/usr/share/acl2-6.3/books/str/digitp.lisp is in acl2-books-source 6.3-5.
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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>
(in-package "STR")
(include-book "ieqv")
(include-book "std/lists/list-fix" :dir :system)
(local (include-book "std/lists/rev" :dir :system))
(local (include-book "arithmetic"))
(defsection digitp
:parents (numbers)
:short "Recognizer for numeric characters (0-9)."
:long "<p>ACL2 provides @(see digit-char-p) which is more flexible and can
recognize numeric characters in other bases. @(call digitp) only recognizes
base-10 digits, but is roughly twice as fast as @('digit-char-p'), at least on
CCL. Here is an experiment you can run in raw lisp, with times reported in CCL
on the machine Lisp2.</p>
@({
(defconstant *chars*
(loop for i from 0 to 256 collect (code-char i)))
;; 21.876 seconds, no garbage
(time (loop for i fixnum from 1 to 10000000 do
(loop for c in *chars* do (digit-char-p c))))
;; 10.819 seconds, no garbage
(time (loop for i fixnum from 1 to 10000000 do
(loop for c in *chars* do (digitp c))))
})"
(definlined digitp (x)
(declare (type character x))
(mbe :logic (let ((code (char-code (char-fix x))))
(and (<= (char-code #\0) code)
(<= code (char-code #\9))))
:exec (let ((code (the (unsigned-byte 8)
(char-code (the character x)))))
(declare (type (unsigned-byte 8) code))
(and (<= (the (unsigned-byte 8) 48)
(the (unsigned-byte 8) code))
(<= (the (unsigned-byte 8) code)
(the (unsigned-byte 8) 57))))))
(local (in-theory (enable digitp)))
(defcong ichareqv equal (digitp x) 1
:hints(("Goal" :in-theory (enable ichareqv
downcase-char
char-fix))))
(defthm characterp-when-digitp
(implies (str::digitp char)
(characterp char))
:rule-classes :compound-recognizer))
(defsection nonzero-digitp
:parents (numbers)
:short "Recognizer for non-zero numeric characters (1-9)."
(definlined nonzero-digitp (x)
(declare (type character x))
(mbe :logic (let ((code (char-code (char-fix x))))
(and (<= (char-code #\1) code)
(<= code (char-code #\9))))
:exec (let ((code (the (unsigned-byte 8)
(char-code (the character x)))))
(declare (type (unsigned-byte 8) code))
(and (<= (the (unsigned-byte 8) 49)
(the (unsigned-byte 8) code))
(<= (the (unsigned-byte 8) code)
(the (unsigned-byte 8) 57))))))
(local (in-theory (enable nonzero-digitp)))
(defcong ichareqv equal (nonzero-digitp x) 1
:hints(("Goal" :in-theory (enable ichareqv
downcase-char
char-fix))))
(defthm digitp-when-nonzero-digitp
(implies (nonzero-digitp x)
(digitp x))
:hints(("Goal" :in-theory (enable digitp)))))
(defsection digit-val
:parents (numbers)
:short "Coerces a @(see digitp) character into an integer."
:long "<p>For instance, @('(digit-val #\\3)') is 3. For any non-@('digitp'),
0 is returned.</p>"
(definlined digit-val (x)
(declare (type character x)
(xargs :guard (digitp x)
:guard-hints (("Goal" :in-theory (enable digitp)))))
(mbe :logic
(if (digitp x)
(- (char-code (char-fix x))
(char-code #\0))
0)
:exec
(the (unsigned-byte 8)
(- (the (unsigned-byte 8) (char-code (the character x)))
(the (unsigned-byte 8) 48)))))
(local (in-theory (enable digitp digit-val char-fix)))
(defcong ichareqv equal (digit-val x) 1
:hints(("Goal" :in-theory (enable ichareqv
downcase-char
char-fix))))
(defthm natp-of-digit-val
(and (integerp (digit-val x))
(<= 0 (digit-val x)))
:rule-classes :type-prescription)
(defthm digit-val-upper-bound
(< (digit-val x) 10)
:rule-classes ((:rewrite) (:linear)))
(defthm equal-of-digit-val-and-digit-val
(implies (and (digitp x)
(digitp y))
(equal (equal (digit-val x)
(digit-val y))
(equal x y))))
(defthm digit-val-of-digit-to-char
(implies (and (natp n)
(< n 10))
(equal (digit-val (digit-to-char n))
n))))
(defsection digit-listp
:parents (numbers)
:short "Recognizes lists of @(see digitp) characters."
; BOZO consider using cutil::deflist
(defund digit-listp (x)
(declare (xargs :guard (character-listp x)))
(if (consp x)
(and (digitp (car x))
(digit-listp (cdr x)))
t))
(local (in-theory (enable digit-listp)))
(defthm digit-listp-when-not-consp
(implies (not (consp x))
(digit-listp x)))
(defthm digit-listp-of-cons
(equal (digit-listp (cons a x))
(and (digitp a)
(digit-listp x))))
(defcong icharlisteqv equal (digit-listp x) 1
:hints(("Goal" :in-theory (enable icharlisteqv))))
(defthm digit-listp-of-list-fix
(equal (digit-listp (list-fix x))
(digit-listp x)))
(defthm digit-listp-of-append
(equal (digit-listp (append x y))
(and (digit-listp x)
(digit-listp y))))
(defthm digit-listp-of-revappend
(equal (digit-listp (revappend x y))
(and (digit-listp x)
(digit-listp y))))
(defthm digit-listp-of-rev
(equal (digit-listp (rev x))
(digit-listp x)))
(defthm digit-listp-of-nthcdr
(implies (digit-listp x)
(digit-listp (nthcdr n x)))))
(defsection digit-list-value
:parents (numbers)
:short "Coerces a @(see digit-listp) into a natural number."
