-theory (disable lemma2)
:use ((:instance lemma2
(n 255)
(m (char-code x))))))))
(local (defthm lemma4
(implies (not (characterp x))
(not (acl2::upper-case-p x)))
:hints(("Goal" :in-theory (enable acl2::upper-case-p)))))
(local (defthm lemma5
(equal (acl2::upper-case-p x)
(and (<= (big-a) (char-code x))
(<= (char-code x) (big-z))))
:hints(("Goal" :cases ((characterp x))))))
(defthm upper-case-p-is-up-alpha-p
(equal (acl2::upper-case-p x)
(up-alpha-p (double-rewrite x))))
;; No longer necessary since we'll rewrite upper-case-p away
(in-theory (disable acl2::upper-case-p-char-upcase)))
(defsection down-alpha-p
:parents (cases acl2::lower-case-p)
:short "Determine if a character is a lower-case letter (a-z)."
:long "<p>@(call down-alpha-p) determines if @('x') is an lower-case
alphabetic character.</p>
<p>ACL2 has a built-in alternative to this function, @(see acl2::lower-case-p),
but it is irritating to use because it has @(see standard-char-p) guards. In
contrast, @('down-alpha-p') works on arbitrary characters.</p>"
(definlined down-alpha-p (x)
(declare (type character x))
(b* (((the (unsigned-byte 8) code) (char-code x)))
(and (<= (little-a) code)
(<= code (little-z)))))
(local (in-theory (enable down-alpha-p)))
(defcong chareqv equal (down-alpha-p x) 1)
;; Rewrite ACL2's lower-case-p to down-alpha-p. It seems simplest to just do
;; the proof by exhaustive testing.
(local (defund exhaustive-test (n)
(and (let ((x (code-char n)))
(equal (acl2::lower-case-p x)
(and (<= (little-a) (char-code x))
(<= (char-code x) (little-z)))))
(or (zp n)
(exhaustive-test (- n 1))))))
(local (defthm lemma1
(implies (and (natp n)
(<= n 255))
(equal (char-code (code-char n))
n))))
(local (defthm lemma2
(implies (and (natp n)
(natp m)
(exhaustive-test n)
(= x (code-char m))
(<= m n)
(<= n 255))
(equal (acl2::lower-case-p x)
(and (<= (little-a) (char-code x))
(<= (char-code x) (little-z)))))
:hints(("Goal"
:induct (exhaustive-test n)
:in-theory (enable exhaustive-test)))))
(local (defthm lemma3
(implies (characterp x)
(equal (acl2::lower-case-p x)
(and (<= (little-a) (char-code x))
(<= (char-code x) (little-z)))))
:hints(("Goal"
:in-theory (disable lemma2)
:use ((:instance lemma2
(n 255)
(m (char-code x))))))))
(local (defthm lemma4
(implies (not (characterp x))
(not (acl2::lower-case-p x)))
:hints(("Goal" :in-theory (enable acl2::lower-case-p)))))
(local (defthm lemma5
(equal (acl2::lower-case-p x)
(and (<= (little-a) (char-code x))
(<= (char-code x) (little-z))))
:hints(("Goal" :cases ((characterp x))))))
(defthm lower-case-p-is-down-alpha-p
(equal (acl2::lower-case-p x)
(down-alpha-p (double-rewrite x))))
;; No longer necessary since we'll rewrite lower-case-p away
(in-theory (disable acl2::lower-case-p-char-downcase))
(defthm down-alpha-p-when-up-alpha-p
(implies (up-alpha-p x)
(not (down-alpha-p x)))
:hints(("Goal" :in-theory (enable up-alpha-p
down-alpha-p)))))
(defsection upcase-char
:parents (cases acl2::char-upcase)
:short "Convert a character to upper-case."
:long "<p>@(call upcase-char) converts lower-case characters into their
upper-case equivalents, and returns other characters unchanged.</p>
<p>ACL2 has a built-in alternative to this function, @(see acl2::char-upcase),
but it is irritating to use because it has @(see standard-char-p) guards. In
contrast, @('upcase-char') works on arbitrary characters.</p>"
(definlined upcase-char (x)
(declare (type character x))
(b* (((the (unsigned-byte 8) code) (char-code x)))
(if (and (<= (little-a) code)
(<= code (little-z)))
(code-char (the (unsigned-byte 8) (- code (case-delta))))
(mbe :logic (char-fix x) :exec x))))
(local (in-theory (enable upcase-char)))
(defcong chareqv equal (upcase-char x) 1)
(defthm upcase-char-does-nothing-unless-down-alpha-p
(implies (not (down-alpha-p x))
(equal (upcase-char x)
(char-fix x)))
:hints(("Goal" :in-theory (enable down-alpha-p))))
(defthm upcase-char-of-upcase-char
(equal (upcase-char (upcase-char x))
(upcase-char x)))
;; Rewrite ACL2's char-upcase to upcase-char. It seems simplest to just do
;; the proof by exhaustive testing.
