perm filename BOYER.IL[TIM,LSP] blob
sn#727366 filedate 1983-10-18 generic text, type T, neo UTF8
(FILECREATED " 5-JUL-83 21:34:28" {PHYLUM}<GABRIEL>BOYER.;1 14661
changes to: (VARS BOYERCOMS))
(PRETTYCOMPRINT BOYERCOMS)
(RPAQQ BOYERCOMS ((FNS ADD-LEMMA ADD-LEMMA-LST APPLY-SUBST APPLY-SUBST-LST FALSEP ONE-WAY-UNIFY
ONE-WAY-UNIFY1 ONE-WAY-UNIFY1-LST PTIME REWRITE REWRITE-ARGS
REWRITE-WITH-LEMMAS SETUP TAUTOLOGYP TAUTP TEST TRANS-OF-IMPLIES
TRANS-OF-IMPLIES1 TRUEP)
(BLOCKS
(BOYER
ADD-LEMMA ADD-LEMMA-LST APPLY-SUBST APPLY-SUBST-LST FALSEP ONE-WAY-UNIFY
ONE-WAY-UNIFY1 ONE-WAY-UNIFY1-LST PTIME REWRITE REWRITE-ARGS
REWRITE-WITH-LEMMAS SETUP TAUTOLOGYP TAUTP TEST TRANS-OF-IMPLIES
TRANS-OF-IMPLIES1 TRUEP
(ENTRIES TEST APPLY-SUBST TAUTP SETUP)))
(GLOBALVARS TEMP-TEMP UNIFY-SUBST)))
(DEFINEQ
(ADD-LEMMA
(LAMBDA (TERM)
(COND
((AND (NOT (ATOM TERM))
(EQ (CAR TERM)
(QUOTE EQUAL))
(NOT (ATOM (CADR TERM))))
(COND
((GETPROP (CAR (CADR TERM))
(QUOTE LEMMAS))
(PUTPROP (CAR (CADR TERM))
(QUOTE LEMMAS)
(CONS TERM (GETPROP (CAR (CADR TERM))
(QUOTE LEMMAS)))))
(T (SETPROPLIST (CAR (CADR TERM))
(CONS (QUOTE LEMMAS)
(CONS (LIST TERM)
(GETPROPLIST (CAR (CADR TERM)))))))))
(T (ERROR (QUOTE ADD-LEMMA-DID-NOT-LIKE-TERM)
TERM)))))
(ADD-LEMMA-LST
(LAMBDA (LST)
(COND
((NULL LST)
T)
(T (ADD-LEMMA (CAR LST))
(ADD-LEMMA-LST (CDR LST))))))
(APPLY-SUBST
(LAMBDA (ALIST TERM)
(COND
((NLISTP TERM)
(COND
((SETQ TEMP-TEMP (FASSOC TERM ALIST))
(CDR TEMP-TEMP))
(T TERM)))
(T (CONS (CAR TERM)
(APPLY-SUBST-LST ALIST (CDR TERM)))))))
(APPLY-SUBST-LST
(LAMBDA (ALIST LST)
(COND
((NULL LST)
NIL)
(T (CONS (APPLY-SUBST ALIST (CAR LST))
(APPLY-SUBST-LST ALIST (CDR LST)))))))
(FALSEP
(LAMBDA (X LST)
(OR (EQUAL X (QUOTE (F)))
(MEMBER X LST))))
(ONE-WAY-UNIFY
(LAMBDA (TERM1 TERM2)
(PROGN (SETQ UNIFY-SUBST NIL)
(ONE-WAY-UNIFY1 TERM1 TERM2))))
(ONE-WAY-UNIFY1
(LAMBDA (TERM1 TERM2)
(COND
((NLISTP TERM2)
(COND
((SETQ TEMP-TEMP (FASSOC TERM2 UNIFY-SUBST))
(EQUAL TERM1 (CDR TEMP-TEMP)))
(T (SETQ UNIFY-SUBST (CONS (CONS TERM2 TERM1)
UNIFY-SUBST))
T)))
((ATOM TERM1)
NIL)
((EQ (CAR TERM1)
(CAR TERM2))
(ONE-WAY-UNIFY1-LST (CDR TERM1)
(CDR TERM2)))
(T NIL))))
(ONE-WAY-UNIFY1-LST
(LAMBDA (LST1 LST2)
(COND
((NULL LST1)
T)
((ONE-WAY-UNIFY1 (CAR LST1)
(CAR LST2))
(ONE-WAY-UNIFY1-LST (CDR LST1)
(CDR LST2)))
(T NIL))))
(PTIME
