%---------------------------------------------------------------------------%
% vim: ts=4 sw=4 et ft=mercury
%---------------------------------------------------------------------------%
% 
% The "depth" Benchmark.
% Part of the DPPD Library.
% 
% A Lam & Kusalik benchmark. It consists of a simple non-ground
% meta-interpreter which has to be specialised for a fully-unfoldable
% object program. It uses neither negations nor built-ins. For a
% slightly different and more intricate example see the ex_depth
% benchmark (which is not fully unfoldable).

depth(rue, 0).
depth((_g1, _gs), _depth) :-
    depth(_g1, _depth_g1),
    depth(_gs, _depth_gs),
    max(_depth_g1, _depth_gs, _depth).
depth(_goal, s(_depth)) :-
    prog_clause(_goal, _body),
    depth(_body, _depth).

max(_num, 0, _num).
max(0, s(_num), s(_num)).
max(s(_x), s(_y), s(_max)) :-
    max(_x, _y, _max).

prog_clause(member(_X, _Xs), append(_, [_X | _], _Xs)).
prog_clause(append([], _L, _L), true).
prog_clause(append([_X | _L1], _L2, [_X | _L3]), append(_L1, _L2, _L3)).

% The partial deduction query
% 
% :- depth(member(X, [a, b, c, m, d, e, m, f, g, m, i, j]), Depth).
% 
% The run-time queries
% 
% :- depth(member(i, [a, b, c, m, d, e, m, f, g, m, i, j]), Depth).
% 
% Example solution
% 
% This benchmark can be fully unfolded. With the ECCE partial deduction
% system one can obtain the following:

depth__1(a, s(s(0))).
depth__1(b, s(s(s(0)))).
depth__1(c, s(s(s(s(0))))).
depth__1(m, s(s(s(s(s(0)))))).
depth__1(d, s(s(s(s(s(s(0))))))).
depth__1(e, s(s(s(s(s(s(s(0)))))))).
depth__1(m, s(s(s(s(s(s(s(s(0))))))))).
depth__1(f, s(s(s(s(s(s(s(s(s(0)))))))))).
depth__1(g, s(s(s(s(s(s(s(s(s(s(0))))))))))).
depth__1(m, s(s(s(s(s(s(s(s(s(s(s(0)))))))))))).
depth__1(i, s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))).
depth__1(j, s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))).

% Michael Leuschel / K.U. Leuven / michael@cs.kuleuven.ac.be