/usr/share/acl2-6.3/books/str/stringify.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.
; stringify.lisp
; Original author: Sol Swords <sswords@centtech.com>
(in-package "STR")
(include-book "cat")
(include-book "natstr")
(defun stringify-integer (x)
(declare (Xargs :guard (integerp x)))
(if (and (mbt (integerp x))
(< x 0))
(cat "-" (natstr (- x)))
(natstr x)))
(encapsulate
nil
(local (defthm natchars-of-non-natp
(implies (not (natp x))
(equal (natchars x) '(#\0)))
:hints(("Goal" :in-theory (enable natchars)))))
(defthmd natstr-of-non-natp
(implies (not (natp x))
(equal (natstr x) "0"))
:hints(("Goal" :in-theory (enable natstr)))))
(encapsulate
nil
(local (defthm not-member-minus-char-digit-listp
(implies (digit-listp x)
(not (member-equal #\- x)))))
(local (defthm not-equal-cons-when-not-member-equal
(implies (not (member-equal a b))
(not (equal b (cons a c))))))
(local (defthm switch-coerce-cons-string
(implies (and (syntaxp (not (quotep b)))
(characterp a)
(character-listp b)
(stringp c))
(and (equal (Equal (implode (cons a b)) c)
(equal (cons a b) (explode c)))
(equal (Equal c (implode (cons a b)))
(equal (cons a b) (explode c)))))))
(defthm stringify-integer-one-to-one
(equal (equal (stringify-integer x)
(stringify-integer y))
(equal (ifix x) (ifix y)))
:hints (("goal" :use ((:instance not-member-minus-char-digit-listp
(x (coerce (natstr x) 'list)))
(:instance not-member-minus-char-digit-listp
(x (coerce (natstr y) 'list)))
(:instance natstr-one-to-one
(n x) (m 0))
(:instance natstr-one-to-one
(n y) (m 0)))
:in-theory (disable not-member-minus-char-digit-listp)))))
(defthm stringify-integer-of-non-integer
(implies (not (integerp x))
(equal (stringify-integer x) "0"))
:hints(("Goal" :in-theory (enable natstr-of-non-natp))))
(encapsulate nil
(local (defthm not-member-slash-char-digit-listp
(implies (digit-listp x)
(not (member-equal #\/ x)))))
(defthm not-member-/-stringify-integer
(not (member-equal #\/ (explode (stringify-integer i)))))
(defthm not-member-/-natstr
(not (member-equal #\/ (explode (natstr i))))))
(in-theory (disable stringify-integer))
(defun stringify-rational (x)
(declare (xargs :guard (rationalp x)))
(if (or (integerp x)
(mbe :logic (not (rationalp x))
:exec nil))
(stringify-integer x)
(cat (stringify-integer (numerator x))
"/"
(natstr (denominator x)))))
(local (defthm member-equal-append
(iff (member-equal k (append a b))
(or (member-equal k a)
(member-equal k b)))))
(local (defun cdr-both-equal (a b)
(if (or (atom a) (atom b))
nil
(and (and (consp a) (consp b)
(equal (car a) (car b)))
(cdr-both-equal (cdr a) (cdr b))))))
(local (defthm equal-appends-with-nonmembers-implies-components-equal
(implies (and (not (member-equal x a))
(not (member-equal x b))
(not (member-equal x c))
(not (member-equal x d))
(true-listp a)
(true-listp c))
(equal (equal (append a (cons x b))
(append c (cons x d)))
(and (equal a c) (equal b d))))
:hints ((and stable-under-simplificationp
`(:induct (cdr-both-equal a c)
:expand ((append a (cons x b))
(append c (cons x d))))))
:otf-flg t))
(encapsulate
nil
(local (defthm switch-coerce-append-string
(implies (and (character-listp a)
(character-listp b)
(stringp c))
(and (equal (Equal (implode (append a b)) c)
(equal (append a b) (explode c)))
(equal (Equal c (implode (append a b)))
(equal (append a b) (explode c)))))))
(local (defthm not-equal-if-not-members-append-cons
(implies (not (member-equal a c))
(not (equal (append b (cons a d)) c)))))
(defthm stringify-rational-one-to-one
(equal (equal (stringify-rational x)
(stringify-rational y))
(equal (rfix x) (rfix y)))
:hints (("goal" :use ((:instance not-member-/-stringify-integer
(i x))
(:instance not-member-/-stringify-integer
(i y))
(:instance not-member-/-stringify-integer
(i (numerator x)))
(:instance not-member-/-stringify-integer
(i (numerator y)))
(:instance stringify-integer-one-to-one
