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|
% -----------------------------------------------------------------------------
% (C) Altran Praxis Limited
% -----------------------------------------------------------------------------
%
% The SPARK toolset is free software; you can redistribute it and/or modify it
% under terms of the GNU General Public License as published by the Free
% Software Foundation; either version 3, or (at your option) any later
% version. The SPARK toolset is distributed in the hope that it will be
% useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
% Public License for more details. You should have received a copy of the GNU
% General Public License distributed with the SPARK toolset; see file
% COPYING3. If not, go to http://www.gnu.org/licenses for a complete copy of
% the license.
%
% =============================================================================
/*** SIMPLIFY(in X,out Y) -- simplify expression X to get Y ***/
/* Simplify expressions of the form 'not(A)' where possible */
/* NOT1 */ simplify(not(true),false) :- !.
/* NOT2 */ simplify(not(false),true) :- !.
/* NOT3 */ simplify(not(not(X)),A) :- simplify(X,A), !.
/* NOT4 */ simplify((not X),B) :-
simplify(X,A),
(
A=true,
B=false
;
A=false,
B=true
;
B=(not A)
), !.
/* Simplify expressions of the form 'A and B' where possible */
/* AND1 */ simplify(false and _X,false) :- !.
/* AND2 */ simplify(_X and false,false) :- !.
/* AND3 */ simplify(X and (not X),false) :- !.
/* AND4 */ simplify((not X) and X,false) :- !.
/* AND5 */ simplify(true and X,Y) :- simplify(X,Y), !.
/* AND6 */ simplify(X and true,Y) :- simplify(X,Y), !.
/* AND7 */ simplify(X and X,Y) :- simplify(X,Y), !.
/* AND8 */ simplify(X and Y,Z) :-
simplify(X,A),
(
A=true,
simplify(Y,Z)
;
A=false,
Z=A
;
simplify(Y,B),
(
(
B=true,
Z=A
;
B=false,
Z=B
)
;
(
A=(not B)
;
A=(not Y)
;
B=(not A)
;
B=(not X)
),
Z=false
;
A=B,
Z=A
;
Z=(A and B)
)
), !.
/* Simplify expressions of the form 'A or B' where possible. */
/* OR1 */ simplify(true or _X,true) :- !.
/* OR2 */ simplify(_X or true,true) :- !.
/* OR3 */ simplify(X or (not X),true) :- !.
/* OR4 */ simplify((not X) or X,true) :- !.
/* OR5 */ simplify(false or X,Y) :- simplify(X,Y), !.
/* OR6 */ simplify(X or false,Y) :- simplify(X,Y), !.
/* OR7 */ simplify(X or X,Y) :- simplify(X,Y), !.
/* OR8 */ simplify(X or Y,Z) :-
simplify(X,A),
(
A=true,
Z=A
;
A=false,
simplify(Y,Z)
;
simplify(Y,B),
(
B=true,
Z=B
;
B=false,
Z=A
;
(
A=(not B)
;
A=(not Y)
;
B=(not A)
;
B=(not X)
),
Z=true
;
A=B,
Z=A
;
Z=(A or B)
)
), !.
/* Simplify expressions of the form 'A -> B' where possible */
/* IMP1 */ simplify(false->_X,true) :- !.
/* IMP2 */ simplify(_X->true,true) :- !.
/* IMP3 */ simplify(X->X,true) :- !.
/* IMP4 */ simplify(true->X,Y) :- simplify(X,Y), !.
/* IMP5 */ simplify(X->false,A) :- simplify((not X),A), !.
/* IMP6 */ simplify(X->(not X),Y) :- simplify((not X),Y), !.
/* IMP7 */ simplify((not X)->X,Y) :- simplify(X,Y), !.
/* IMP8 */ simplify(X -> (Y -> Z),A) :- simplify((X and Y) -> Z,A), !.
/* IMP9 */ simplify(X->Y,Z) :-
simplify(X,A),
(
A=true,
simplify(Y,Z)
;
A=false,
Z=true
;
simplify(Y,B),
(
B=true,
Z=B
;
B=false,
simplify((not X),Z)
;
(
A=(not B)
;
A=(not Y)
;
B=(not A)
;
B=(not X)
),
Z=B
;
A=B,
Z=true
;
Z=(A->B)
)
), !.
/* Simplify expressions of the form 'A <-> B' where possible */
/* EQV1 */ simplify(X<->X,true) :- !.
