eclipseclp/Contrib/cardinal_comments.pl

36 :-comment(desc, html("Cardinal is a sets constraints library with especial inferences
37 	on sets cardinality and other optional set functions (minimum and maximum for
38 	sets of integers, and union for sets of sets.)
43 	solved if constraint reasoning prunes search space when the sets are not fully
46 	Many complex relations between sets can be expressed with constraints such as set
48 	operators as intersection, union or difference of sets. Also, as it is often the
50 	function of one or more sets (e.g. the cardinality of a set). For instance, the
52 	for satisfaction problems, some sets, although still variables, may be constrained
60 	specified by an interval [A,B] where A and B are known sets ordered by set inclusion,
64 	bijective function since two distinct sets may have the same cardinality. Still,
88 	constraint propagation on sets cardinality.
93 	Set intervals define a lattice of sets. The set inclusion relation between two
94 	sets defines a partial order on P(U), the powerset over a certain universe U,
97 	Due to the transitivity rule, the top set, U, includes all sets of P(U);
98 	while the bottom set, {}, is included in all sets of P(U). Consequently,
99 	sets U and {} constitute an upper bound and a lower bound of P(U), respectively.
105 	(thus also including sets {a,b} and {b,d}). Sets {} and {a,b,c,d} are still a
110 	by its interval (lattice); all other sets outside this domain are excluded from
118 	this interval should be kept as small as possible, in order to discard all sets
120 	possible values (sets). The smallest such domain is the one with equal glb and lub,
122 	variable that can assume any set value from a collection of known sets, such as
125 	for n possible arbitrary sets S1...Sn, the corresponding set variable X has an
131 	In Cardinal, all sets are represented as sorted lists, which eases working with
132 	sets and lists interchangeably.
142 	(other than cardinality): minimum and maximum, for sets of integers, and union,
143 	for sets of sets. Refer to the available predicates for details.
226 		If SetVariable is a set of sets and a union function attribute has been set,
253 		If SetVariable is a set of sets and a union function attribute has been set,
280 		If SetVariable is a set of sets and a union function attribute has been set,
307 		If SetVariable is a set of sets and a union function attribute has been set,
361 		If SetVariable is a set of sets and a union function attribute has been set,
407 	see_also:[minimum/2,set/4,sets/4,cardinality/2]
436 	see_also:[maximum/2,set/4,sets/4,cardinality/2]
442 	args:  ["SetVariable": "A Set (variable or ground) of sets.",
444 	summary: "Union of a set of sets",
445 	desc: html("UnionVar is the union of sets in SetVariable. If UnionVar is given
458 	see_also:[set/4,sets/4,cardinality/2]
465 	args:  ["SetVariable": "A Set (variable or ground) of sets.",
467 	summary: "Union Attribute of a set of sets",
470 		UnionVar: union of sets in SetVariable<P>
473 			list of all elements in the sets of SetVariable's poss (lub\\glb)
477 	fail_if: "Fails if SetVariable is not a set of sets or if its union attributte
489 	see_also:[union_var/2,union_att/3,set/4,sets/4,cardinality/2]
522 	see_also:[set/4,sets/4,cardinality/2,union_var/2,minimum/2,maximum/2,set_labeling/1]
541   union: (SetVariable must be a set of sets.) FunctionValue can be a set, a set variable
566 	see_also:[sets/4,(`::)/2,cardinality/2,union_var/2,minimum/2,maximum/2,set_labeling/1]
570 :-comment(sets/4, [
571 	amode: sets(+,++,++,+),
584   union: (SetVariable must be a set of sets.) FunctionValue can be a set, a set variable
603 ?- sets([S],[],[a,b],[]).
604 ?- sets([S,T],[],[a,b],[cardinality:1]).
605 ?- sets([X,Y,Z],[],[a,b],[cardinality:C]).
606 ?- sets([X,Y,Z],[],[a,b],[cardinality:[0,2]]).
607 ?- sets([X,Y,Z],[c],[a,b,d,e,f,g,h,i,j,k],[cardinality:[2,4..7]]).
608 ?- sets([X,Y,Z],[],[1,3,4,5,7],[minimum:Min,maximum:1..9]), fd:(Max #> Min+2).
609 ?- sets([X,Y,Z], [], [[1,2,5],[2,4],[3,5],[1,3,4]], [union:[1]+[2,4,5]]).
