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|
;FILENAME: SETM >
;This file contains 2 packages for Set Theory -
;the first is for LISP and the second is for MACSYMA.
;The LISP Set Package:
;contents of the LISP Set Package:
;INTERSECT+ INTERSECT2
;UNION+ UNION2
;COMPLEMENT
;SETDIFFERENCE
;SYMMDIFFERENCE
;POWERSET
;SETIFY
;SUBSET SUBLIST
;SETP
;SETEQUALP
;SUBSETP
;DISJOINTP
;auxiliary functions: XEROX
(DECLARE #-NIL(MAPEX T)
(SPECIAL CANONLT $CANONLT SUPERCANONLT)
#-NIL(*FEXPR ERRM1 ERRM2)
)
(DEFmacro XEROX (X)
(LIST 'APPEND (CADR X) NIL))
;XEROX COPIES A LIST.
(DEFUN INTERSECT+ N
(DO ((X (LISTIFY N) (DO ((Y X (CDDR Y))
(A NIL (CONS (INTERSECT2 (CAR Y) (CADR Y)) A)))
((NULL Y) A))))
((NULL (CDR X)) (CAR X))))
(DEFUN INTERSECT2 (A B)
(SETQ A (SETIFY A) B (SETIFY B))
(PROG (U)
1 (COND ((OR (NULL A) (NULL B))
(RETURN (NREVERSE U)))
((FUNCALL CANONLT (CAR A) (CAR B))
(SETQ A (CDR A)))
((FUNCALL CANONLT (CAR B) (CAR A))
(SETQ B (CDR B)))
(T (SETQ U (CONS (CAR A) U)
A (CDR A)
B (CDR B))))
(GO 1)))
(DEFUN UNION+ N
(DO ((X (LISTIFY N) (DO ((Y X (CDDR Y))
(A NIL (CONS (UNION2 (CAR Y) (CADR Y)) A)))
((NULL Y) A))))
((NULL (CDR X)) (CAR X))))
(DEFUN UNION2 (A B)
(SETQ A (SETIFY A) B (SETIFY B))
(PROG (U)
1 (COND ((NULL A) (RETURN (APPEND (NREVERSE U) B)))
((NULL B) (RETURN (APPEND (NREVERSE U) A)))
((FUNCALL CANONLT (CAR A) (CAR B))
(SETQ U (CONS (CAR A) U)
A (CDR A)))
((FUNCALL CANONLT (CAR B) (CAR A))
(SETQ U (CONS (CAR B) U)
B (CDR B)))
(T (SETQ U (CONS (CAR A) U)
A (CDR A)
B (CDR B))))
(GO 1)))
(DEFUN COMPLEMENT (A B)
(SETQ A (SETIFY A) B (SETIFY B))
(PROG (U)
1 (COND ((NULL A) (RETURN (APPEND (NREVERSE U) B)))
((NULL B) (RETURN (NREVERSE U)))
((FUNCALL CANONLT (CAR A) (CAR B))
(SETQ A (CDR A)))
((FUNCALL CANONLT (CAR B) (CAR A))
(SETQ U (CONS (CAR B) U)
B (CDR B)))
(T (SETQ A (CDR A) B (CDR B))))
(GO 1)))
(DEFUN SETDIFFERENCE (A B) (COMPLEMENT B A))
(DEFUN SYMMDIFFERENCE (A B)
(UNION2 (COMPLEMENT A B) (COMPLEMENT B A)))
(DEFUN POWERSET (X)
(SETQ X (SETIFY X))
(DO ((X X (CDR X))
(A (LIST NIL)))
((NULL X) (MAPCAR (FUNCTION REVERSE) (NREVERSE A)))
(SETQ A
(APPEND
(DO ((A A (CDR A))
(Y (CAR X))
(B))
((NULL A) (NREVERSE B))
(SETQ B (CONS (CONS Y (CAR A)) B)))
A))))
(DEFUN SETIFY (X)
(COND ((SETP X) X)
(T (SETQ X (SORT (XEROX X) SUPERCANONLT))
