Data commit

Task/Set/Prolog/set-1.pro

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+:- use_module(library(lists)).
+
+set :-
+	A = [2, 4, 1, 3],
+	B = [5, 2, 3, 2],
+	(   is_set(A) -> format('~w is a set~n', [A])
+	;   format('~w is not a set~n', [A])),
+	(   is_set(B) -> format('~w is a set~n', [B])
+	;   format('~w is not a set~n', [B])),
+
+	% create a set from a list
+
+	list_to_set(B, BS),
+	(   is_set(BS) -> format('~nCreate a set from a list~n~w is a set~n', [BS])
+	;   format('~w is not a set~n', [BS])),
+
+	intersection(A, BS, I),
+	format('~n~w intersection ~w => ~w~n', [A, BS, I]),
+	union(A, BS, U),
+	format('~w union ~w => ~w~n', [A, BS, U]),
+	difference(A, BS, D),
+	format('~w difference ~w => ~w~n', [A, BS, D]),
+
+	X = [1,2],
+	(   subset(X, A) -> format('~n~w is a subset of ~w~n', [X, A])
+	;   format('~w is not a subset of ~w~n', [X, A])),
+	Y = [1,5],
+	(   subset(Y, A) -> format('~w is a subset of ~w~n', [Y, A])
+	;   format('~w is not a subset of ~w~n', [Y, A])),
+	Z = [1, 2, 3, 4],
+	(  equal(Z, A) -> format('~n~w is equal to ~w~n', [Z, A])
+	;   format('~w is not equal to ~w~n', [Z, A])),
+	T = [1, 2, 3],
+	(  equal(T, A) -> format('~w is equal to ~w~n', [T, A])
+	;   format('~w is not equal to ~w~n', [T, A])).
+
+
+
+% compute difference of sets
+difference(A, B, D) :-
+	exclude(member_(B), A, D).
+
+member_(L, X) :-
+	member(X, L).
+
+equal([], []).
+equal([H1 | T1], B) :-
+	select(H1, B, B1),
+	equal(T1, B1).

Task/Set/Prolog/set-2.pro

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+%%  Set creation
+
+?- list_to_ord_set([1,2,3,4], A), list_to_ord_set([2,4,6,8], B).
+A = [1, 2, 3, 4],
+B = [2, 4, 6, 8].
+
+%% Test m ∈ S -- "m is an element in set S"
+
+?- ord_memberchk(2, $A).
+true.
+
+%% A ∪ B -- union; a set of all elements either in set A or in set B.
+
+?- ord_union($A, $B, Union).
+Union = [1, 2, 3, 4, 6, 8].
+
+%% A ∩ B -- intersection; a set of all elements in both set A and set B.
+
+?- ord_intersection($A, $B, Intersection).
+Intersection = [2, 4].
+
+%% A ∖ B -- difference; a set of all elements in set A, except those in set B.
+
+?- ord_subtract($A, $B, Diff).
+Diff = [1, 3].
+
+%% A ⊆ B -- subset; true if every element in set A is also in set B.
+
+?- ord_subset($A, $B).
+false.
+
+?- ord_subset([2,4], $B).
+true.
+
+%% A = B -- equality; true if every element of set A is in set B and vice-versa.
+
+?- $A == $B.
+false.
+
+?- $A == [1,2,3,4].
+true.
+
+%% Definition of a proper subset:
+
+ord_propsubset(A, B) :-
+    ord_subset(A, B),
+    \+(A == B).
+
+%% add/remove elements
+
+?- ord_add_element($A, 19, NewA).
+NewA = [1, 2, 3, 4, 19].
+
+?- ord_del_element($NewA, 3, NewerA).
+NewerA = [1, 2, 4, 19].