871 	desc: html("Constrain sets SetVar1 and SetVar2 to be disjoint. I.e. SetVar1 and
882 ?- sets([X,Y], [],[8,9], [cardinality:1]), X `$ Y, set_labeling([X,Y]).
890 ?- sets([X,Y], [],[7,8,9], [cardinality:2]), X `$ Y.
893 ?- sets([X,Y], [],[7,8,9], [cardinality:[1,2]]), X `$ Y, #(X,2), #(Y,C).
909 	desc: html("Constrain sets SetVar1 and SetVar2 to be disjoint.<P>
919 	summary: "All sets disjointness global constraint",
920 	desc: html("Constrain all pairs of sets in SetVars to be disjoint. I.e. No two sets
936 ?- sets([X,Y,Z], [],[1,2,7,8,9], [cardinality:2]), all_disjoint([X,Y,Z]).
939 ?- sets([X,Y,Z], [],[1,2,7,8,9], [cardinality:2]), all_disjoint([X,Y,Z]), 2 `@ X, lub(Y,LubY), lub(Z,LubZ)
955 	desc: html("Constrain sets SetVar1 and SetVar2 so that SetVar1 contains SetVar2.<P>
989 	desc: html("Constrain sets SetVar1 and SetVar2 so that SetVar2 contains SetVar1.<P>
1003 	summary: "Union constraint of a list of sets",
1019 ?- sets([X,Y,Z],[a,b],[d,g,h,j],[cardinality:4]), all_union([X,Y,Z],U), #(U,C), fd:dom(C,DomC).
1022 ?- sets([X,Y,Z],[a,b],[d,g,h,j],[]), all_union([X,Y,Z],U), #(U,4), #(Y,C), fd:dom(C,DomC).
1038 	desc: html("Constrain sets SetVar1 and SetVar2 to be different.<P>
1039 		This constraint is suspended until one of the two sets is bound
1050 ?- sets([X,Y], [],[8,9], [cardinality:1]), X `/= Y, set_labeling([X,Y]).
1055 ?- sets([X,Y], [],[8,9], []), X `/= Y, X=Y.
1074 	desc: html("Constrain sets so that Complement is the complement set of SetVar,
1107 	desc: html("Constrain sets so that Complement is the complement set of SetVar.
1121 ?- sets([X,Y], [],[7,8,9], []), complement(X,Y), 8 `@ Y, glb_poss(X,GX,PX), glb_poss(Y,GY,PY).
1124 ?- sets([X,Y], [],[7,8,9], [cardinality:C]), complement(X,Y), card_labeling([X]).
1127 ?- sets([X,Y], [],[7,8,9], []), complement(X,Y), X `>= Y, set_labeling(up,[Y]).
1131 ?- sets([X,Y], [],[7,8,9], [minimum:Min]), complement(X,Y), refine(up,X).
1134 ?- sets([X,Y], [],[7,8,9], []), complement(X,Y), #(X,1), #(Y,CY).
1150 	desc: html("Constrain sets in both hand sides of equation so that SetExp1 and
1182 ?- sets([A,B],[a,b],[d,g,h,j],[cardinality:4]), A`\\/B`=U, #(U,C), fd:dom(C,DomC).
1185 ?- sets([X,Y],[a,b],[d,g,h,j],[]), X`\\/Y`=U, #(U,4), #(Y,C), fd:dom(C,DomC).
1188 ?- sets([S,X], [],[a,b], [cardinality:[0,2]]), U `= X `\\/ S, #(U,C), fd:dom(C,DomC).
1211 ?- sets([A,B],[a,b],[d,g,h,j],[cardinality:5]), A`/\\B`=I, #(I,C), fd:dom(C,DomC).
1234 ?- sets([A,B],[a,b],[d,g,h,j],[cardinality:5]), A`\\B`=D, #(D,C), fd:dom(C,DomC).
1237 ?- sets([X,Y],[a,b],[d,g,h,j],[]), X`\\Y`=D, #(D,4).
1260 			If it is a set of sets and a union function attribute has been
1265 			for sets of integers. Free variable if unused.",
1267 			for sets of integers. Free variable if unused.",
1268 		union: html("Union function, for sets of sets. Free variable if unused;
1272 	(sets themselves);
1275 	list of all elements in the sets in set's poss (lub\\glb)