(LAMBDA NIL
(PROG (GCTM)
(SETQ GCTM (CLOCK 3))
(RETURN (CONS (IPLUS (CLOCK 2)
GCTM)
GCTM)))))
(REWRITE
(LAMBDA (TERM)
(COND
((NLISTP TERM)
TERM)
(T (REWRITE-WITH-LEMMAS (CONS (CAR TERM)
(REWRITE-ARGS (CDR TERM)))
(GETPROP (CAR TERM)
(QUOTE LEMMAS)))))))
(REWRITE-ARGS
(LAMBDA (LST)
(COND
((NULL LST)
NIL)
(T (CONS (REWRITE (CAR LST))
(REWRITE-ARGS (CDR LST)))))))
(REWRITE-WITH-LEMMAS
(LAMBDA (TERM LST)
(COND
((NULL LST)
TERM)
((ONE-WAY-UNIFY TERM (CADR (CAR LST)))
(REWRITE (APPLY-SUBST UNIFY-SUBST (CADDR (CAR LST)))))
(T (REWRITE-WITH-LEMMAS TERM (CDR LST))))))
(SETUP
(LAMBDA NIL
(ADD-LEMMA-LST (QUOTE ((EQUAL (COMPILE FORM)
(REVERSE (CODEGEN (OPTIMIZE FORM)
(NIL))))
(EQUAL (EQP X Y)
(EQUAL (FIX X)
(FIX Y)))
(EQUAL (GREATERP X Y)
(LESSP Y X))
(EQUAL (LESSEQP X Y)
(NOT (LESSP Y X)))
(EQUAL (GREATEREQP X Y)
(NOT (LESSP X Y)))
(EQUAL (BOOLEAN X)
(OR (EQUAL X (T))
(EQUAL X (F))))
(EQUAL (IFF X Y)
(AND (IMPLIES X Y)
(IMPLIES Y X)))
(EQUAL (EVEN1 X)
(IF (ZEROP X)
(T)
(ODD (SUB1 X))))
(EQUAL (COUNTPS- L PRED)
(COUNTPS-LOOP L PRED (ZERO)))
(EQUAL (FACT- I)
(FACT-LOOP I 1))
(EQUAL (REVERSE- X)
(REVERSE-LOOP X (NIL)))
(EQUAL (DIVIDES X Y)
(ZEROP (REMAINDER Y X)))
(EQUAL (ASSUME-TRUE VAR ALIST)
(CONS (CONS VAR (T))
ALIST))
(EQUAL (ASSUME-FALSE VAR ALIST)
(CONS (CONS VAR (F))
ALIST))
(EQUAL (TAUTOLOGY-CHECKER X)
(TAUTOLOGYP (NORMALIZE X)
(NIL)))
(EQUAL (FALSIFY X)
(FALSIFY1 (NORMALIZE X)
(NIL)))
(EQUAL (PRIME X)
(AND (NOT (ZEROP X))
(NOT (EQUAL X (ADD1 (ZERO))))
(PRIME1 X (SUB1 X))))
(EQUAL (AND P Q)
(IF P (IF Q (T)
(F))
(F)))
(EQUAL (OR P Q)
(IF P (T)
(IF Q (T)
(F))
(F)))
(EQUAL (NOT P)
(IF P (F)
(T)))
(EQUAL (IMPLIES P Q)
(IF P (IF Q (T)
(F))
(T)))
(EQUAL (FIX X)
(IF (NUMBERP X)
X
(ZERO)))
(EQUAL (IF (IF A B C)
D E)
(IF A (IF B D E)
(IF C D E)))
(EQUAL (ZEROP X)
(OR (EQUAL X (ZERO))
(NOT (NUMBERP X))))
(EQUAL (PLUS (PLUS X Y)
Z)
(PLUS X (PLUS Y Z)))
(EQUAL (EQUAL (PLUS A B)
(ZERO))
(AND (ZEROP A)
(ZEROP B)))
(EQUAL (DIFFERENCE X X)
(ZERO))
(EQUAL (EQUAL (PLUS A B)
(PLUS A C))
(EQUAL (FIX B)
(FIX C)))
(EQUAL (EQUAL (ZERO)
(DIFFERENCE X Y))
(NOT (LESSP Y X)))
(EQUAL (EQUAL X (DIFFERENCE X Y))
(AND (NUMBERP X)
(OR (EQUAL X (ZERO))
(ZEROP Y))))
(EQUAL (MEANING (PLUS-TREE (APPEND X Y))
A)
(PLUS (MEANING (PLUS-TREE X)
A)
(MEANING (PLUS-TREE Y)
A)))
