% Thom Fruehwirth, LMU, 980129ff, 980312, 980611, 980711 :- use_module( library(chr)). handler interval. option(debug_compile,off). option(already_in_store, off). option(check_guard_bindings, off). option(already_in_heads, off). % for domain constraints operator( 700,xfx,'::'). %operator( 600,xfx,':'). % operator already defined in Sicstus Prolog % for inequality constraints %operator( 700,xfx,lt). % not implemented operator( 700,xfx,le). operator( 700,xfx,ne). operator( 700,xfx,eq). constraints (::)/2, le/2, eq/2, ne/2, add/3, mult/3. % X::Min:Max - X is between the numbers Min and Max, inclusively % X must always be a unbound variable (!), and Min and Max evaluable % (i.e. ground) arithmetic expressions (or numbers) constraints int/1. % int(X) says that X is an integer (default is a real) constraints bool/1. % bool(X) says that X is a boolean (default is a real) constraints browse/1. % watch how domain of X evolves browse(X), X::A:B ==> write((X::A:B)),nl. % define the smallest intervals you want to get: % the smaller, the more precise, the longer the computation small(A:B):- A+2.0e-05>=B. % Intersection ------------------------------- redundant @ X::A:B \ X::C:D <=> %var(X), (C= %var(X) | X::max(A,C):min(B,D). % Special Cases ------------------------------- failure @ X::A:B <=> A>B | fail. compute @ X::A:B <=> \+ (number(A),number(B)) | C is A, D is B, X::C:D. integer @ int(X), X::A:B ==> \+ (integer(A),integer(B)) | C is integer(ceiling(float(A))), D is integer(floor(float(B))), X::C:D. bool @ bool(X), X::A:B ==> B<1 | X::0:0. bool @ bool(X), X::A:B ==> A>0 | X::1:1. bool @ bool(X) ==> X::0:1. % Inequality ------------------------------- (le) @ X le Y, X::A:B, Y::C:D ==> Y::A:D, X::A:D. (eq) @ X eq Y, X::A:B, Y::C:D ==> Y::A:B, X::C:D. (ne) @ X ne Y, X::A:A, Y::A:A <=> fail. (ne_int) @ int(X) \ X ne Y, X::A:B <=> A=Y | X::A+1:B. (ne_int) @ int(X) \ X ne Y, X::A:B <=> B=Y | X::A:B-1. (ne_int) @ int(X) \ Y ne X, X::A:B <=> A=Y | X::A+1:B. (ne_int) @ int(X) \ Y ne X, X::A:B <=> B=Y | X::A:B-1. % Addition X+Y=Z ------------------------------- add @ add(X,Y,Z), X::A:B, Y::C:D, Z::E:F ==> X::E-D:F-C, Y::E-B:F-A, Z::A+C:B+D. % Multiplication X*Y=Z ------------------------------- mitnull(A:B) :- A=<0, 0= M1 is A*C, M2 is A*D, M3 is B*C, M4 is B*D, Z::min(min(M1,M2),min(M3,M4)):max(max(M1,M2),max(M3,M4)). mult_y @ mult(X,Y,Z), X::A:B, Z::E:F ==> \+ mitnull(A:B) | M1 is E/A, M2 is E/B, M3 is F/A, M4 is F/B, Y::min(min(M1,M2),min(M3,M4)):max(max(M1,M2),max(M3,M4)). mult_x @ mult(Y,X,Z), X::A:B, Z::E:F ==> \+ mitnull(A:B) | M1 is E/A, M2 is E/B, M3 is F/A, M4 is F/B, Y::min(min(M1,M2),min(M3,M4)):max(max(M1,M2),max(M3,M4)). mult_xyz @ mult(X,Y,Z), X::A:B, Y::C:D, Z::E:F ==> mitnull(A:B), mitnull(C:D), \+ mitnull(E:F) | (A*C D>0, X::E/D:B ; true), (B*D C<0, X::A:E/C ; true), (F C<0, X::F/C:B ; true), (F D>0, X::A:F/D ; true). % Labeling -------------------------------------------------------- constraints split0/1. constraints split/1. % repeated split/1: constraints label/1. label @ split0(X), X::A:B <=> \+ small(A:B), A<0,0 \+ small(A:B) | Half is (A+B)/2, (X::A:Half ; X::Half:B). label @ label(X), X::A:B <=> \+ small(A:B) | Half is (A+B)/2, (X::A:Half ; X::Half:B), label(X). % EXAMPLES ================================================================ /* ?- X::3:5,X::2:4. X::3:4 ? ?- X::3:5, Y::2:4, X=Y. Y = X, X::3:4 ? ?- X::3:3. X::3:3 ? ?- X le Y, X::3:5,X::2:4. X le Y, X::3:4 ? ?- X le Y, X::3:5, Y::3:5. X le Y, X::3:5, Y::3:5 ? ?- X le Y, X::3:5, Y::2:4. X le Y, Y::3:4, X::3:4 ? ?- add(X,Y,Z), X::2:5, Y::3:4, Z::1:7. Y::3:4, Z::5:7, X::2:4, add(X,Y,Z)? ?- mult(X,Y,Z), X:: -2:3, Y:: -3:4, Z::7:12. Z::7:12, X::1.75:3, Y::2.3333333333333335:4.0, mult(X,Y,Z) ? ; ?- mult(X,Y,Z), X:: -2:3, Y:: -3:4, Z:: -12: -9. ?- A::(-3):3, B::(-3):3, C::4:4, mult(A,B,C), A eq B. ?- A::(-3):3, B::(-3):3, C::4:4, mult(A,B,C), A eq B, split(A). ?- int(A), A::(-3):3, B::(-3):3, C::4:4, mult(A,B,C), A eq B, split(A). ?- A::(-3):3, B::(-3):3, C::4:4, mult(A,B,C), A eq B, split(A),split(A),split(A),split(A). ?- A::(-3):3, B::(-3):3, C::4:4, mult(A,B,C), A eq B, label(A). ?- int(A),int(B),int(C), mult(A,B,C), A::0:0.3, B::0:0.3, C::0:0.3, A le C, B le C, C le A, C le B, A le B, B le A. ?- int(A),int(B),int(C), mult(A,B,C), A::0:0.3, B::0:0.3, C::0:0.3, A eq B, B eq C. ?- mult(A,B,C), A::0:0.3, B::0:0.3, C::0:0.3, A eq B, B eq C. A eq B, B eq C, C::0.0:4.304672099999998e-9, B::0.0:4.304672099999998e-9, A::0.0:4.304672099999998e-9, mult(A,B,C) ? ; ?- mult(A,B,C), A::0:0.3, B::0:0.3, C::0:0.3, A le C. B::0:0.3, A le C, C::0.0:1.9682999999999995e-5, A::0:1.9682999999999995e-5, mult(A,B,C) ? ; ?- mult(A,B,C), A::(-0.3):0.3, B::(-0.3):0.3, C::(-0.3):0.3, A eq C. B:: -0.3:0.3, A eq C, C:: -5.9048999999999996e-6:5.9048999999999996e-6, A:: -5.9048999999999996e-6:5.9048999999999996e-6, mult(A,B,C) ? ; ?- mult(A,B,C), A::(-3):3, B::(-3):3, C::(-3):3, A eq C. % solutions A=C=0 or B=1, impossible to enumerate A:: -3:3, B:: -3:3, C:: -3:3, A eq C, mult(A,B,C) ? ; ?- mult(A,B,AB), A eq B, add(AB,C,F), F::5:5, mult(C,D,CD), C eq D, add(CD,A,G), G::3:3, A:: -10:10, B:: -10:10, C:: -10:10, D:: -10:10, split0(A),split0(C). ?- int(A), mult(A,B,AB), A eq B, add(AB,C,F), F::5:5, mult(C,D,CD), C eq D, add(CD,A,G), G::3:3, A:: -10:10, B:: -10:10, C:: -10:10, D:: -10:10, label(A). ?- mult(A,B,AB), A eq B, add(AB,C,F), F::5:5, mult(C,D,CD), C eq D, add(CD,A,G), G::3:3, A:: -10:10, B:: -10:10, C:: -10:10, D:: -10:10, label(A). */ % end of handler interval ===================================================