/* EQV2 */ simplify(X<->(not X),false) :- !.
/* EQV3 */ simplify((not X)<->X,false) :- !.
/* EQV4 */ simplify(X<->true,Y) :- simplify(X,Y), !.
/* EQV5 */ simplify(true<->X,Y) :- simplify(X,Y), !.
/* EQV6 */ simplify(X<->false,Y) :- simplify((not X),Y), !.
/* EQV7 */ simplify(false<->X,Y) :- simplify((not X),Y), !.
/* EQV8 */ simplify(X <-> (Y <-> Z),B) :-
simplify(X <-> Y,A),
simplify(A <-> Z,B), !.
/* EQV9 */ simplify(X <-> Y <-> Z,B) :-
simplify(Y <-> Z,A),
(Y <-> Z)\=A,
simplify(X <-> A,B), !.
/* EQV10 */ simplify(X <-> Y <-> Z,B) :-
simplify(X <-> Z,A),
(X <-> Z)\=A,
simplify(A <-> Y,B), !.
/* EQV11 */ simplify(X<->Y,Z) :-
simplify(X,A),
(
A=true,
simplify(Y,Z)
;
A=false,
simplify((not Y),Z)
;
simplify(Y,B),
(
B=true,
Z=A
;
B=false,
simplify((not X),Z)
;
(
A=(not B)
;
A=(not Y)
;
B=(not A)
;
B=(not X)
),
Z=false
;
A=B,
Z=true
;
Z=(A<->B)
)
), !.
/* Simplify 'for_all( )' exprs. where possible */
/* ALL3 */ simplify(for_all(V:T,X),NEW) :-
find_core_type(T, CT),
(
var_const(V, CT, _),
STATE = dont_retract
;
asserta(var_const(V, CT, temp)),
STATE = retract
),
simplify(X,Y),
(
Y = true,
NEW = true
;
Y = false,
NEW = false
;
NEW = (for_all(V:T, Y))
),
!,
(
STATE = dont_retract
;
retract(var_const(V, CT, temp))
),
!.
/* Simplify 'for_some( )' exprs. where possible */
/* EXI3 */ simplify(for_some(V:T,X),NEW) :-
find_core_type(T, CT),
(
var_const(V, CT, _),
STATE = dont_retract
;
asserta(var_const(V, CT, temp)),
STATE = retract
),
simplify(X,Y),
(
Y = true,
NEW = true
;
Y = false,
NEW = false
;
NEW = (for_some(V:T, Y))
),
!,
(
STATE = dont_retract
;
retract(var_const(V, CT, temp))
),
!.
/* Simplify set-type expressions where possible */
/* SET1 */ simplify(A \/ B, S) :-
!,
set_simplify(A \/ B, S),
!.
/* SET2 */ simplify(A \ B, S) :-
!,
set_simplify(A \ B, S),
!.
/* SET3 */ simplify(A /\ B, S) :-
!,
set_simplify(A /\ B, S),
!.
/* SET4 */ simplify((set A), S) :-
!,
set_simplify((set A), S),
!.
/* SET5 */ simplify(A subset_of B, S) :-
!,
set_simplify(A subset_of B, S),
!.
/* SET6 */ simplify(A strict_subset_of B, S) :-
!,
set_simplify(A strict_subset_of B, S),
!.
/* SET7 */ simplify(A in B, S) :-
!,
set_simplify(A in B, S),
!.
/* SET8 */ simplify(A not_in B, S) :-
!,
set_simplify(A not_in B, S),
!.
/* Simplify atomic formulae where possible */
/* REL1 */ simplify(X=Y,Z) :-
checktype(X,T),
(
type(T, set(_)),
!,
set_simplify(X=Y,Z)
;
type(T,enumerated),
!,
enumerated_simplify(X=Y,Z)
;
simplify(X,A),
simplify(Y,B),
(
A=B,
Z=true
;
signed_integer(A),
( /* CFR050 */
signed_integer(B), /* CFR050 */
A\=B, /* CFR050 */
Z=false /* CFR050 */
; /* CFR050 */
B=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(A-P,R), /* CFR050 */
Z=(Q=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A-Q,R), /* CFR050 */
Z=(P=R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-A,R), /* CFR050 */
Z=(Q=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A+Q,R), /* CFR050 */
Z=(P=R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(B-P,R), /* CFR050 */
Z=(Q=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B-Q,R), /* CFR050 */
Z=(P=R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
A=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-B,R), /* CFR050 */
Z=(Q=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B+Q,R), /* CFR050 */
Z=(P=R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
Z=(A=B) /* CFR050 */
) /* CFR050 */
), !.