(EQUAL (MEANING (PLUS-TREE (PLUS-FRINGE X))
A)
(FIX (MEANING X A)))
(EQUAL (APPEND (APPEND X Y)
Z)
(APPEND X (APPEND Y Z)))
(EQUAL (REVERSE (APPEND A B))
(APPEND (REVERSE B)
(REVERSE A)))
(EQUAL (TIMES X (PLUS Y Z))
(PLUS (TIMES X Y)
(TIMES X Z)))
(EQUAL (TIMES (TIMES X Y)
Z)
(TIMES X (TIMES Y Z)))
(EQUAL (EQUAL (TIMES X Y)
(ZERO))
(OR (ZEROP X)
(ZEROP Y)))
(EQUAL (EXEC (APPEND X Y)
PDS ENVRN)
(EXEC Y (EXEC X PDS ENVRN)
ENVRN))
(EQUAL (MC-FLATTEN X Y)
(APPEND (FLATTEN X)
Y))
(EQUAL (MEMBER X (APPEND A B))
(OR (MEMBER X A)
(MEMBER X B)))
(EQUAL (MEMBER X (REVERSE Y))
(MEMBER X Y))
(EQUAL (LENGTH (REVERSE X))
(LENGTH X))
(EQUAL (MEMBER A (INTERSECT B C))
(AND (MEMBER A B)
(MEMBER A C)))
(EQUAL (NTH (ZERO)
I)
(ZERO))
(EQUAL (EXP I (PLUS J K))
(TIMES (EXP I J)
(EXP I K)))
(EQUAL (EXP I (TIMES J K))
(EXP (EXP I J)
K))
(EQUAL (REVERSE-LOOP X Y)
(APPEND (REVERSE X)
Y))
(EQUAL (REVERSE-LOOP X (NIL))
(REVERSE X))
(EQUAL (COUNT-LIST Z (SORT-LP X Y))
(PLUS (COUNT-LIST Z X)
(COUNT-LIST Z Y)))
(EQUAL (EQUAL (APPEND A B)
(APPEND A C))
(EQUAL B C))
(EQUAL (PLUS (REMAINDER X Y)
(TIMES Y (QUOTIENT X Y)))
(FIX X))
(EQUAL (POWER-EVAL (BIG-PLUS1 L I BASE)
BASE)
(PLUS (POWER-EVAL L BASE)
I))
(EQUAL (POWER-EVAL (BIG-PLUS X Y I BASE)
BASE)
(PLUS I (PLUS (POWER-EVAL X BASE)
(POWER-EVAL Y BASE))))
(EQUAL (REMAINDER Y 1)
(ZERO))
(EQUAL (LESSP (REMAINDER X Y)
Y)
(NOT (ZEROP Y)))
(EQUAL (REMAINDER X X)
(ZERO))
(EQUAL (LESSP (QUOTIENT I J)
I)
(AND (NOT (ZEROP I))
(OR (ZEROP J)
(NOT (EQUAL J 1)))))
(EQUAL (LESSP (REMAINDER X Y)
X)
(AND (NOT (ZEROP Y))
(NOT (ZEROP X))
(NOT (LESSP X Y))))
(EQUAL (POWER-EVAL (POWER-REP I BASE)
BASE)
(FIX I))
(EQUAL (POWER-EVAL (BIG-PLUS (POWER-REP I BASE)
(POWER-REP J BASE)
(ZERO)
BASE)
BASE)
(PLUS I J))
(EQUAL (GCD X Y)
(GCD Y X))
(EQUAL (NTH (APPEND A B)
I)
(APPEND (NTH A I)
(NTH B (DIFFERENCE I (LENGTH A)))))
(EQUAL (DIFFERENCE (PLUS X Y)
X)
(FIX Y))
(EQUAL (DIFFERENCE (PLUS Y X)
X)
(FIX Y))
(EQUAL (DIFFERENCE (PLUS X Y)
(PLUS X Z))
(DIFFERENCE Y Z))
(EQUAL (TIMES X (DIFFERENCE C W))
(DIFFERENCE (TIMES C X)
(TIMES W X)))
(EQUAL (REMAINDER (TIMES X Z)
Z)
(ZERO))
(EQUAL (DIFFERENCE (PLUS B (PLUS A C))
A)
(PLUS B C))
(EQUAL (DIFFERENCE (ADD1 (PLUS Y Z))
Z)
(ADD1 Y))
(EQUAL (LESSP (PLUS X Y)
(PLUS X Z))
(LESSP Y Z))
(EQUAL (LESSP (TIMES X Z)
(TIMES Y Z))
(AND (NOT (ZEROP Z))
