/usr/share/acl2-6.3/books/str/istrpos.cert is in acl2-books-certs 6.3-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | (IN-PACKAGE "ACL2")
"ACL2 Version 6.3"
:BEGIN-PORTCULLIS-CMDS
(INCLUDE-BOOK "cutil/portcullis" :DIR :SYSTEM)
:END-PORTCULLIS-CMDS
:EXPANSION-ALIST
((4 RECORD-EXPANSION (DEFSECTION STR::ISTRPOS :PARENTS (STR::SUBSTRINGS) :SHORT "Case-insensitivly locate the first occurrence of a substring." :LONG "<p>@(call istrpos) is like @(see strpos), but the comparisons are done
in a case insensitive manner. It returns @('nil') if @('x') never occurs in
@('y'), or returns the index of the first character of the first occurrence
otherwise.</p>
<p>The function is \"efficient\" in the sense that it does not coerce its
arguments into lists, but rather traverses both strings with @(see char). On
the other hand, it is a naive string search which operates by repeatedly
calling @(see istrprefixp) rather than some better algorithm.</p>
<p>The \"soundness\" and \"completness\" of strpos are established in the
theorems @('iprefixp-of-istrpos') and @('completeness-of-istrpos').</p>" (DEFUND STR::ISTRPOS-IMPL (X Y N STR::XL STR::YL) (DECLARE (TYPE STRING X Y) (TYPE (INTEGER 0 *) N STR::XL STR::YL) (XARGS :GUARD (AND (STRINGP X) (STRINGP Y) (NATP STR::XL) (NATP STR::YL) (NATP N) (<= N (LENGTH Y)) (= STR::XL (LENGTH X)) (= STR::YL (LENGTH Y))) :MEASURE (NFIX (- (NFIX STR::YL) (NFIX N))))) (COND ((MBE :LOGIC (STR::IPREFIXP (EXPLODE X) (NTHCDR N (EXPLODE Y))) :EXEC (STR::ISTRPREFIXP-IMPL (THE STRING X) (THE STRING Y) (THE (INTEGER 0 *) 0) (THE (INTEGER 0 *) N) (THE (INTEGER 0 *) STR::XL) (THE (INTEGER 0 *) STR::YL))) (LNFIX N)) ((MBE :LOGIC (ZP (- (NFIX STR::YL) (NFIX N))) :EXEC (INT= N STR::YL)) NIL) (T (STR::ISTRPOS-IMPL (THE STRING X) (THE STRING Y) (THE (INTEGER 0 *) (+ 1 (THE (INTEGER 0 *) (LNFIX N)))) (THE (INTEGER 0 *) STR::XL) (THE (INTEGER 0 *) STR::YL))))) (DEFINLINED STR::ISTRPOS (X Y) (DECLARE (TYPE STRING X Y)) (LET* ((STR::XL (MBE :LOGIC (LEN (EXPLODE X)) :EXEC (LENGTH (THE STRING X)))) (STR::YL (MBE :LOGIC (LEN (EXPLODE Y)) :EXEC (LENGTH (THE STRING Y))))) (DECLARE (TYPE (INTEGER 0 *) STR::XL STR::YL)) (STR::ISTRPOS-IMPL (THE STRING X) (THE STRING Y) (THE (INTEGER 0 *) 0) STR::XL STR::YL))) (LOCAL (IN-THEORY (ENABLE STR::ISTRPOS STR::ISTRPOS-IMPL))) (DEFTHM STR::ISTRPOS-TYPE (OR (AND (INTEGERP (STR::ISTRPOS X Y)) (<= 0 (STR::ISTRPOS X Y))) (NOT (STR::ISTRPOS X Y))) :RULE-CLASSES :TYPE-PRESCRIPTION) (ENCAPSULATE NIL (LOCAL (DEFTHM STR::LEMMA (IMPLIES (AND (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) (NATP STR::XL) (NATP STR::YL) (NATP N) (<= N (LEN (EXPLODE Y))) (= STR::XL (LEN (EXPLODE X))) (= STR::YL (LEN (EXPLODE Y)))) (STR::IPREFIXP (EXPLODE X) (NTHCDR (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) (EXPLODE Y)))) :HINTS (("Goal" :INDUCT (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL))))) (DEFTHM STR::IPREFIXP-OF-ISTRPOS (IMPLIES (STR::ISTRPOS X Y) (STR::IPREFIXP (EXPLODE X) (NTHCDR (STR::ISTRPOS X Y) (EXPLODE Y)))))) (ENCAPSULATE NIL (LOCAL (DEFUN STR::MY-INDUCTION (X Y N M STR::XL STR::YL) (DECLARE (XARGS :MEASURE (NFIX (- (NFIX STR::YL) (NFIX N))))) (COND ((STR::IPREFIXP (EXPLODE X) (NTHCDR N (EXPLODE Y))) NIL) ((ZP (- (NFIX STR::YL) (NFIX N))) (LIST X Y N M STR::XL STR::YL)) (T (STR::MY-INDUCTION X Y (+ (NFIX N) 1) (IF (= (NFIX N) (NFIX M)) (+ (NFIX M) 1) (NFIX M)) STR::XL STR::YL))))) (LOCAL (DEFTHM STR::LEMMA (IMPLIES (AND (STR::IPREFIXP (EXPLODE X) (NTHCDR M (EXPLODE Y))) (NATP STR::XL) (NATP STR::YL) (NATP N) (NATP M) (<= N (NFIX M)) (<= N (LEN (EXPLODE Y))) (= STR::XL (LEN (EXPLODE X))) (= STR::YL (LEN (EXPLODE Y)))) (AND (NATP (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL)) (<= (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) M))) :HINTS (("Goal" :INDUCT (STR::MY-INDUCTION X Y N M STR::XL STR::YL) :DO-NOT (QUOTE (GENERALIZE FERTILIZE)))))) (DEFTHM STR::COMPLETENESS-OF-ISTRPOS (IMPLIES (AND (STR::IPREFIXP (EXPLODE X) (NTHCDR M (EXPLODE Y))) (FORCE (NATP M))) (AND (NATP (STR::ISTRPOS X Y)) (<= (STR::ISTRPOS X Y) M))))) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) 1) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) 2) (LOCAL (IN-THEORY (DISABLE STR::ISTREQV))) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS X Y) 1) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS X Y) 2)) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::ISTRPOS)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (DEFUND STR::ISTRPOS-IMPL (X Y N STR::XL STR::YL) (DECLARE (TYPE STRING X Y) (TYPE (INTEGER 0 *) N STR::XL STR::YL) (XARGS :GUARD (AND (STRINGP X) (STRINGP Y) (NATP STR::XL) (NATP STR::YL) (NATP N) (<= N (LENGTH Y)) (= STR::XL (LENGTH X)) (= STR::YL (LENGTH Y))) :MEASURE (NFIX (- (NFIX STR::YL) (NFIX N))))) (COND ((MBE :LOGIC (STR::IPREFIXP (EXPLODE X) (NTHCDR N (EXPLODE Y))) :EXEC (STR::ISTRPREFIXP-IMPL (THE STRING X) (THE STRING Y) (THE (INTEGER 0 *) 0) (THE (INTEGER 0 *) N) (THE (INTEGER 0 *) STR::XL) (THE (INTEGER 0 *) STR::YL))) (LNFIX N)) ((MBE :LOGIC (ZP (- (NFIX STR::YL) (NFIX N))) :EXEC (INT= N STR::YL)) NIL) (T (STR::ISTRPOS-IMPL (THE STRING X) (THE STRING Y) (THE (INTEGER 0 *) (+ 1 (THE (INTEGER 0 *) (LNFIX N)))) (THE (INTEGER 0 *) STR::XL) (THE (INTEGER 0 *) STR::YL))))) (DEFINLINED STR::ISTRPOS (X Y) (DECLARE (TYPE STRING X Y)) (LET* ((STR::XL (MBE :LOGIC (LEN (EXPLODE X)) :EXEC (LENGTH (THE STRING X)))) (STR::YL (MBE :LOGIC (LEN (EXPLODE Y)) :EXEC (LENGTH (THE STRING Y))))) (DECLARE (TYPE (INTEGER 0 *) STR::XL STR::YL)) (STR::ISTRPOS-IMPL (THE STRING X) (THE STRING Y) (THE (INTEGER 0 *) 0) STR::XL STR::YL))) (LOCAL (IN-THEORY (ENABLE STR::ISTRPOS STR::ISTRPOS-IMPL))) (DEFTHM STR::ISTRPOS-TYPE (OR (AND (INTEGERP (STR::ISTRPOS X Y)) (<= 0 (STR::ISTRPOS X Y))) (NOT (STR::ISTRPOS X Y))) :RULE-CLASSES :TYPE-PRESCRIPTION) (ENCAPSULATE NIL (LOCAL (DEFTHM STR::LEMMA (IMPLIES (AND (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) (NATP STR::XL) (NATP STR::YL) (NATP N) (<= N (LEN (EXPLODE Y))) (= STR::XL (LEN (EXPLODE X))) (= STR::YL (LEN (EXPLODE Y)))) (STR::IPREFIXP (EXPLODE X) (NTHCDR (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) (EXPLODE Y)))) :HINTS (("Goal" :INDUCT (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL))))) (DEFTHM STR::IPREFIXP-OF-ISTRPOS (IMPLIES (STR::ISTRPOS X Y) (STR::IPREFIXP (EXPLODE X) (NTHCDR (STR::ISTRPOS X Y) (EXPLODE Y)))))) (ENCAPSULATE NIL (LOCAL (DEFUN STR::MY-INDUCTION (X Y N M STR::XL STR::YL) (DECLARE (XARGS :MEASURE (NFIX (- (NFIX STR::YL) (NFIX N))))) (COND ((STR::IPREFIXP (EXPLODE X) (NTHCDR N (EXPLODE Y))) NIL) ((ZP (- (NFIX STR::YL) (NFIX N))) (LIST X Y N M STR::XL STR::YL)) (T (STR::MY-INDUCTION X Y (+ (NFIX N) 1) (IF (= (NFIX N) (NFIX M)) (+ (NFIX M) 1) (NFIX M)) STR::XL STR::YL))))) (LOCAL (DEFTHM STR::LEMMA (IMPLIES (AND (STR::IPREFIXP (EXPLODE X) (NTHCDR M (EXPLODE Y))) (NATP STR::XL) (NATP STR::YL) (NATP N) (NATP M) (<= N (NFIX M)) (<= N (LEN (EXPLODE Y))) (= STR::XL (LEN (EXPLODE X))) (= STR::YL (LEN (EXPLODE Y)))) (AND (NATP (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL)) (<= (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) M))) :HINTS (("Goal" :INDUCT (STR::MY-INDUCTION X Y N M STR::XL STR::YL) :DO-NOT (QUOTE (GENERALIZE FERTILIZE)))))) (DEFTHM STR::COMPLETENESS-OF-ISTRPOS (IMPLIES (AND (STR::IPREFIXP (EXPLODE X) (NTHCDR M (EXPLODE Y))) (FORCE (NATP M))) (AND (NATP (STR::ISTRPOS X Y)) (<= (STR::ISTRPOS X Y) M))))) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) 1) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS-IMPL X Y N STR::XL STR::YL) 2) (LOCAL (IN-THEORY (DISABLE STR::ISTREQV))) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS X Y) 1) (DEFCONG STR::ISTREQV EQUAL (STR::ISTRPOS X Y) 2))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::ISTRPOS)) (XDOC::PARENTS (QUOTE (STR::SUBSTRINGS))) (XDOC::SHORT (QUOTE "Case-insensitivly locate the first occurrence of a substring.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::ISTRPOS))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>@(call istrpos) is like @(see strpos), but the comparisons are done
in a case insensitive manner. It returns @('nil') if @('x') never occurs in
@('y'), or returns the index of the first character of the first occurrence
otherwise.</p>
<p>The function is \"efficient\" in the sense that it does not coerce its
arguments into lists, but rather traverses both strings with @(see char). On
the other hand, it is a naive string search which operates by repeatedly
calling @(see istrprefixp) rather than some better algorithm.</p>
<p>The \"soundness\" and \"completness\" of strpos are established in the
theorems @('iprefixp-of-istrpos') and @('completeness-of-istrpos').</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . STR::ISTRPOS) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::SUBSTRINGS) (:SHORT . "Case-insensitivly locate the first occurrence of a substring.") (:LONG . "<p>@(call istrpos) is like @(see strpos), but the comparisons are done
in a case insensitive manner. It returns @('nil') if @('x') never occurs in
@('y'), or returns the index of the first character of the first occurrence
otherwise.</p>
<p>The function is \"efficient\" in the sense that it does not coerce its
arguments into lists, but rather traverses both strings with @(see char). On
the other hand, it is a naive string search which operates by repeatedly
calling @(see istrprefixp) rather than some better algorithm.</p>
<p>The \"soundness\" and \"completness\" of strpos are established in the
theorems @('iprefixp-of-istrpos') and @('completeness-of-istrpos').</p>
<h3>Definitions and Theorems</h3>@(def |STR|::|ISTRPOS-IMPL|)
@(def |STR|::|ISTRPOS$INLINE|)
@(def |STR|::|ISTRPOS-TYPE|)
@(def |STR|::|IPREFIXP-OF-ISTRPOS|)
@(def |STR|::|COMPLETENESS-OF-ISTRPOS|)
@(def |STR|::|ISTREQV-IMPLIES-EQUAL-ISTRPOS-IMPL-1|)
@(def |STR|::|ISTREQV-IMPLIES-EQUAL-ISTRPOS-IMPL-2|)
@(def |STR|::|ISTREQV-IMPLIES-EQUAL-ISTRPOS-1|)
@(def |STR|::|ISTREQV-IMPLIES-EQUAL-ISTRPOS-2|)") (:FROM . "[books]/str/istrpos.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::ISTRPOS)))))) (VALUE-TRIPLE (QUOTE STR::ISTRPOS))))))
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