/* REL2 */ simplify(X>Y,Z) :-
checktype(X,T),
(
type(T,enumerated),
!,
enumerated_simplify(X>Y,Z)
;
simplify(X,A),
simplify(Y,B),
(
signed_integer(A),
( /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
B less_than A, /* CFR050 */
Z=true /* CFR050 */
; /* CFR050 */
( /* CFR050 */
A=B /* CFR050 */
; /* CFR050 */
A less_than B /* CFR050 */
), /* CFR050 */
Z=false /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(A-P,R), /* CFR050 */
Z=(Q<R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A-Q,R), /* CFR050 */
Z=(P<R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-A,R), /* CFR050 */
Z=(Q>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A+Q,R), /* CFR050 */
Z=(P<R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(B-P,R), /* CFR050 */
Z=(Q>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B-Q,R), /* CFR050 */
Z=(P>R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
A=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-B,R), /* CFR050 */
Z=(Q<R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B+Q,R), /* CFR050 */
Z=(P>R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
Z=(A>B) /* CFR050 */
) /* CFR050 */
), !.
/* REL3 */ simplify(X<Y,Z) :-
checktype(X,T),
(
type(T,enumerated),
!,
enumerated_simplify(X<Y,Z)
;
simplify(X,A),
simplify(Y,B),
(
signed_integer(A),
( /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A less_than B, /* CFR050 */
Z=true /* CFR050 */
; /* CFR050 */
( /* CFR050 */
A=B /* CFR050 */
; /* CFR050 */
B less_than A /* CFR050 */
), /* CFR050 */
Z=false /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(A-P,R), /* CFR050 */
Z=(Q>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A-Q,R), /* CFR050 */
Z=(P>R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-A,R), /* CFR050 */
Z=(Q<R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A+Q,R), /* CFR050 */
Z=(P>R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(B-P,R), /* CFR050 */
Z=(Q<R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B-Q,R), /* CFR050 */
Z=(P<R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
A=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-B,R), /* CFR050 */
Z=(Q>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B+Q,R), /* CFR050 */
Z=(P<R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
Z=(A<B) /* CFR050 */
) /* CFR050 */
), !.
/* REL4 */ simplify(X<>Y,Z) :-
checktype(X,T),
(
type(T, set(_)),
!,
set_simplify(X<>Y,Z)
;
type(T,enumerated),
!,
enumerated_simplify(X<>Y,Z)
;
simplify(X,A),
simplify(Y,B),
(
A=B,
Z=false
;
signed_integer(A),
( /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A\=B, /* CFR050 */
Z=true /* CFR050 */
; /* CFR050 */
A=B, /* CFR050 */
Z=true /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(A-P,R), /* CFR050 */
Z=(Q<>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A-Q,R), /* CFR050 */
Z=(P<>R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-A,R), /* CFR050 */
Z=(Q<>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A+Q,R), /* CFR050 */
Z=(P<>R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(B-P,R), /* CFR050 */
Z=(Q<>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B-Q,R), /* CFR050 */
Z=(P<>R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
A=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-B,R), /* CFR050 */
Z=(Q<>R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B+Q,R), /* CFR050 */
Z=(P<>R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
Z=(A<>B) /* CFR050 */
) /* CFR050 */
), !.
/* REL5 */ simplify(X<=Y,Z) :-
checktype(X,T),
(
type(T,enumerated),
!,
enumerated_simplify(X<=Y,Z)
;
simplify(X,A),
simplify(Y,B),
(
A=B, /* CFR050 */
Z=true /* CFR050 */
; /* CFR050 */
signed_integer(A), /* CFR050 */
( /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A less_than B, /* CFR050 */
Z=true /* CFR050 */
; /* CFR050 */
B less_than A, /* CFR050 */
Z=false /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(A-P,R), /* CFR050 */
Z=(R<=Q) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A-Q,R), /* CFR050 */
Z=(R<=P) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-A,R), /* CFR050 */
Z=(Q<=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A+Q,R), /* CFR050 */
Z=(R<=P) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(B-P,R), /* CFR050 */
Z=(Q<=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B-Q,R), /* CFR050 */
Z=(P<=R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
A=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-B,R), /* CFR050 */
Z=(R<=Q) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B+Q,R), /* CFR050 */
Z=(P<=R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
Z=(A<=B) /* CFR050 */
) /* CFR050 */
), !.
