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

(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::BASIC-NATCHARS :PARENTS (STR::NATCHARS) :SHORT "Logically simple definition that is mostly similar to @(see natchars)." :LONG "<p>@(call basic-natchars) almost computes @('(natchars n)'), but when
@('n') is zero it returns @('nil') instead of @('(#\\0)').</p>" (DEFUND STR::BASIC-NATCHARS (N) (DECLARE (XARGS :GUARD (NATP N))) (IF (ZP N) NIL (CONS (DIGIT-TO-CHAR (MOD N 10)) (STR::BASIC-NATCHARS (FLOOR N 10))))) (LOCAL (IN-THEORY (ENABLE STR::BASIC-NATCHARS))) (DEFTHM STR::BASIC-NATCHARS-WHEN-ZP (IMPLIES (ZP N) (EQUAL (STR::BASIC-NATCHARS N) NIL))) (DEFTHM STR::TRUE-LISTP-OF-BASIC-NATCHARS (TRUE-LISTP (STR::BASIC-NATCHARS N)) :RULE-CLASSES :TYPE-PRESCRIPTION) (DEFTHM STR::CHARACTER-LISTP-OF-BASIC-NATCHARS (CHARACTER-LISTP (STR::BASIC-NATCHARS N))) (DEFTHM STR::DIGIT-LISTP-OF-BASIC-NATCHARS (STR::DIGIT-LISTP (STR::BASIC-NATCHARS N))) (DEFTHM STR::BASIC-NATCHARS-UNDER-IFF (IFF (STR::BASIC-NATCHARS N) (NOT (ZP N)))) (DEFTHM STR::CONSP-OF-BASIC-NATCHARS (EQUAL (CONSP (STR::BASIC-NATCHARS N)) (IF (STR::BASIC-NATCHARS N) T NIL))) (ENCAPSULATE NIL (LOCAL (DEFUN STR::MY-INDUCTION (N M) (IF (OR (ZP N) (ZP M)) NIL (STR::MY-INDUCTION (FLOOR N 10) (FLOOR M 10))))) (DEFTHM STR::BASIC-NATCHARS-ONE-TO-ONE (EQUAL (EQUAL (STR::BASIC-NATCHARS N) (STR::BASIC-NATCHARS M)) (EQUAL (NFIX N) (NFIX M))) :HINTS (("Goal" :INDUCT (STR::MY-INDUCTION N M)))))) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::BASIC-NATCHARS)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (DEFUND STR::BASIC-NATCHARS (N) (DECLARE (XARGS :GUARD (NATP N))) (IF (ZP N) NIL (CONS (DIGIT-TO-CHAR (MOD N 10)) (STR::BASIC-NATCHARS (FLOOR N 10))))) (LOCAL (IN-THEORY (ENABLE STR::BASIC-NATCHARS))) (DEFTHM STR::BASIC-NATCHARS-WHEN-ZP (IMPLIES (ZP N) (EQUAL (STR::BASIC-NATCHARS N) NIL))) (DEFTHM STR::TRUE-LISTP-OF-BASIC-NATCHARS (TRUE-LISTP (STR::BASIC-NATCHARS N)) :RULE-CLASSES :TYPE-PRESCRIPTION) (DEFTHM STR::CHARACTER-LISTP-OF-BASIC-NATCHARS (CHARACTER-LISTP (STR::BASIC-NATCHARS N))) (DEFTHM STR::DIGIT-LISTP-OF-BASIC-NATCHARS (STR::DIGIT-LISTP (STR::BASIC-NATCHARS N))) (DEFTHM STR::BASIC-NATCHARS-UNDER-IFF (IFF (STR::BASIC-NATCHARS N) (NOT (ZP N)))) (DEFTHM STR::CONSP-OF-BASIC-NATCHARS (EQUAL (CONSP (STR::BASIC-NATCHARS N)) (IF (STR::BASIC-NATCHARS N) T NIL))) (ENCAPSULATE NIL (LOCAL (DEFUN STR::MY-INDUCTION (N M) (IF (OR (ZP N) (ZP M)) NIL (STR::MY-INDUCTION (FLOOR N 10) (FLOOR M 10))))) (DEFTHM STR::BASIC-NATCHARS-ONE-TO-ONE (EQUAL (EQUAL (STR::BASIC-NATCHARS N) (STR::BASIC-NATCHARS M)) (EQUAL (NFIX N) (NFIX M))) :HINTS (("Goal" :INDUCT (STR::MY-INDUCTION N M))))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::BASIC-NATCHARS)) (XDOC::PARENTS (QUOTE (STR::NATCHARS))) (XDOC::SHORT (QUOTE "Logically simple definition that is mostly similar to @(see natchars).")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::BASIC-NATCHARS))) 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 basic-natchars) almost computes @('(natchars n)'), but when