(LESSP X Y)))
(EQUAL (LESSP Y (PLUS X Y))
(NOT (ZEROP X)))
(EQUAL (GCD (TIMES X Z)
(TIMES Y Z))
(TIMES Z (GCD X Y)))
(EQUAL (VALUE (NORMALIZE X)
A)
(VALUE X A))
(EQUAL (EQUAL (FLATTEN X)
(CONS Y (NIL)))
(AND (NLISTP X)
(EQUAL X Y)))
(EQUAL (LISTP (GOPHER X))
(LISTP X))
(EQUAL (SAMEFRINGE X Y)
(EQUAL (FLATTEN X)
(FLATTEN Y)))
(EQUAL (EQUAL (GREATEST-FACTOR X Y)
(ZERO))
(AND (OR (ZEROP Y)
(EQUAL Y 1))
(EQUAL X (ZERO))))
(EQUAL (EQUAL (GREATEST-FACTOR X Y)
1)
(EQUAL X 1))
(EQUAL (NUMBERP (GREATEST-FACTOR X Y))
(NOT (AND (OR (ZEROP Y)
(EQUAL Y 1))
(NOT (NUMBERP X)))))
(EQUAL (TIMES-LIST (APPEND X Y))
(TIMES (TIMES-LIST X)
(TIMES-LIST Y)))
(EQUAL (PRIME-LIST (APPEND X Y))
(AND (PRIME-LIST X)
(PRIME-LIST Y)))
(EQUAL (EQUAL Z (TIMES W Z))
(AND (NUMBERP Z)
(OR (EQUAL Z (ZERO))
(EQUAL W 1))))
(EQUAL (GREATEREQPR X Y)
(NOT (LESSP X Y)))
(EQUAL (EQUAL X (TIMES X Y))
(OR (EQUAL X (ZERO))
(AND (NUMBERP X)
(EQUAL Y 1))))
(EQUAL (REMAINDER (TIMES Y X)
Y)
(ZERO))
(EQUAL (EQUAL (TIMES A B)
1)
(AND (NOT (EQUAL A (ZERO)))
(NOT (EQUAL B (ZERO)))
(NUMBERP A)
(NUMBERP B)
(EQUAL (SUB1 A)
(ZERO))
(EQUAL (SUB1 B)
(ZERO))))
(EQUAL (LESSP (LENGTH (DELETE X L))
(LENGTH L))
(MEMBER X L))
(EQUAL (SORT2 (DELETE X L))
(DELETE X (SORT2 L)))
(EQUAL (DSORT X)
(SORT2 X))
(EQUAL (LENGTH (CONS X1 (CONS X2 (CONS X3 (CONS X4
(CONS X5
(CONS X6 X7)))))))
(PLUS 6 (LENGTH X7)))
(EQUAL (DIFFERENCE (ADD1 (ADD1 X))
2)
(FIX X))
(EQUAL (QUOTIENT (PLUS X (PLUS X Y))
2)
(PLUS X (QUOTIENT Y 2)))
(EQUAL (SIGMA (ZERO)
I)
(QUOTIENT (TIMES I (ADD1 I))
2))
(EQUAL (PLUS X (ADD1 Y))
(IF (NUMBERP Y)
(ADD1 (PLUS X Y))
(ADD1 X)))
(EQUAL (EQUAL (DIFFERENCE X Y)
(DIFFERENCE Z Y))
(IF (LESSP X Y)
(NOT (LESSP Y Z))
(IF (LESSP Z Y)
(NOT (LESSP Y X))
(EQUAL (FIX X)
(FIX Z)))))
(EQUAL (MEANING (PLUS-TREE (DELETE X Y))
A)
(IF (MEMBER X Y)
(DIFFERENCE (MEANING (PLUS-TREE Y)
A)
(MEANING X A))
(MEANING (PLUS-TREE Y)
A)))
(EQUAL (TIMES X (ADD1 Y))
(IF (NUMBERP Y)
(PLUS X (TIMES X Y))
(FIX X)))
(EQUAL (NTH (NIL)
I)
(IF (ZEROP I)
(NIL)
(ZERO)))
(EQUAL (LAST (APPEND A B))
(IF (LISTP B)
(LAST B)
(IF (LISTP A)
(CONS (CAR (LAST A))
B)
B)))
(EQUAL (EQUAL (LESSP X Y)
Z)
(IF (LESSP X Y)
(EQUAL T Z)
(EQUAL F Z)))
(EQUAL (ASSIGNMENT X (APPEND A B))
(IF (ASSIGNEDP X A)
(ASSIGNMENT X A)
(ASSIGNMENT X B)))
(EQUAL (CAR (GOPHER X))