/* REL6 */ simplify(X>=Y,Z) :-
checktype(X,T),
(
type(T,enumerated),
!,
enumerated_simplify(X>=Y,Z)
;
simplify(X,A),
simplify(Y,B),
(
A=B,
Z=true
;
signed_integer(A),
( /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
B less_than A, /* CFR050 */
Z=true /* CFR050 */
; /* CFR050 */
A less_than B, /* CFR050 */
Z=false /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(A-P,R), /* CFR050 */
Z=(Q<=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A-Q,R), /* CFR050 */
Z=(P<=R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
B=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-A,R), /* CFR050 */
Z=(Q>=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(A+Q,R), /* CFR050 */
Z=(P<=R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
signed_integer(B), /* CFR050 */
( /* CFR050 */
A=P+Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(B-P,R), /* CFR050 */
Z=(Q>=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B-Q,R), /* CFR050 */
Z=(P>=R) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
A=P-Q, /* CFR050 */
( /* CFR050 */
signed_integer(P), /* CFR050 */
simplify(P-B,R), /* CFR050 */
Z=(Q<=R) /* CFR050 */
; /* CFR050 */
signed_integer(Q), /* CFR050 */
simplify(B+Q,R), /* CFR050 */
Z=(P>=R) /* CFR050 */
) /* CFR050 */
) /* CFR050 */
; /* CFR050 */
Z=(A>=B) /* CFR050 */
) /* CFR050 */
), !.
/* ODD */ simplify(odd(X), ODD) :-
simplify(X, NEWX),
(
signed_integer(NEWX),
X1 iss NEWX*NEWX,
(
X2 iss (X1 div 2)*2,
X1 =:= X2,
ODD=false
;
X2 iss (X1 div 2)*2,
X1 =\= X2,
ODD=true
)
;
NEWX=A*B,
simplify(odd(A), TFA),
simplify(odd(B), TFB),
(
(
TFA = false
;
TFB = false
),
ODD = false
;
TFA = true,
ODD = TFB
;
TFB = true,
ODD = TFA
)
;
(
NEWX=A+B
;
NEWX=A-B
),
simplify(odd(A), TFA),
simplify(odd(B), TFB),
(
TFA = true,
(
TFB = true,
ODD = false
;
TFB = false,
ODD = true
;
ODD = (not TFB)
)
;
TFA = false,
ODD = TFB
;
TFB = true,
ODD = (not TFA)
;
TFB = false,
ODD = TFA
)
;
NEWX = (-A),
simplify(odd(A), ODD)
;
ODD = odd(NEWX)
), !.
/* SQR1*/ simplify(sqr(abs(X)), SQR) :- simplify(X*X, SQR), !.
/* SQR2*/ simplify(sqr(X), SQR) :- simplify(X*X, SQR), !.
/* ABS */ simplify(abs(X), ABS) :-
simplify(X, NEWX),
(
signed_integer(NEWX),
(
NEWX >= 0,
ABS = NEWX
;
NEWX < 0,
ABS is -NEWX
)
;
NEWX = A*A,
ABS = NEWX
;
NEWX = A*B,
simplify(abs(A), ABSA),
simplify(abs(B), ABSB),
ABS = ABSA*ABSB
;
NEWX = abs(_EXPR),
ABS = NEWX
;
ABS = abs(NEWX)
), !.
/* Simplify array, record & sequence type objects if possible */
/* ARR */ simplify(X, Y) :- array_simplify(X, Y), !.
/* REC */ simplify(X, Y) :- record_simplify(X, Y), !.
/* SEQ */ simplify(X, Y) :- sequence_simplify(X, Y), !.
/* ENU1 */ simplify(succ(X), Y) :- enumerated_simplify(succ(X), Y), !.
/* ENU2 */ simplify(pred(X), Y) :- enumerated_simplify(pred(X), Y), !.
/* Final catch-all */
/* EVAL */ simplify(X,Y) :- evaluate(X,Y), !.
/*** EVALUATE(in X,out Y) -- evaluate (non-boolean) X to get Y ***/
/* EVAL_BASE1 */ evaluate(X,X) :-
(
signed_integer(X)
;
X=true
;
X=false
), !.
/* EVAL_BASE2 */ evaluate(X,Y) :-
integer(X), X<0,
Y iss X, !.
/* UMIN1 */ evaluate(-(-X),A) :- simplify(X,A), !.