:long "<p>For instance, @('(digit-list-value '(#\1 #\0 #\3))') is 103.</p>
<p>See also @(see parse-nat-from-charlist) for a more flexible function that
can tolerate non-numeric characters after the number.</p>"
(defund digit-list-value1 (x val)
(declare (type (integer 0 *) val)
(xargs :guard (and (character-listp x)
(digit-listp x))
:guard-hints (("Goal" :in-theory (enable digit-val digitp)))))
(mbe :logic (if (consp x)
(digit-list-value1 (cdr x)
(+ (digit-val (car x))
(* 10 (nfix val))))
(nfix val))
:exec (if (consp x)
(digit-list-value1
(cdr x)
(the (integer 0 *)
(+ (the (unsigned-byte 8)
(- (the (unsigned-byte 8)
(char-code (the character (car x))))
(the (unsigned-byte 8) 48)))
(* (the (integer 0 *) 10)
(the (integer 0 *) val)))))
(the (integer 0 *) val))))
(definlined digit-list-value (x)
(declare (xargs :guard (and (character-listp x)
(digit-listp x))
:verify-guards nil))
(mbe :logic (if (consp x)
(+ (* (expt 10 (1- (len x)))
(digit-val (car x)))
(digit-list-value (cdr x)))
0)
:exec (digit-list-value1 x 0)))
(local (in-theory (enable digit-list-value)))
(defcong icharlisteqv equal (digit-list-value x) 1
:hints(("Goal" :in-theory (enable icharlisteqv))))
(defthm natp-of-digit-list-value
(natp (digit-list-value x))
:rule-classes :type-prescription)
(encapsulate
()
(set-non-linearp t) ;; implicitly local
(defthm digit-list-value-upper-bound
(< (digit-list-value x)
(expt 10 (len x)))))
(defthm digit-list-value-upper-bound-free
(implies (equal n (len x))
(< (digit-list-value x) (expt 10 n))))
(defthm digit-list-value1-removal
(equal (digit-list-value1 x val)
(+ (digit-list-value x)
(* (nfix val) (expt 10 (len x)))))
:hints(("Goal"
:in-theory (enable digit-list-value1)
:induct (digit-list-value1 x val))))
(verify-guards digit-list-value$inline)
(defthm digit-list-value-of-append
(equal (digit-list-value (append x (list a)))
(+ (* 10 (digit-list-value x))
(digit-val a)))))
(defsection skip-leading-digits
(defund skip-leading-digits (x)
(declare (xargs :guard (character-listp x)))
(if (consp x)
(if (digitp (car x))
(skip-leading-digits (cdr x))
x)
nil))
(local (in-theory (enable skip-leading-digits)))
(defcong charlisteqv charlisteqv (skip-leading-digits x) 1
:hints(("Goal" :in-theory (enable charlisteqv))))
(defcong icharlisteqv icharlisteqv (skip-leading-digits x) 1
:hints(("Goal" :in-theory (enable icharlisteqv))))
(defthm len-of-skip-leading-digits
(implies (digitp (car x))
(< (len (skip-leading-digits x))
(len x))))
(defthm character-listp-of-skip-leading-digits
(implies (character-listp x)
(character-listp (skip-leading-digits x)))))
(defsection take-leading-digits
(defund take-leading-digits (x)
(declare (xargs :guard (character-listp x)))
(if (consp x)
(if (digitp (car x))
(cons (car x) (take-leading-digits (cdr x)))
nil)
nil))
(local (in-theory (enable take-leading-digits)))
(defcong icharlisteqv equal (take-leading-digits x) 1
:hints(("Goal" :in-theory (enable icharlisteqv
;; Gross, but gets us equal.
ichareqv
downcase-char
digitp
char-fix))))
(defthm character-listp-of-take-leading-digits
(character-listp (take-leading-digits x))
:hints(("Goal" :in-theory (enable digitp))))
(defthm digit-listp-of-take-leading-digits
(digit-listp (take-leading-digits x)))
(defthm bound-of-len-of-take-leading-digits
(<= (len (take-leading-digits x)) (len x))
:rule-classes :linear)
(defthm take-leading-digits-when-digit-listp
(implies (digit-listp x)
(equal (take-leading-digits x)
(list-fix x)))))
(defsection digit-string-p
(defund digit-string-p-aux (x n xl)
(declare (type string x)
(type (integer 0 *) n)
(type (integer 0 *) xl)
(xargs :guard (and (<= n xl)
(= xl (length x)))
:measure (nfix (- (nfix xl) (nfix n)))))
(if (mbe :logic (zp (- (nfix xl) (nfix n)))
:exec (eql n xl))
t
(and (digitp (char x n))
(digit-string-p-aux x
(mbe :logic (+ 1 (nfix n))
:exec
(the (integer 0 *) (+ 1 n)))
xl))))
(defthm digit-string-p-aux-removal
(implies (and (stringp x)
(natp n)
(equal xl (length x)))
(equal (digit-string-p-aux x n xl)
(digit-listp (nthcdr n (explode x)))))
:hints(("Goal" :in-theory (enable digit-string-p-aux
digit-listp))))
(definline digit-string-p (x)
(declare (type string x))
; 0.5485 seconds, no garbage
;
; (let ((x "1234"))
; (time$ (loop for i fixnum from 1 to 10000000 do
; (str::digit-string-p x))))
;
; 1.3762 seconds, 640 MB allocated
;
; (let ((x "1234"))
; (time$ (loop for i fixnum from 1 to 10000000 do
; (str::digit-listp (coerce x 'list)))))
(mbe :logic (digit-listp (explode x))
:exec (digit-string-p-aux x 0 (length x))))
(defcong istreqv equal (digit-string-p x) 1))
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