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:- module associative.

:- interface.

:- type expr
    --->    base
    ;       op(expr, expr).

:- pred normal_form(expr, expr).
:- mode normal_form(in, out) is det.

:- implementation.

normal_form(F, N) :-
    ( rewrite(F, F1) ->
        normal_form(F1, N)
    ;
        N = F
    ).

:- pred rewrite(expr, expr).
:- mode rewrite(in, out) is semidet.

rewrite(In, Out) :-
    ( In = op(op(A, B), C) ->
        Out = op(A, op(B, C))
    ;
        In = op(A, op(B, C)),
        Out = op(A, L),
        rewrite(op(B, C), L)
    ).