@('n') is zero it returns @('nil') instead of @('(#\\0)').</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::BASIC-NATCHARS) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::NATCHARS) (:SHORT . "Logically simple definition that is mostly similar to @(see natchars).") (:LONG . "<p>@(call basic-natchars) almost computes @('(natchars n)'), but when
@('n') is zero it returns @('nil') instead of @('(#\\0)').</p>

<h3>Definitions and Theorems</h3>@(def |STR|::|BASIC-NATCHARS|)
@(def |STR|::|BASIC-NATCHARS-WHEN-ZP|)
@(def |STR|::|TRUE-LISTP-OF-BASIC-NATCHARS|)
@(def |STR|::|CHARACTER-LISTP-OF-BASIC-NATCHARS|)
@(def |STR|::|DIGIT-LISTP-OF-BASIC-NATCHARS|)
@(def |STR|::|BASIC-NATCHARS-UNDER-IFF|)
@(def |STR|::|CONSP-OF-BASIC-NATCHARS|)
@(def |STR|::|BASIC-NATCHARS-ONE-TO-ONE|)") (:FROM . "[books]/str/natstr.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::BASIC-NATCHARS)))))) (VALUE-TRIPLE (QUOTE STR::BASIC-NATCHARS))))) (5 RECORD-EXPANSION (DEFSECTION STR::NATCHARS :PARENTS (STR::NUMBERS) :SHORT "Convert a natural number into a list of characters." :LONG "<p>For instance, @('(natchars 123)') is @('(#\\1 #\\2 #\\3)').</p>" (LOCAL (DEFTHM STR::DIGIT-LIST-VALUE-OF-REV-OF-BASIC-NATCHARS (EQUAL (STR::DIGIT-LIST-VALUE (REV (STR::BASIC-NATCHARS N))) (NFIX N)) :HINTS (("Goal" :INDUCT (STR::BASIC-NATCHARS N) :IN-THEORY (E/D (STR::BASIC-NATCHARS) (DIGIT-TO-CHAR)))))) (DEFUND STR::NATCHARS-AUX (N STR::ACC) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N) :VERIFY-GUARDS NIL)) (IF (ZP N) STR::ACC (STR::NATCHARS-AUX (THE INTEGER (TRUNCATE (THE INTEGER N) 10)) (CONS (THE CHARACTER (CODE-CHAR (THE (UNSIGNED-BYTE 8) (+ (THE (UNSIGNED-BYTE 8) 48) (THE (UNSIGNED-BYTE 8) (REM (THE INTEGER N) 10)))))) STR::ACC)))) (DEFINLINED STR::NATCHARS (N) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N) :VERIFY-GUARDS NIL)) (OR (STR::NATCHARS-AUX N NIL) (QUOTE (#\0)))) (DEFTHM STR::NATCHARS-AUX-REDEFINITION (EQUAL (STR::NATCHARS-AUX N STR::ACC) (REVAPPEND (STR::BASIC-NATCHARS N) STR::ACC)) :RULE-CLASSES :DEFINITION :HINTS (("Goal" :IN-THEORY (ENABLE STR::NATCHARS-AUX STR::BASIC-NATCHARS)))) (VERIFY-GUARDS STR::NATCHARS-AUX) (VERIFY-GUARDS STR::NATCHARS$INLINE) (LOCAL (IN-THEORY (ENABLE STR::NATCHARS))) (DEFTHM STR::TRUE-LISTP-OF-NATCHARS (TRUE-LISTP (STR::NATCHARS N)) :RULE-CLASSES :TYPE-PRESCRIPTION) (DEFTHM STR::CHARACTER-LISTP-OF-NATCHARS (CHARACTER-LISTP (STR::NATCHARS N))) (DEFTHM STR::DIGIT-LISTP-OF-NATCHARS (STR::DIGIT-LISTP (STR::NATCHARS N))) (ENCAPSULATE NIL (LOCAL (DEFTHM STR::LEMMA1 (EQUAL (EQUAL (REV X) (LIST Y)) (AND (CONSP X) (NOT (CONSP (CDR X))) (EQUAL (CAR X) Y))) :HINTS (("Goal" :IN-THEORY (ENABLE REV))))) (LOCAL (DEFTHMD STR::LEMMA2 (NOT (EQUAL (STR::BASIC-NATCHARS N) (QUOTE (#\0)))) :HINTS (("Goal" :IN-THEORY (ENABLE STR::BASIC-NATCHARS))))) (DEFTHM STR::NATCHARS-ONE-TO-ONE (EQUAL (EQUAL (STR::NATCHARS N) (STR::NATCHARS M)) (EQUAL (NFIX N) (NFIX M))) :HINTS (("Goal" :IN-THEORY (DISABLE STR::BASIC-NATCHARS-ONE-TO-ONE) :USE ((:INSTANCE STR::BASIC-NATCHARS-ONE-TO-ONE) (:INSTANCE STR::LEMMA2) (:INSTANCE STR::LEMMA2 (N M))))))) (DEFTHM STR::DIGIT-LIST-VALUE-OF-NATCHARS (EQUAL (STR::DIGIT-LIST-VALUE (STR::NATCHARS N)) (NFIX N)))) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::NATCHARS)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOCAL (DEFTHM STR::DIGIT-LIST-VALUE-OF-REV-OF-BASIC-NATCHARS (EQUAL (STR::DIGIT-LIST-VALUE (REV (STR::BASIC-NATCHARS N))) (NFIX N)) :HINTS (("Goal" :INDUCT (STR::BASIC-NATCHARS N) :IN-THEORY (E/D (STR::BASIC-NATCHARS) (DIGIT-TO-CHAR)))))) (DEFUND STR::NATCHARS-AUX (N STR::ACC) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N) :VERIFY-GUARDS NIL)) (IF (ZP N) STR::ACC (STR::NATCHARS-AUX (THE INTEGER (TRUNCATE (THE INTEGER N) 10)) (CONS (THE CHARACTER (CODE-CHAR (THE (UNSIGNED-BYTE 8) (+ (THE (UNSIGNED-BYTE 8) 48) (THE (UNSIGNED-BYTE 8) (REM (THE INTEGER N) 10)))))) STR::ACC)))) (DEFINLINED STR::NATCHARS (N) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N) :VERIFY-GUARDS NIL)) (OR (STR::NATCHARS-AUX N NIL) (QUOTE (#\0)))) (DEFTHM STR::NATCHARS-AUX-REDEFINITION (EQUAL (STR::NATCHARS-AUX N STR::ACC) (REVAPPEND (STR::BASIC-NATCHARS N) STR::ACC)) :RULE-CLASSES :DEFINITION :HINTS (("Goal" :IN-THEORY (ENABLE STR::NATCHARS-AUX STR::BASIC-NATCHARS)))) (VERIFY-GUARDS STR::NATCHARS-AUX) (VERIFY-GUARDS STR::NATCHARS$INLINE) (LOCAL (IN-THEORY (ENABLE STR::NATCHARS))) (DEFTHM STR::TRUE-LISTP-OF-NATCHARS (TRUE-LISTP (STR::NATCHARS N)) :RULE-CLASSES :TYPE-PRESCRIPTION) (DEFTHM STR::CHARACTER-LISTP-OF-NATCHARS (CHARACTER-LISTP (STR::NATCHARS N))) (DEFTHM STR::DIGIT-LISTP-OF-NATCHARS (STR::DIGIT-LISTP (STR::NATCHARS N))) (ENCAPSULATE NIL (LOCAL (DEFTHM STR::LEMMA1 (EQUAL (EQUAL (REV X) (LIST Y)) (AND (CONSP X) (NOT (CONSP (CDR X))) (EQUAL (CAR X) Y))) :HINTS (("Goal" :IN-THEORY (ENABLE REV))))) (LOCAL (DEFTHMD STR::LEMMA2 (NOT (EQUAL (STR::BASIC-NATCHARS N) (QUOTE (#\0)))) :HINTS (("Goal" :IN-THEORY (ENABLE STR::BASIC-NATCHARS))))) (DEFTHM STR::NATCHARS-ONE-TO-ONE (EQUAL (EQUAL (STR::NATCHARS N) (STR::NATCHARS M)) (EQUAL (NFIX N) (NFIX M))) :HINTS (("Goal" :IN-THEORY (DISABLE STR::BASIC-NATCHARS-ONE-TO-ONE) :USE ((:INSTANCE STR::BASIC-NATCHARS-ONE-TO-ONE) (:INSTANCE STR::LEMMA2) (:INSTANCE STR::LEMMA2 (N M))))))) (DEFTHM STR::DIGIT-LIST-VALUE-OF-NATCHARS (EQUAL (STR::DIGIT-LIST-VALUE (STR::NATCHARS N)) (NFIX N))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::NATCHARS)) (XDOC::PARENTS (QUOTE (STR::NUMBERS))) (XDOC::SHORT (QUOTE "Convert a natural number into a list of characters.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::NATCHARS))) 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>For instance, @('(natchars 123)') is @('(#\\1 #\\2 #\\3)').</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::NATCHARS) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::NUMBERS) (:SHORT . "Convert a natural number into a list of characters.") (:LONG . "<p>For instance, @('(natchars 123)') is @('(#\\1 #\\2 #\\3)').</p>