(x y) (y 0))
(:instance stringify-integer-one-to-one
(x x) (y 0))
(:instance rational-implies2)
(:instance rational-implies2 (x y)))
:in-theory (disable not-member-/-stringify-integer
rational-implies2)))))
(encapsulate nil
(local (defthm not-member-sharp-char-digit-listp
(implies (digit-listp x)
(not (member-equal #\# x)))))
(defthm not-member-sharp-natstr
(not (member-equal #\# (explode (natstr i)))))
(defthm not-member-sharp-stringify-integer
(not (member-equal #\# (explode (stringify-integer i))))
:hints(("Goal" :in-theory (enable stringify-integer))))
(defthm not-member-sharp-stringify-rational
(not (member-equal #\# (explode (stringify-rational r))))))
(encapsulate nil
(local (defthm not-member-space-char-digit-listp
(implies (digit-listp x)
(not (member-equal #\Space x)))))
(defthm not-member-space-natstr
(not (member-equal #\Space (explode (natstr i)))))
(defthm not-member-space-stringify-integer
(not (member-equal #\Space (explode (stringify-integer i))))
:hints(("Goal" :in-theory (enable stringify-integer))))
(defthm not-member-space-stringify-rational
(not (member-equal #\Space (explode (stringify-rational r))))))
(in-theory (disable stringify-rational))
(defun stringify-number (x)
(declare (xargs :guard (acl2-numberp x)))
(if (or (rationalp x)
(mbe :logic (not (acl2-numberp x))
:exec nil))
(stringify-rational x)
(cat "#C(" (stringify-rational (realpart x))
" " (stringify-rational (imagpart x)) ")")))
(encapsulate
nil
(local (defthm switch-coerce-list*-append-string
(implies (and (character-listp a)
(character-listp b)
(characterp e)
(characterp f)
(characterp g)
(stringp c))
(and (equal (Equal (implode (list* e f g (append a b))) c)
(equal (list* e f g (append a b)) (explode c)))
(equal (Equal c (implode (list* e f g (append a b))))
(equal (list* e f g (append a b)) (explode c)))))))
(local (defthmd not-equal-by-len
(implies (not (equal (len x) (len y)))
(not (Equal x y)))))
(local (defthm len-append-linear
(<= (len x) (len (append z x)))
:rule-classes :linear))
(local (defthm not-equal-x-cons-y-append-z-x
(not (equal x (cons y (append z x))))
:hints (("goal" :in-theory (enable not-equal-by-len)))))
(local (defthm equal-append-to-tail
(implies (and (true-listp a) (true-listp b))
(equal (equal (append a c) (append b c))
(equal a b)))
:hints (("goal" :induct (cdr-both-equal a b)
:expand ((append a c) (append b c))))))
(defthm stringify-number-one-to-one
(equal (equal (stringify-number x)
(stringify-number y))
(equal (fix x) (fix y)))
:hints (("goal" :use ((:instance not-member-space-stringify-rational
(r x))
(:instance not-member-space-stringify-rational
(r y))
(:instance not-member-space-stringify-rational
(r (realpart x)))
(:instance not-member-space-stringify-rational
(r (realpart y)))
(:instance not-member-space-stringify-rational
(r (imagpart x)))
(:instance not-member-space-stringify-rational
(r (imagpart y)))
(:instance stringify-rational-one-to-one
(x y) (y 0))
(:instance stringify-rational-one-to-one
(x x) (y 0))
(:instance realpart-imagpart-elim)
(:instance realpart-imagpart-elim (x y)))
:in-theory (disable not-member-space-stringify-rational
realpart-imagpart-elim)))))
(defun upper-case-or-digit-listp (x)
(declare (xargs :guard (character-listp x)))
(if (atom x)
t
(and (or (up-alpha-p (car X)) (digitp (car x)))
(upper-case-or-digit-listp (cdr x)))))
(in-theory (disable upper-case-or-digit-listp up-alpha-p))
(local (defthm characterp-car-of-character-listp
(implies (and (character-listp x)
(consp x))
(characterp (car x)))))
(local (defthm character-listp-cdr-of-character-listp
(implies (character-listp x)
(character-listp (cdr x)))))
;; Like may-need-slashes-fn, but hard-coded base 10. Mainly we just need to be
;; able to show that we can't confuse this with a character, number, or string,
;; for which it's enough to show that it can't start with #, ", -, or a digit.
