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:- module pl4_5_2.

:- interface.

:- type expr
    --->    expr + expr
    ;       num(int).

:- pred s(expr::in, expr::out) is nondet.

:- implementation.

:- import_module int.
:- import_module prolog.

s(A + (B + C), D) :-
    s((A + B) + C, D).
s(A + B, C) :-
    s(B + A, C).
s(X + num(0), X).
s(X + Y, Z) :-
    s(X, A),
    s(Y, B),
    s(A + B, Z).
s(A + B, C) :-
    A = num(Anum),
    B = num(Bnum),
    Cnum = Anum + Bnum,
    C = num(Cnum).