acl2-books-certs 6.3-5 / usr / share / acl2-6.3 / books / str / strprefixp.cert

(IN-PACKAGE "ACL2")
"ACL2 Version 6.3"
:BEGIN-PORTCULLIS-CMDS
(INCLUDE-BOOK "cutil/portcullis" :DIR :SYSTEM)
:END-PORTCULLIS-CMDS
:EXPANSION-ALIST
((7 RECORD-EXPANSION (DEFSECTION STR::STRPREFIXP-IMPL :PARENTS (STR::STRPREFIXP) :SHORT "Fast implementation of @(see strprefixp)." (DEFUND STR::STRPREFIXP-IMPL (X Y STR::XN STR::YN STR::XL STR::YL) (DECLARE (TYPE STRING X) (TYPE STRING Y) (TYPE INTEGER STR::XN) (TYPE INTEGER STR::YN) (TYPE INTEGER STR::XL) (TYPE INTEGER STR::YL) (XARGS :GUARD (AND (STRINGP X) (STRINGP Y) (NATP STR::XN) (NATP STR::YN) (NATP STR::XL) (NATP STR::YL) (= STR::XL (LENGTH X)) (= STR::YL (LENGTH Y)) (<= STR::XN (LENGTH X)) (<= STR::YN (LENGTH Y))) :MEASURE (MIN (NFIX (- (NFIX STR::XL) (NFIX STR::XN))) (NFIX (- (NFIX STR::YL) (NFIX STR::YN)))))) (COND ((MBE :LOGIC (ZP (- (NFIX STR::XL) (NFIX STR::XN))) :EXEC (INT= STR::XN STR::XL)) T) ((MBE :LOGIC (ZP (- (NFIX STR::YL) (NFIX STR::YN))) :EXEC (INT= STR::YN STR::YL)) NIL) ((EQL (THE CHARACTER (CHAR X STR::XN)) (THE CHARACTER (CHAR Y STR::YN))) (MBE :LOGIC (STR::STRPREFIXP-IMPL X Y (+ (NFIX STR::XN) 1) (+ (NFIX STR::YN) 1) STR::XL STR::YL) :EXEC (STR::STRPREFIXP-IMPL (THE STRING X) (THE STRING Y) (THE INTEGER (+ (THE INTEGER STR::XN) 1)) (THE INTEGER (+ (THE INTEGER STR::YN) 1)) (THE INTEGER STR::XL) (THE INTEGER STR::YL)))) (T NIL))) (LOCAL (IN-THEORY (ENABLE STR::STRPREFIXP-IMPL))) (DEFTHM STR::STRPREFIXP-IMPL-ELIM (IMPLIES (AND (FORCE (STRINGP X)) (FORCE (STRINGP Y)) (FORCE (NATP STR::XN)) (FORCE (NATP STR::YN)) (FORCE (= STR::XL (LENGTH X))) (FORCE (= STR::YL (LENGTH Y))) (FORCE (<= STR::XN STR::XL)) (FORCE (<= STR::YN STR::YL))) (EQUAL (STR::STRPREFIXP-IMPL X Y STR::XN STR::YN STR::XL STR::YL) (PREFIXP (NTHCDR STR::XN (EXPLODE X)) (NTHCDR STR::YN (EXPLODE Y))))))) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::STRPREFIXP-IMPL)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (DEFUND STR::STRPREFIXP-IMPL (X Y STR::XN STR::YN STR::XL STR::YL) (DECLARE (TYPE STRING X) (TYPE STRING Y) (TYPE INTEGER STR::XN) (TYPE INTEGER STR::YN) (TYPE INTEGER STR::XL) (TYPE INTEGER STR::YL) (XARGS :GUARD (AND (STRINGP X) (STRINGP Y) (NATP STR::XN) (NATP STR::YN) (NATP STR::XL) (NATP STR::YL) (= STR::XL (LENGTH X)) (= STR::YL (LENGTH Y)) (<= STR::XN (LENGTH X)) (<= STR::YN (LENGTH Y))) :MEASURE (MIN (NFIX (- (NFIX STR::XL) (NFIX STR::XN))) (NFIX (- (NFIX STR::YL) (NFIX STR::YN)))))) (COND ((MBE :LOGIC (ZP (- (NFIX STR::XL) (NFIX STR::XN))) :EXEC (INT= STR::XN STR::XL)) T) ((MBE :LOGIC (ZP (- (NFIX STR::YL) (NFIX STR::YN))) :EXEC (INT= STR::YN STR::YL)) NIL) ((EQL (THE CHARACTER (CHAR X STR::XN)) (THE CHARACTER (CHAR Y STR::YN))) (MBE :LOGIC (STR::STRPREFIXP-IMPL X Y (+ (NFIX STR::XN) 1) (+ (NFIX STR::YN) 1) STR::XL STR::YL) :EXEC (STR::STRPREFIXP-IMPL (THE STRING X) (THE STRING Y) (THE INTEGER (+ (THE INTEGER STR::XN) 1)) (THE INTEGER (+ (THE INTEGER STR::YN) 1)) (THE INTEGER STR::XL) (THE INTEGER STR::YL)))) (T NIL))) (LOCAL (IN-THEORY (ENABLE STR::STRPREFIXP-IMPL))) (DEFTHM STR::STRPREFIXP-IMPL-ELIM (IMPLIES (AND (FORCE (STRINGP X)) (FORCE (STRINGP Y)) (FORCE (NATP STR::XN)) (FORCE (NATP STR::YN)) (FORCE (= STR::XL (LENGTH X))) (FORCE (= STR::YL (LENGTH Y))) (FORCE (<= STR::XN STR::XL)) (FORCE (<= STR::YN STR::YL))) (EQUAL (STR::STRPREFIXP-IMPL X Y STR::XN STR::YN STR::XL STR::YL) (PREFIXP (NTHCDR STR::XN (EXPLODE X)) (NTHCDR STR::YN (EXPLODE Y)))))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::STRPREFIXP-IMPL)) (XDOC::PARENTS (QUOTE (STR::STRPREFIXP))) (XDOC::SHORT (QUOTE "Fast implementation of @(see strprefixp).")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::STRPREFIXP-IMPL))) 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 "") (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::STRPREFIXP-IMPL) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::STRPREFIXP) (:SHORT . "Fast implementation of @(see strprefixp).") (:LONG . "