(DO ((X (CDR X) (CDR X))
(Y (NCONS (CAR X)))
(A (CAR X)))
((NULL X) (NREVERSE Y))
(COND ((FUNCALL CANONLT A (CAR X))
(SETQ A (CAR X) Y (CONS A Y))))))))
(DEFUN SUBSET (A F) (SUBLIST (SETIFY A) F))
(DEFUN SUBLIST (A F)
(DO ((A A (CDR A))
(X))
((NULL A) (NREVERSE X))
(COND ((FUNCALL F (CAR A))
(SETQ X (CONS (CAR A) X))))))
(DEFUN SETP (L)
(DO ((L (CDR L) (CDR L))
(A (CAR L) (CAR L)))
((NULL L) T)
(OR (FUNCALL CANONLT A (CAR L))
(RETURN NIL))))
(DEFUN SETEQUALP (A B)
(AND (= (LENGTH A) (LENGTH B))
(DO ((A A (CDR A))
(B B (CDR B)))
((NULL A) T)
(COND ((OR (FUNCALL CANONLT (CAR A) (CAR B))
(FUNCALL CANONLT (CAR B) (CAR A)))
(RETURN NIL))))))
;SETEQUALP ASSUMES A AND B ARE SETS
(DEFUN SUBSETP (A B)
(SETQ A (SETIFY A) B (SETIFY B))
(SETEQUALP A (INTERSECT2 A B)))
(DEFUN DISJOINTP (A B)
(NULL (INTERSECT2 A B)))
;The MACSYMA Set Package:
;contents of MACSYMA Set Package:
;$INTERSECT $UNION
;$COMPLEMENT $SETDIFFERENCE $SYMMDIFFERENCE
;$POWERSET
;$SETIFY $SUBSET
;$SETP $SUBSETP $DISJOINTP
;auxiliary functions:
;INLIST OUTLIST SUBLISTM CANONLT-SET
(DEFMACRO INLIST (X)
(CONS 'CDR (CDR X)))
(DEFMACRO OUTLIST (X)
(LIST 'CONS
(LIST 'QUOTE
(LIST 'MLIST 'SIMP))
(CADR X)))
(DEFUN $INTERSECT N
((LAMBDA (X CANONLT SUPERCANONLT)
(COND ((LLISTP X)
(CANONLT-SET)
(OUTLIST
(APPLY (FUNCTION INTERSECT+)
(MAPCAR (FUNCTION INLIST) X))))
(T (ERRM2 NIL '|INTERSECT| '|lists|))))
(LISTIFY N)
$CANONLT
$CANONLT))
(DEFUN $UNION N
((LAMBDA (X CANONLT SUPERCANONLT)
(COND ((LLISTP X)
(CANONLT-SET)
(OUTLIST
(APPLY (FUNCTION UNION+)
(MAPCAR (FUNCTION INLIST) X))))
(T (ERRM2 NIL '|UNION| '|lists|))))
(LISTIFY N)
$CANONLT
$CANONLT))
(DEFUN $COMPLEMENT (A B)
(COND ((AND ($LISTP A) ($LISTP B))
(OUTLIST
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(COMPLEMENT (INLIST A) (INLIST B)))
$CANONLT
$CANONLT)))
(T (ERRM2 NIL '|COMPLEMENT| '|lists|))))
(DEFUN $SETDIFFERENCE (A B)
(COND ((AND ($LISTP A) ($LISTP B))
(OUTLIST
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(COMPLEMENT (INLIST B) (INLIST A)))
$CANONLT
$CANONLT)))
(T (ERRM2 NIL '|SETDIFFERENCE| '|lists|))))
(DEFUN $SYMMDIFFERENCE (A B)
(COND ((AND ($LISTP A) ($LISTP B))
(OUTLIST
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(SYMMDIFFERENCE (INLIST A) (INLIST B)))
$CANONLT
$CANONLT)))