(local (defund exhaustive-test (n)
(and (let ((x (code-char n)))
(equal (acl2::char-upcase x)
(if (and (<= (little-a) (char-code x))
(<= (char-code x) (little-z)))
(code-char (- (char-code x) (case-delta)))
x)))
(or (zp n)
(exhaustive-test (- n 1))))))
(local (defthm lemma1
(implies (and (natp n)
(<= n 255))
(equal (char-code (code-char n))
n))))
(local (defthm lemma2
(implies (and (natp n)
(natp m)
(exhaustive-test n)
(= x (code-char m))
(<= m n)
(<= n 255))
(equal (acl2::char-upcase x)
(if (and (<= (little-a) (char-code x))
(<= (char-code x) (little-z)))
(code-char (- (char-code x) (case-delta)))
x)))
:hints(("Goal"
:induct (exhaustive-test n)
:in-theory (enable exhaustive-test)))))
(local (defthm lemma3
(implies (characterp x)
(equal (acl2::char-upcase x)
(if (and (<= (little-a) (char-code x))
(<= (char-code x) (little-z)))
(code-char (- (char-code x) (case-delta)))
x)))
:hints(("Goal"
:in-theory (disable lemma2)
:use ((:instance lemma2
(n 255)
(m (char-code x))))))))
(local (defthm lemma4
(implies (not (characterp x))
(equal (acl2::char-upcase x)
(code-char 0)))
:hints(("Goal" :in-theory (enable acl2::char-upcase)))))
(local (defthm lemma5
(equal (acl2::char-upcase x)
(if (characterp x)
(if (and (<= (little-a) (char-code x))
(<= (char-code x) (little-z)))
(code-char (- (char-code x) (case-delta)))
x)
(code-char 0)))))
(defthm char-upcase-is-upcase-char
(equal (acl2::char-upcase x)
(upcase-char (double-rewrite x)))))
(defsection downcase-char
:parents (cases acl2::char-downcase)
:short "Convert a character to lower-case."
:long "<p>@(call downcase-char) converts upper-case characters into their
lower-case equivalents, and returns other characters unchanged.</p>
<p>ACL2 has a built-in alternative to this function, @(see
acl2::char-downcase), but it is irritating to use because it has @(see
standard-char-p) guards. In contrast, @('downcase-char') works on arbitrary
characters.</p>"
(definlined downcase-char (x)
(declare (type character x))
(b* (((the (unsigned-byte 8) code) (char-code x)))
(if (and (<= (big-a) code)
(<= code (big-z)))
(code-char (the (unsigned-byte 8) (+ code (case-delta))))
(mbe :logic (char-fix x) :exec x))))
(local (in-theory (enable downcase-char)))
(defcong chareqv equal (downcase-char x) 1)
(defthm downcase-char-does-nothing-unless-up-alpha-p
(implies (not (up-alpha-p x))
(equal (downcase-char x)
(char-fix x)))
:hints(("Goal" :in-theory (enable up-alpha-p))))
(defthm downcase-char-of-downcase-char
(equal (downcase-char (downcase-char x))
(downcase-char x)))
(defthm downcase-char-of-upcase-char
(equal (downcase-char (upcase-char x))
(downcase-char x))
:hints(("Goal" :in-theory (enable upcase-char
char-fix))))
(defthm upcase-char-of-downcase-char
(equal (upcase-char (downcase-char x))
(upcase-char x))
:hints(("Goal" :in-theory (enable upcase-char
char-fix))))
;; Rewrite ACL2's char-downcase to downcase-char. It seems simplest to just do
;; the proof by exhaustive testing.
(local (defund exhaustive-test (n)
(and (let ((x (code-char n)))
(equal (acl2::char-downcase x)
(if (and (<= (big-a) (char-code x))
(<= (char-code x) (big-z)))
(code-char (+ (char-code x) (case-delta)))
x)))
(or (zp n)
(exhaustive-test (- n 1))))))
(local (defthm lemma1
(implies (and (natp n)
(<= n 255))
(equal (char-code (code-char n))
n))))
(local (defthm lemma2
(implies (and (natp n)
(natp m)
(exhaustive-test n)
(= x (code-char m))
(<= m n)
(<= n 255))
(equal (acl2::char-downcase x)
(if (and (<= (big-a) (char-code x))
(<= (char-code x) (big-z)))
(code-char (+ (char-code x) (case-delta)))
x)))
:hints(("Goal"
:induct (exhaustive-test n)
:in-theory (enable exhaustive-test)))))
(local (defthm lemma3
(implies (characterp x)
(equal (acl2::char-downcase x)
(if (and (<= (big-a) (char-code x))
(<= (char-code x) (big-z)))
(code-char (+ (char-code x) (case-delta)))
x)))
:hints(("Goal"
:in-theory (disable lemma2)
:use ((:instance lemma2
(n 255)
(m (char-code x))))))))
(local (defthm lemma4
(implies (not (characterp x))
(equal (acl2::char-downcase x)
(code-char 0)))
:hints(("Goal" :in-theory (enable acl2::char-downcase)))))
(local (defthm lemma5
(equal (acl2::char-downcase x)
(if (characterp x)
(if (and (<= (big-a) (char-code x))
(<= (char-code x) (big-z)))
(code-char (+ (char-code x) (case-delta)))
x)
(code-char 0)))))
(defthm char-downcase-is-downcase-char
(equal (acl2::char-downcase x)
(downcase-char (double-rewrite x)))))
(defsection upcase-char-str
:parents (cases)
:short "Convert a character into an upper-case one-element string."