<h3>Definitions and Theorems</h3>@(def |STR|::|STRPREFIXP-IMPL|)
@(def |STR|::|STRPREFIXP-IMPL-ELIM|)") (:FROM . "[books]/str/strprefixp.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::STRPREFIXP-IMPL)))))) (VALUE-TRIPLE (QUOTE STR::STRPREFIXP-IMPL))))) (8 RECORD-EXPANSION (DEFSECTION STR::STRPREFIXP :PARENTS (STR::SUBSTRINGS) :SHORT "Case-sensitive string prefix test." :LONG "<p>@(call strprefixp) determines if the string @('x') is a prefix of
the string @('y'), in a case-sensitive manner.</p>

<p>Logically, this is identical to</p>

@({
 (prefixp (explode x) (explode y))
})

<p>But we use a more efficient implementation which avoids coercing the strings
into character lists.</p>" (DEFINLINE STR::STRPREFIXP (X Y) (DECLARE (TYPE STRING X) (TYPE STRING Y)) (MBE :LOGIC (PREFIXP (EXPLODE X) (EXPLODE Y)) :EXEC (STR::STRPREFIXP-IMPL (THE STRING X) (THE STRING Y) (THE INTEGER 0) (THE INTEGER 0) (THE INTEGER (LENGTH (THE STRING X))) (THE INTEGER (LENGTH (THE STRING Y)))))) (DEFCONG STR::STREQV EQUAL (STR::STRPREFIXP X Y) 1) (DEFCONG STR::STREQV EQUAL (STR::STRPREFIXP X Y) 2)) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::STRPREFIXP)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (DEFINLINE STR::STRPREFIXP (X Y) (DECLARE (TYPE STRING X) (TYPE STRING Y)) (MBE :LOGIC (PREFIXP (EXPLODE X) (EXPLODE Y)) :EXEC (STR::STRPREFIXP-IMPL (THE STRING X) (THE STRING Y) (THE INTEGER 0) (THE INTEGER 0) (THE INTEGER (LENGTH (THE STRING X))) (THE INTEGER (LENGTH (THE STRING Y)))))) (DEFCONG STR::STREQV EQUAL (STR::STRPREFIXP X Y) 1) (DEFCONG STR::STREQV EQUAL (STR::STRPREFIXP X Y) 2))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::STRPREFIXP)) (XDOC::PARENTS (QUOTE (STR::SUBSTRINGS))) (XDOC::SHORT (QUOTE "Case-sensitive string prefix test.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::STRPREFIXP))) 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 strprefixp) determines if the string @('x') is a prefix of
the string @('y'), in a case-sensitive manner.</p>

<p>Logically, this is identical to</p>

@({
 (prefixp (explode x) (explode y))
})

<p>But we use a more efficient implementation which avoids coercing the strings
into character lists.</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::STRPREFIXP) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::SUBSTRINGS) (:SHORT . "Case-sensitive string prefix test.") (:LONG . "<p>@(call strprefixp) determines if the string @('x') is a prefix of
the string @('y'), in a case-sensitive manner.</p>

<p>Logically, this is identical to</p>

@({
 (prefixp (explode x) (explode y))
})

<p>But we use a more efficient implementation which avoids coercing the strings
into character lists.</p>