(T (ERRM2 NIL '|SYMMDIFFERENCE| '|lists|))))
(DEFUN $POWERSET (X)
(COND (($LISTP X)
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(OUTLIST
(MAPCAR (FUNCTION OUTLIST)
(POWERSET (INLIST X)))))
$CANONLT
$CANONLT))
(T (ERRM1 NIL '|POWERSET| '|a list|))))
(DEFUN $SETIFY (X)
(COND (($LISTP X)
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(OUTLIST (SETIFY (INLIST X))))
$CANONLT
$CANONLT))
(T (ERRM1 NIL '|SETIFY| '|a list|))))
(DEFUN $SUBSET (A F)
(COND (($LISTP A)
(OUTLIST
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(SUBLISTM (INLIST A) F))
$CANONLT
$CANONLT)))
(T (ERRM1 '|first| '|SUBSET| '|a list|))))
(DEFUN $SETP (X)
(COND (($LISTP X)
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(SETP (INLIST X)))
$CANONLT
$CANONLT))
(T (ERRM1 NIL '|SETP| '|a list|))))
(DEFUN $SUBSETP (A B)
(COND ((AND ($LISTP A) ($LISTP B))
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(SUBSETP (INLIST A) (INLIST B)))
$CANONLT
$CANONLT))
(T (ERRM2 NIL '|SUBSETP| '|lists|))))
(DEFUN $DISJOINTP (A B)
(COND ((AND ($LISTP A) ($LISTP B))
((LAMBDA (CANONLT SUPERCANONLT)
(CANONLT-SET)
(DISJOINTP (INLIST A) (INLIST B)))
$CANONLT
$CANONLT))
(T (ERRM2 NIL '|DISJOINTP| '|lists|))))
(DEFUN LLISTP (L)
(DO ((L L (CDR L)))
((NULL L) T)
(OR ($LISTP (CAR L)) (RETURN NIL))))
(DEFUN SUBLISTM (A F)
(DO ((A A (CDR A))
(X))
((NULL A) (NREVERSE X))
(COND ((MEVALP (LIST (NCONS F) (CAR A)))
(SETQ X (CONS (CAR A) X))))))
(DEFUN CANONLT-SET NIL
(OR (EQ $CANONLT '$ORDERLESSP)
(SETQ CANONLT '(LAMBDA (X Y) (MCALL $CANONLT X Y))
SUPERCANONLT '(LAMBDA (X Y)
(COND ((MCALL $CANONLT X Y) T)
((MCALL $CANONLT Y X) NIL)
(T ($ORDERLESSP X Y)))))))
#-NIL(DECLARE (READ) (READ))
(DEFUN INLIST (X) (CDR X))
(DEFUN OUTLIST (X) (CONS '(MLIST SIMP) X))
(SETQ $CANONLT '$ORDERLESSP
CANONLT '$ORDERLESSP
SUPERCANONLT '$ORDERLESSP)
(DEFUN ERRM0 (&rest X)
(PRINC '|Incorrect argument syntax to function |)
(PRINC (CAR X))
(PRINC '|.|)
(ERR))
(DEFUN ERRM1 (&rest X)
(PRINC '|The |)
(COND ((CAR X)
(PRINC (CAR X))
(PRINC '| |)))
(PRINC '|argument to |)
(PRINC (CADR X))
(PRINC '| must be |)
(PRINC (CADDR X))
(PRINC '|.|)
(ERR))
(DEFUN ERRM2 (&rest X)
(PRINC '|The |)
(COND ((CAR X)
(PRINC (CAR X))
(PRINC '| |)))
(PRINC '|arguments to |)
(PRINC (CADR X))
(PRINC '| must be |)
(PRINC (CADDR X))
(PRINC '|.|)
(ERR))
|