:long "<p>@(call upcase-char-str) is logically equal to:</p>
@({
(implode (list (upcase-char c)))
})
<p>But we store these strings in a table so that they don't have to be
recomputed. This is mainly useful to reduce the creation of temporary strings
during @(see upcase-first).</p>"
(defun make-upcase-first-strtbl (n)
(declare (xargs :guard (and (natp n)
(<= n 255))
:ruler-extenders :all))
(cons (cons n (implode (list (upcase-char (code-char n)))))
(if (zp n)
nil
(make-upcase-first-strtbl (- n 1)))))
(defconst *upcase-first-strtbl*
(compress1 '*upcase-first-strtbl*
(cons '(:header :dimensions (256)
:maximum-length 257)
(make-upcase-first-strtbl 255))))
(local (in-theory (disable aref1)))
(local (defun test (n)
(declare (xargs :ruler-extenders :all))
(and (equal (aref1 '*upcase-first-strtbl* *upcase-first-strtbl* n)
(implode (list (upcase-char (code-char n)))))
(if (zp n)
t
(test (- n 1))))))
(local (defthm l0
(implies (and (natp i)
(natp n)
(<= i n)
(<= n 255)
(test n))
(equal (aref1 '*upcase-first-strtbl* *upcase-first-strtbl* i)
(implode (list (upcase-char (code-char i))))))
:hints(("Goal" :induct (test n)))))
(local (defthm l1
(implies (and (natp i)
(<= i 255))
(equal (aref1 '*upcase-first-strtbl* *upcase-first-strtbl* i)
(implode (list (upcase-char (code-char i))))))
:hints(("Goal" :use ((:instance l0 (n 255)))))))
(definline upcase-char-str (c)
(declare (type character c))
(mbe :logic (implode (list (upcase-char c)))
:exec (aref1 '*upcase-first-strtbl* *upcase-first-strtbl* (char-code c)))))
(defsection downcase-char-str
:parents (cases)
:short "Convert a character into a lower-case one-element string."
:long "<p>@(call downcase-char-str) is logically equal to:</p>
@({
(implode (downcase-char c))
})
<p>But we store these strings in a table so that they don't have to be
recomputed. This is mainly useful to reduce the creation of temporary strings
during @(see downcase-first).</p>"
(defun make-downcase-first-strtbl (n)
(declare (xargs :guard (and (natp n)
(<= n 255))
:ruler-extenders :all))
(cons (cons n (implode (list (downcase-char (code-char n)))))
(if (zp n)
nil
(make-downcase-first-strtbl (- n 1)))))
(defconst *downcase-first-strtbl*
(compress1 '*downcase-first-strtbl*
(cons '(:header :dimensions (256)
:maximum-length 257)
(make-downcase-first-strtbl 255))))
(local (in-theory (disable aref1)))
(local (defun test (n)
(declare (xargs :ruler-extenders :all))
(and (equal (aref1 '*downcase-first-strtbl* *downcase-first-strtbl* n)
(implode (list (downcase-char (code-char n)))))
(if (zp n)
t
(test (- n 1))))))
(local (defthm l0
(implies (and (natp i)
(natp n)
(<= i n)
(<= n 255)
(test n))
(equal (aref1 '*downcase-first-strtbl* *downcase-first-strtbl* i)
(implode (list (downcase-char (code-char i))))))
:hints(("Goal" :induct (test n)))))
(local (defthm l1
(implies (and (natp i)
(<= i 255))
(equal (aref1 '*downcase-first-strtbl* *downcase-first-strtbl* i)
(implode (list (downcase-char (code-char i))))))
:hints(("Goal" :use ((:instance l0 (n 255)))))))
(definline downcase-char-str (c)
(declare (type character c))
(mbe :logic (implode (list (downcase-char c)))
:exec (aref1 '*downcase-first-strtbl* *downcase-first-strtbl* (char-code c)))))
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