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:- module rotateprune_impl.

:- interface.

:- pred rp(tree(nat)::in, tree(nat)::out) is multi.

:- type tree(T)
    --->    tree(tree(T), T, tree(T))
    ;       leaf(T).

:- type nat
    --->    s(nat)
    ;       zero.

:- implementation.

rp(T1, T2) :-
    rotate(T1, U),
    prune(U, T2).

:- pred rotate(tree(T)::in, tree(T)::out) is multi.

rotate(leaf(N), leaf(N)).
rotate(tree(L, N, R), tree(RL, N, RR)) :-
    rotate(L, RL), rotate(R, RR).
rotate(tree(L, N, R), tree(RR, N, RL)) :-
    rotate(L, RL), rotate(R, RR).

:- pred prune(tree(nat)::in, tree(nat)::out) is det.

prune(leaf(N), leaf(N)).
prune(tree(_, zero, _), leaf(zero)).
prune(tree(L, s(N), R), tree(PL, s(N), PR)) :-
    prune(L, PL), prune(R, PR).