/* UMIN2 */ evaluate(-X,A) :-
simplify(X,B),
(
signed_integer(B),
A iss -B
;
A=(-B)
), !.
/* UPLUS */ evaluate(+X, A) :- simplify(X, A), !. /* CFR039 */
/*SPECIAL*/ evaluate(X+N-N,Y) :- simplify(X,Y), !.
evaluate(X-N+N,Y) :- simplify(X,Y), !.
/* PLUS */ evaluate(X+Y,Z) :-
simplify(X,A),
simplify(Y,B),
(
signed_integer(A),
signed_integer(B),
Z iss A+B
;
A=0,
Z=B
;
B=0,
Z=A
;
Z=A+B
), !.
/* MINUS */ evaluate(X-Y,Z) :-
simplify(X,A),
simplify(Y,B),
(
signed_integer(A),
signed_integer(B),
Z iss A-B
;
B=0,
Z=A
;
A=0,
simplify(-Y,Z)
;
Z=A-B
), !.
/* MULT */ evaluate(X*Y,Z) :-
simplify(X,A),
simplify(Y,B),
(
signed_integer(A),
signed_integer(B),
Z iss A*B
;
(
A=0
;
B=0
),
Z=0
;
A=1,
Z=B
;
B=1,
Z=A
;
Z=A*B
), !.
/* DIV */ evaluate(X div Y,Z) :-
simplify(X,A),
simplify(Y,B),
(
signed_integer(A),
signed_integer(B),
B\=0,
Z iss A div B
;
B=1,
Z=A
;
Z=A div B
), !.
/* / */ evaluate(X / Y,Z) :- /*1.4*/
simplify(X,A), /*1.4*/
simplify(Y,B), /*1.4*/
( /*1.4*/
signed_integer(A), /*1.4*/
signed_integer(B), /*1.4*/
B\=0, /*1.4*/
Z iss A div B, /*1.4*/
A =:= Z * B /*1.4*/
; /*1.4*/
B=1, /*1.4*/
Z=A /*1.4*/
; /*1.4*/
Z=A / B /*1.4*/
), !. /*1.4*/
/* MOD */ evaluate(X mod Y,A mod B) :-
simplify(X,A),
simplify(Y,B),
!. /* TEMPORARILY */
/* OLD MOD STUFF:
(
signed_integer(A),
signed_integer(B),
B\=0,
Z iss A mod B
;
B=1,
Z=0
;
Z=(A mod B)
), !. DELETED */
/* EXP */ evaluate(X**Y,Z) :- /* CFR038 */
simplify(X,A), /* CFR038 */
simplify(Y,B), /* CFR038 */
( /* CFR038 */
signed_integer(A), /* CFR038 */
signed_integer(B), /* CFR038 */
Z iss A**B /* CFR038 */
; /* CFR038 */
B=0, /* CFR038 */
Z=1 /* CFR038 */
; /* CFR038 */
B=1, /* CFR038 */
Z=A /* CFR038 */
; /* CFR038 */
B=2, /* CFR038 */
Z=A*A /* CFR038 */
; /* CFR038 */
Z=A**B /* CFR038 */
), !. /* CFR038 */
/* EVAL_VAL */ evaluate(X,Y) :- val(X,Y), !.
/* FUNC_SPLIT */ evaluate(X,Z) :-
(\+ atomic(X)),
X=..[H|T],
eval_list(T,U),
Z=..[H|U],
!.
/*** EVAL_LIST(in XL,out YL) -- simplify/evaluate each element
of XL to get YL ***/
/* EVL1 */ eval_list([],[]) :- !.
/* EVL2 */ eval_list([H1|T1],[H2|T2]) :-
simplify(H1,H2),
eval_list(T1,T2),
!.
/*** VAL(in X,out Y) -- additional simplification rules slot in here ***/
val(X,X) :- atomic(X), !.
/*** SIGNED_INTEGER(I) -- is I an integer (with an optional -)? ***/
signed_integer(I) :-
(
integer(I), I>=0
;
I=(-I1), integer(I1), I1>0
).
/*** X LESS_THAN Y -- compare two signed_integers ***/
-X less_than -Y :- integer(X), X>0, integer(Y), Y>0, Y less_than X.
-X less_than Y :- integer(X), X>0, integer(Y), Y>=0.
X less_than Y :- integer(X), X>=0, integer(Y), Y>X.
%###############################################################################
%END-OF-FILE
|