<h3>Definitions and Theorems</h3>@(def |STR|::|NATCHARS-AUX|)
@(def |STR|::|NATCHARS$INLINE|)
@(def |STR|::|NATCHARS-AUX-REDEFINITION|)
@(def |STR|::|TRUE-LISTP-OF-NATCHARS|)
@(def |STR|::|CHARACTER-LISTP-OF-NATCHARS|)
@(def |STR|::|DIGIT-LISTP-OF-NATCHARS|)
@(def |STR|::|NATCHARS-ONE-TO-ONE|)
@(def |STR|::|DIGIT-LIST-VALUE-OF-NATCHARS|)") (:FROM . "[books]/str/natstr.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::NATCHARS)))))) (VALUE-TRIPLE (QUOTE STR::NATCHARS))))) (6 RECORD-EXPANSION (DEFSECTION STR::NATSTR :PARENTS (STR::NUMBERS) :SHORT "Convert a natural number into a string." :LONG "<p>For instance, @('(natstr 123)') is @('\"123\"').</p>" (DEFINLINED STR::NATSTR (N) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N))) (IMPLODE (STR::NATCHARS N))) (LOCAL (IN-THEORY (ENABLE STR::NATSTR))) (DEFTHM STR::STRINGP-OF-NATSTR (STRINGP (STR::NATSTR N)) :RULE-CLASSES :TYPE-PRESCRIPTION) (DEFTHM STR::DIGIT-LISTP-OF-NATSTR (STR::DIGIT-LISTP (EXPLODE (STR::NATSTR N)))) (DEFTHM STR::NATSTR-ONE-TO-ONE (EQUAL (EQUAL (STR::NATSTR N) (STR::NATSTR M)) (EQUAL (NFIX N) (NFIX M)))) (DEFTHM STR::DIGIT-LIST-VALUE-OF-NATSTR (EQUAL (STR::DIGIT-LIST-VALUE (EXPLODE (STR::NATSTR N))) (NFIX N))) (DEFTHM STR::NATSTR-NONEMPTY (NOT (EQUAL (STR::NATSTR N) "")))) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::NATSTR)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (DEFINLINED STR::NATSTR (N) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N))) (IMPLODE (STR::NATCHARS N))) (LOCAL (IN-THEORY (ENABLE STR::NATSTR))) (DEFTHM STR::STRINGP-OF-NATSTR (STRINGP (STR::NATSTR N)) :RULE-CLASSES :TYPE-PRESCRIPTION) (DEFTHM STR::DIGIT-LISTP-OF-NATSTR (STR::DIGIT-LISTP (EXPLODE (STR::NATSTR N)))) (DEFTHM STR::NATSTR-ONE-TO-ONE (EQUAL (EQUAL (STR::NATSTR N) (STR::NATSTR M)) (EQUAL (NFIX N) (NFIX M)))) (DEFTHM STR::DIGIT-LIST-VALUE-OF-NATSTR (EQUAL (STR::DIGIT-LIST-VALUE (EXPLODE (STR::NATSTR N))) (NFIX N))) (DEFTHM STR::NATSTR-NONEMPTY (NOT (EQUAL (STR::NATSTR N) ""))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::NATSTR)) (XDOC::PARENTS (QUOTE (STR::NUMBERS))) (XDOC::SHORT (QUOTE "Convert a natural number into a string.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::NATSTR))) 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>For instance, @('(natstr 123)') is @('\"123\"').</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::NATSTR) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::NUMBERS) (:SHORT . "Convert a natural number into a string.") (:LONG . "<p>For instance, @('(natstr 123)') is @('\"123\"').</p>

