Data commit

Task/Eulers-identity/Prolog/eulers-identity.pro

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+% reduce() prints the intermediate results so that one can see Prolog "thinking."
+%
+reduce(A, C) :-
+    simplify(A, B),
+    (B = A -> C = A; io:format("= ~w~n", [B]), reduce(B, C)).
+
+simplify(exp(i*X), cos(X) + i*sin(X)) :- !.
+
+simplify(0 + A, A) :- !.
+simplify(A + 0, A) :- !.
+simplify(A + B, C) :-
+    integer(A),
+    integer(B), !,
+    C is A + B.
+simplify(A + B, C + D) :- !,
+    simplify(A, C),
+    simplify(B, D).
+
+simplify(0 * _, 0) :- !.
+simplify(_ * 0, 0) :- !.
+simplify(1 * A, A) :- !.
+simplify(A * 1, A) :- !.
+simplify(A * B, C) :-
+    integer(A),
+    integer(B), !,
+    C is A * B.
+simplify(A * B, C * D) :- !,
+    simplify(A, C),
+    simplify(B, D).
+
+simplify(cos(0),  1)  :- !.
+simplify(sin(0),  0)  :- !.
+simplify(cos(pi), -1) :- !.
+simplify(sin(pi), 0)  :- !.
+
+simplify(X, X).