<h3>Definitions and Theorems</h3>@(def |STR|::|STRPREFIXP$INLINE|)
@(def |STR|::|STREQV-IMPLIES-EQUAL-STRPREFIXP-1|)
@(def |STR|::|STREQV-IMPLIES-EQUAL-STRPREFIXP-2|)") (:FROM . "[books]/str/strprefixp.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::STRPREFIXP)))))) (VALUE-TRIPLE (QUOTE STR::STRPREFIXP))))))
(("/usr/share/acl2-6.3/books/cutil/portcullis.lisp" "cutil/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1188104018) ("/usr/share/acl2-6.3/books/std/osets/portcullis.lisp" "std/osets/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1689687557) ("/usr/share/acl2-6.3/books/xdoc/portcullis.lisp" "xdoc/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1473208573) ("/usr/share/acl2-6.3/books/str/portcullis.lisp" "str/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 2077071243))
(("/usr/share/acl2-6.3/books/str/strprefixp.lisp" "strprefixp" "strprefixp" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 2141614236) ("/usr/share/acl2-6.3/books/std/lists/prefixp.lisp" "std/lists/prefixp" "prefixp" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 689235789) ("/usr/share/acl2-6.3/books/std/lists/equiv.lisp" "equiv" "equiv" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1948483556) ("/usr/share/acl2-6.3/books/str/eqv.lisp" "eqv" "eqv" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1920438599) (LOCAL ("/usr/share/acl2-6.3/books/str/arithmetic.lisp" "arithmetic" "arithmetic" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 216355320)) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/repeat.lisp" "std/lists/repeat" "repeat" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 293545519)) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/nthcdr.lisp" "nthcdr" "nthcdr" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1415704060)) ("/usr/share/acl2-6.3/books/std/lists/rev.lisp" "rev" "rev" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 327117871) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/nthcdr.lisp" "std/lists/nthcdr" "nthcdr" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1415704060)) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/len.lisp" "std/lists/len" "len" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 963137114)) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/take.lisp" "std/lists/take" "take" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1496833916)) ("/usr/share/acl2-6.3/books/std/lists/rev.lisp" "std/lists/rev" "rev" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 327117871) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/append.lisp" "append" "append" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 567759210)) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/revappend.lisp" "revappend" "revappend" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1368863429)) ("/usr/share/acl2-6.3/books/std/lists/equiv.lisp" "std/lists/equiv" "equiv" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1948483556) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/take.lisp" "take" "take" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1496833916)) ("/usr/share/acl2-6.3/books/str/coerce.lisp" "coerce" "coerce" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1053051260) ("/usr/share/acl2-6.3/books/str/make-character-list.lisp" "make-character-list" "make-character-list" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1622566814) (LOCAL ("/usr/share/acl2-6.3/books/std/lists/append.lisp" "std/lists/append" "append" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 567759210)) ("/usr/share/acl2-6.3/books/std/lists/list-fix.lisp" "list-fix" "list-fix" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1844974260) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/top.lisp" "arithmetic/top" "top" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 956305966)) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/rationals.lisp" "rationals" "rationals" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1403689963)) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/mod-gcd.lisp" "mod-gcd" "mod-gcd" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1629957550)) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/natp-posp.lisp" "natp-posp" "natp-posp" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 2140150970)) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/inequalities.lisp" "inequalities" "inequalities" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1221989523)) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/nat-listp.lisp" "nat-listp" "nat-listp" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1767896370)) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/rational-listp.lisp" "rational-listp" "rational-listp" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1775556314)) (LOCAL ("/usr/share/acl2-6.3/books/arithmetic/equalities.lisp" "equalities" "equalities" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 597034595)) (LOCAL ("/usr/share/acl2-6.3/books/cowles/acl2-crg.lisp" "cowles/acl2-crg" "acl2-crg" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 761519866)) (LOCAL ("/usr/share/acl2-6.3/books/cowles/acl2-agp.lisp" "acl2-agp" "acl2-agp" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 2007324914)) (LOCAL ("/usr/share/acl2-6.3/books/cowles/acl2-asg.lisp" "acl2-asg" "acl2-asg" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1939433116)) ("/usr/share/acl2-6.3/books/str/char-fix.lisp" "char-fix" "char-fix" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 70055851) ("/usr/share/acl2-6.3/books/misc/definline.lisp" "misc/definline" "definline" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1571016648) ("/usr/share/acl2-6.3/books/xdoc/top.lisp" "xdoc/top" "top" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1214825095) ("/usr/share/acl2-6.3/books/xdoc/book-thms.lisp" "book-thms" "book-thms" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1105796063) ("/usr/share/acl2-6.3/books/xdoc/base.lisp" "base" "base" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 454271148) ("/usr/share/acl2-6.3/books/xdoc/portcullis.lisp" "portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1473208573) ("/usr/share/acl2-6.3/books/cutil/portcullis.lisp" "cutil/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1188104018) ("/usr/share/acl2-6.3/books/std/osets/portcullis.lisp" "std/osets/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1689687557) ("/usr/share/acl2-6.3/books/xdoc/portcullis.lisp" "xdoc/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1473208573) ("/usr/share/acl2-6.3/books/str/portcullis.lisp" "str/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 2077071243))
1471852373