<h3>Definitions and Theorems</h3>@(def |STR|::|NATSTR$INLINE|)
@(def |STR|::|STRINGP-OF-NATSTR|)
@(def |STR|::|DIGIT-LISTP-OF-NATSTR|)
@(def |STR|::|NATSTR-ONE-TO-ONE|)
@(def |STR|::|DIGIT-LIST-VALUE-OF-NATSTR|)
@(def |STR|::|NATSTR-NONEMPTY|)") (:FROM . "[books]/str/natstr.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::NATSTR)))))) (VALUE-TRIPLE (QUOTE STR::NATSTR))))) (7 RECORD-EXPANSION (DEFSECTION STR::NATSTR-LIST :PARENTS (STR::NUMBERS) :SHORT "Convert a list of natural numbers into a list of strings." (DEFUND STR::NATSTR-LIST (X) (DECLARE (XARGS :GUARD (NAT-LISTP X))) (IF (ATOM X) NIL (CONS (STR::NATSTR (CAR X)) (STR::NATSTR-LIST (CDR X))))) (LOCAL (IN-THEORY (ENABLE STR::NATSTR-LIST))) (DEFTHM STR::NATSTR-LIST-WHEN-ATOM (IMPLIES (ATOM X) (EQUAL (STR::NATSTR-LIST X) NIL))) (DEFTHM STR::NATSTR-LIST-OF-CONS (EQUAL (STR::NATSTR-LIST (CONS A X)) (CONS (STR::NATSTR A) (STR::NATSTR-LIST X)))) (DEFTHM STR::STRING-LISTP-OF-NATSTR-LIST (STRING-LISTP (STR::NATSTR-LIST X)))) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::NATSTR-LIST)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (DEFUND STR::NATSTR-LIST (X) (DECLARE (XARGS :GUARD (NAT-LISTP X))) (IF (ATOM X) NIL (CONS (STR::NATSTR (CAR X)) (STR::NATSTR-LIST (CDR X))))) (LOCAL (IN-THEORY (ENABLE STR::NATSTR-LIST))) (DEFTHM STR::NATSTR-LIST-WHEN-ATOM (IMPLIES (ATOM X) (EQUAL (STR::NATSTR-LIST X) NIL))) (DEFTHM STR::NATSTR-LIST-OF-CONS (EQUAL (STR::NATSTR-LIST (CONS A X)) (CONS (STR::NATSTR A) (STR::NATSTR-LIST X)))) (DEFTHM STR::STRING-LISTP-OF-NATSTR-LIST (STRING-LISTP (STR::NATSTR-LIST X))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::NATSTR-LIST)) (XDOC::PARENTS (QUOTE (STR::NUMBERS))) (XDOC::SHORT (QUOTE "Convert a list of natural numbers into a list of strings.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::NATSTR-LIST))) 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::NATSTR-LIST) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::NUMBERS) (:SHORT . "Convert a list of natural numbers into a list of strings.") (:LONG . "

<h3>Definitions and Theorems</h3>@(def |STR|::|NATSTR-LIST|)
@(def |STR|::|NATSTR-LIST-WHEN-ATOM|)
@(def |STR|::|NATSTR-LIST-OF-CONS|)
@(def |STR|::|STRING-LISTP-OF-NATSTR-LIST|)") (:FROM . "[books]/str/natstr.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::NATSTR-LIST)))))) (VALUE-TRIPLE (QUOTE STR::NATSTR-LIST))))) (8 RECORD-EXPANSION (DEFSECTION STR::REVAPPEND-NATCHARS :PARENTS (STR::NUMBERS) :SHORT "More efficient version of @('(revappend (natchars n) acc).')" :LONG "<p>This can be useful when building strings by consing together