;; Then we'll also want to use bars for anything lower-case. We can afford to
;; be a bit more conservative than may-need-slashes-fn in order to ease the
;; logic, but we still don't want to use vertical bars for absolutely
;; everything.
;; We'll allow the first letter to be only an upper-case letter, and the rest
;; to be either upper-case or digits.
(defun escape-free-symnamep (x)
(declare (xargs :guard (stringp x)))
(let ((lst (explode x)))
(and (consp lst) ;; not the empty string
(up-alpha-p (car lst))
(upper-case-or-digit-listp (cdr lst)))))
(local (defthm assoc-append
(equal (append (append a b) c)
(append a b c))))
(local (defthm fold-constants-append
(implies (syntaxp (and (quotep a) (quotep b)))
(equal (append a b c)
(append (append a b) c)))))
;; This may perform somewhat poorly due to the coerce to list in the
;; escape-free-symname check.
(defun stringify-symbol (x)
(declare (type symbol x))
(let ((name (symbol-name x))
(pkg (symbol-package-name x)))
(mbe :logic
(if (symbolp x)
(let ((pkg-string
(if (equal pkg "ACL2")
""
(if (escape-free-symnamep pkg)
(cat pkg "::")
(cat "|" pkg "|::"))))
(name-string
(if (escape-free-symnamep name)
name
(cat "|" name "|"))))
(cat pkg-string name-string))
"COMMON-LISP::NIL")
:exec
(if (equal pkg "ACL2")
(if (escape-free-symnamep name)
name
(cat "|" name "|"))
(if (escape-free-symnamep pkg)
(if (escape-free-symnamep name)
(cat pkg "::" name)
(cat pkg "::|" name "|"))
(if (escape-free-symnamep name)
(cat "|" pkg "|::" name)
(cat "|" pkg "|::|" name "|")))))))
(in-theory (disable escape-free-symnamep))
;; Maybe someday we can prove this and go on with the rest of the proof --
;; seems pretty tedious though.
;; (defthm stringify-symbol-unique
;; (equal (equal (stringify-symbol x)
;; (stringify-symbol y))
;; (equal (and (symbolp x) x)
;; (and (symbolp y) y)))
;; :hints ((and stable-under-simplificationp
;; (equal (caar (last clause)) 'not)
;; (symbolp (cadar (last clause)))
;; `(:use ((:instance symbol-equality
;; (acl2::s1 ,(cadar (last clause))) (acl2::s2 nil)))))))
(defun stringify-atom (x)
;; BOZO escaping of strings, proper escaping of characters, ...
(declare (xargs :guard (atom x)))
(cond ((symbolp x) (stringify-symbol x))
((stringp x) (cat "\"" x "\""))
((acl2-numberp x) (stringify-number x))
((characterp x) (cat "#\\" (implode (list x))))
(t "##**BAD-ATOM**##")))
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