library(ic_sets)

Predicates

#(?Set, ?Card)

Card is the cardinality of the integer set Set

?Set :: ++Lwb..++Upb

Set is an integer set within the given bounds

all_disjoint(+Sets)

Sets is a list of integers sets which are all disjoint

all_intersection(+Sets, ?Intersection)

Intersection is the intersection of all the sets in the list Sets

all_union(+Sets, ?SetUnion)

SetUnion is the union of all the sets in the list Sets

difference(?Set1, ?Set2, ?Set3)

Set3 is the difference of the integer sets Set1 and Set2

?Set1 disjoint ?Set2

The integer sets Set1 and Set2 are disjoint

get_set_attribute(?Set, -Attr)

Get the set-attribute corresponding to Set

?X in ?Set

The integer X is member of the integer set Set

in(?X, ?Set, ?Bool)

Reified version of the set membership constraint

?Set in_set_range ++Lwb..++Upb

Set is an integer set within the given bounds

?Set1 includes ?Set2

Set1 includes (is a superset of) the integer set Set2

insetdomain(?Set, ?CardSel, ?ElemSel, ?Order)

Instantiate Set to a possible value

intersection(?Set1, ?Set2, ?Set3)

Set3 is the intersection of the integer sets Set1 and Set2

intset(?Set, +Min, +Max)

Set is a set containing numbers between Min and Max

intsets(?Sets, ?N, +Min, +Max)

Sets is a list of N sets containing numbers between Min and Max

is_exact_solver_var(?)

No description available

is_solver_type(?Term)

Succeeds if Term is a ground set or a set variable

is_solver_var(?Term)

Succeeds if Term is a set variable

membership_booleans(?Set, ?BoolArr)

BoolArr is an array of booleans describing Set

msg(?, ?, ?)

No description available

?X notin ?Set

The integer X is not a member of the integer set Set

potential_members(?Set, -List)

List is the list of elements of whose membership in Set is currently uncertain

?Set1 sameset ?Set2

The sets Set1 and Set2 are equal

set_range(?Set, -Lwb, -Upb)

Lwb and Upb are the current lower and upper bounds on Set

?Set1 subset ?Set2

Set1 is a (non-strict) subset of the integer set Set2

?Set1 subsetof ?Set2

Set1 is a (non-strict) subset of the integer set Set2

symdiff(?Set1, ?Set2, ?Set3)

Set3 is the symmetric difference of the integer sets Set1 and Set2

union(?Set1, ?Set2, ?Set3)

Set3 is the union of the integer sets Set1 and Set2

watch(?)

No description available

weight(?Set, ++ElementWeights, ?Weight)

According to the array of element weights, the weight of set Set is Weight

Structures

struct int_sets(dom, off, lcard, ucard, added, removed, add, rem, card, booleans, value)

Attribute structure for set variables (and constants)

Other Exports

export op(500, yfx, \)

export op(700, xfx, in_set_range)

export op(700, xfx, disjoint)

export op(700, xfx, sameset)

export op(700, xfx, in)

export op(700, xfx, notin)

export op(700, xfx, includes)

export op(700, xfx, subset)

export op(700, xfx, subsetof)

    	SetOfThree = [1,3,7]
    	EmptySet = []
    

    	SetVar in_set_range []..[1,2,3,4,5,6,7],
    

    	SetVar subset [1,2,3,4,5,6,7],
    

    	intset(SetVar, 1, 7)
    

    Set1 /\ Set2       % intersection
    Set1 \/ Set2       % union
    Set1 \ Set2        % difference
    

% Example program: Steiner triplets
% Compute NB triplets of numbers from 1 to N such that
% any two triplets have at most one element in common.
% Try steiner(9,Sets).

:- lib(ic_sets).
:- lib(ic).

steiner(N, Sets) :-
	NB is N * (N-1) // 6,		% compute number of triplets
	intsets(Sets, NB, 1, N),	% initialise the set variables
	( foreach(S,Sets) do
	    #(S,3)			% constrain their cardinality
	),
	( fromto(Sets,[S1|Ss],Ss,[]) do
	    ( foreach(S2,Ss), param(S1) do
		#(S1 /\ S2, C),		% constrain the cardinality
		C #=< 1			% of pairwise intersections
	    )
	),
        label_sets(Sets).		% search

label_sets([]).
label_sets([S|Ss]) :-
        insetdomain(S,_,_,_),
	label_sets(Ss).