characters in reverse order.</p>" (DEFUND STR::REVAPPEND-NATCHARS-AUX (N STR::ACC) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (AND (NATP N)))) (IF (ZP N) STR::ACC (CONS (THE CHARACTER (CODE-CHAR (THE (UNSIGNED-BYTE 8) (+ (THE (UNSIGNED-BYTE 8) 48) (THE (UNSIGNED-BYTE 8) (REM (THE INTEGER N) 10)))))) (STR::REVAPPEND-NATCHARS-AUX (THE INTEGER (TRUNCATE (THE INTEGER N) 10)) STR::ACC)))) (DEFTHM STR::REVAPPEND-NATCHARS-AUX-REDEF (EQUAL (STR::REVAPPEND-NATCHARS-AUX N STR::ACC) (APPEND (STR::BASIC-NATCHARS N) STR::ACC)) :HINTS (("Goal" :IN-THEORY (ENABLE STR::REVAPPEND-NATCHARS-AUX STR::BASIC-NATCHARS)))) (DEFINLINE STR::REVAPPEND-NATCHARS (N STR::ACC) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N) :GUARD-HINTS (("Goal" :IN-THEORY (ENABLE STR::NATCHARS))))) (MBE :LOGIC (REVAPPEND (STR::NATCHARS N) STR::ACC) :EXEC (IF (ZP N) (CONS #\0 STR::ACC) (STR::REVAPPEND-NATCHARS-AUX N STR::ACC))))) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE STR::REVAPPEND-NATCHARS)) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (DEFUND STR::REVAPPEND-NATCHARS-AUX (N STR::ACC) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (AND (NATP N)))) (IF (ZP N) STR::ACC (CONS (THE CHARACTER (CODE-CHAR (THE (UNSIGNED-BYTE 8) (+ (THE (UNSIGNED-BYTE 8) 48) (THE (UNSIGNED-BYTE 8) (REM (THE INTEGER N) 10)))))) (STR::REVAPPEND-NATCHARS-AUX (THE INTEGER (TRUNCATE (THE INTEGER N) 10)) STR::ACC)))) (DEFTHM STR::REVAPPEND-NATCHARS-AUX-REDEF (EQUAL (STR::REVAPPEND-NATCHARS-AUX N STR::ACC) (APPEND (STR::BASIC-NATCHARS N) STR::ACC)) :HINTS (("Goal" :IN-THEORY (ENABLE STR::REVAPPEND-NATCHARS-AUX STR::BASIC-NATCHARS)))) (DEFINLINE STR::REVAPPEND-NATCHARS (N STR::ACC) (DECLARE (TYPE INTEGER N) (XARGS :GUARD (NATP N) :GUARD-HINTS (("Goal" :IN-THEORY (ENABLE STR::NATCHARS))))) (MBE :LOGIC (REVAPPEND (STR::NATCHARS N) STR::ACC) :EXEC (IF (ZP N) (CONS #\0 STR::ACC) (STR::REVAPPEND-NATCHARS-AUX N STR::ACC)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE STR::REVAPPEND-NATCHARS)) (XDOC::PARENTS (QUOTE (STR::NUMBERS))) (XDOC::SHORT (QUOTE "More efficient version of @('(revappend (natchars n) acc).')")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE STR::REVAPPEND-NATCHARS))) 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>This can be useful when building strings by consing together
characters in reverse order.</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::REVAPPEND-NATCHARS) (:BASE-PKG . STR::ACL2-PKG-WITNESS) (:PARENTS STR::NUMBERS) (:SHORT . "More efficient version of @('(revappend (natchars n) acc).')") (:LONG . "<p>This can be useful when building strings by consing together
characters in reverse order.</p>

<h3>Definitions and Theorems</h3>@(def |STR|::|REVAPPEND-NATCHARS-AUX|)
@(def |STR|::|REVAPPEND-NATCHARS-AUX-REDEF|)
@(def |STR|::|REVAPPEND-NATCHARS$INLINE|)") (:FROM . "[books]/str/natstr.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC STR::REVAPPEND-NATCHARS)))))) (VALUE-TRIPLE (QUOTE STR::REVAPPEND-NATCHARS))))))
(("/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))
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