(IF (LISTP X)
(CAR (FLATTEN X))
(ZERO)))
(EQUAL (FLATTEN (CDR (GOPHER X)))
(IF (LISTP X)
(CDR (FLATTEN X))
(CONS (ZERO)
(NIL))))
(EQUAL (QUOTIENT (TIMES Y X)
Y)
(IF (ZEROP Y)
(ZERO)
(FIX X)))
(EQUAL (GET J (SET I VAL MEM))
(IF (EQP J I)
VAL
(GET J MEM))))))))
(TAUTOLOGYP
(LAMBDA (X TRUE-LST FALSE-LST)
(COND
((TRUEP X TRUE-LST)
T)
((FALSEP X FALSE-LST)
NIL)
((NLISTP X)
NIL)
((EQ (CAR X)
(QUOTE IF))
(COND
((TRUEP (CADR X)
TRUE-LST)
(TAUTOLOGYP (CADDR X)
TRUE-LST FALSE-LST))
((FALSEP (CADR X)
FALSE-LST)
(TAUTOLOGYP (CADDDR X)
TRUE-LST FALSE-LST))
(T (AND (TAUTOLOGYP (CADDR X)
(CONS (CADR X)
TRUE-LST)
FALSE-LST)
(TAUTOLOGYP (CADDDR X)
TRUE-LST
(CONS (CADR X)
FALSE-LST))))))
(T NIL))))
(TAUTP
(LAMBDA (X)
(TAUTOLOGYP (REWRITE X)
NIL NIL)))
(TEST
(LAMBDA NIL
(PROG (TM1 TM2 ANS TERM)
(SETQ TM1 (PTIME))
(SETQ TERM (APPLY-SUBST (QUOTE ((X F (PLUS (PLUS A B)
(PLUS C (ZERO))))
(Y F (TIMES (TIMES A B)
(PLUS C D)))
(Z F (REVERSE (APPEND (APPEND A B)
(NIL))))
(U EQUAL (PLUS A B)
(DIFFERENCE X Y))
(W LESSP (REMAINDER A B)
(MEMBER A (LENGTH B)))))
(QUOTE (IMPLIES (AND (IMPLIES X Y)
(AND (IMPLIES Y Z)
(AND (IMPLIES Z U)
(IMPLIES U W))))
(IMPLIES X W)))))
(SETQ ANS (TAUTP TERM))
(SETQ TM2 (PTIME))
(RETURN (LIST ANS (DIFFERENCE (CAR TM2)
(CAR TM1))
(DIFFERENCE (CDR TM2)
(CDR TM1)))))))
(TRANS-OF-IMPLIES
(LAMBDA (N)
(LIST (QUOTE IMPLIES)
(TRANS-OF-IMPLIES1 N)
(LIST (QUOTE IMPLIES)
0 N))))
(TRANS-OF-IMPLIES1
(LAMBDA (N)
(COND
((EQUAL N 1)
(LIST (QUOTE IMPLIES)
0 1))
(T (LIST (QUOTE AND)
(LIST (QUOTE IMPLIES)
(SUB1 N)
N)
(TRANS-OF-IMPLIES1 (SUB1 N)))))))
(TRUEP
(LAMBDA (X LST)
(OR (EQUAL X (QUOTE (T)))
(MEMBER X LST))))
)
(DECLARE: DOEVAL@COMPILE DONTCOPY
(ADDTOVAR GLOBALVARS TEMP-TEMP UNIFY-SUBST)
)
(PUTPROPS BOYER COPYRIGHT (NONE))
(DECLARE: DONTCOPY
(FILEMAP (NIL (461 14524 (ADD-LEMMA 471 . 995) (ADD-LEMMA-LST 997 . 1134) (APPLY-SUBST 1136 . 1368) (
APPLY-SUBST-LST 1370 . 1546) (FALSEP 1548 . 1626) (ONE-WAY-UNIFY 1628 . 1744) (ONE-WAY-UNIFY1 1746 .
2136) (ONE-WAY-UNIFY1-LST 2138 . 2348) (PTIME 2350 . 2493) (REWRITE 2495 . 2713) (REWRITE-ARGS 2715 .
2863) (REWRITE-WITH-LEMMAS 2865 . 3112) (SETUP 3114 . 12630) (TAUTOLOGYP 12632 . 13231) (TAUTP 13233
. 13306) (TEST 13308 . 14084) (TRANS-OF-IMPLIES 14086 . 14211) (TRANS-OF-IMPLIES1 14213 . 14443) (
TRUEP 14445 . 14522)))))
STOP