%ID: $Id$
%Author: Jia Meng, NICTA
%typed combinator reduction for full-types (include S)
clause(
forall([A, B, P, Q],
or( equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(P,A)),tc_fun(B,A)),typeinfo(Q,B)),A),typeinfo(P,A)))),
a1 ).
clause(
forall([A, B, C, P, Q, R],
or( equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBS,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(tc_fun(A,B),tc_fun(A,C)))),typeinfo(P,tc_fun(A,tc_fun(B,C)))),tc_fun(tc_fun(A,B),tc_fun(A,C))),typeinfo(Q,tc_fun(A,B))),tc_fun(A,C)),typeinfo(R,A)),C),typeinfo(hAPP(typeinfo(hAPP(typeinfo(P,tc_fun(A,tc_fun(B,C))),typeinfo(R,A)),tc_fun(B,C)),typeinfo(hAPP(typeinfo(Q,tc_fun(A,B)),typeinfo(R,A)),B)),C)))),
a2 ).
clause(
forall([P, T],
or( equal(typeinfo(hAPP(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(P,T)),T),typeinfo(P,T)))),
a3 ).
clause(
forall([A, B, C, P, Q, R],
or( equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBB,tc_fun(tc_fun(A,B),tc_fun(tc_fun(C,A),tc_fun(C,B)))),typeinfo(P,tc_fun(A,B))),tc_fun(tc_fun(C,A),tc_fun(C,B))),typeinfo(Q,tc_fun(C,A))),tc_fun(C,B)),typeinfo(R,C)),B),typeinfo(hAPP(typeinfo(P,tc_fun(A,B)),typeinfo(hAPP(typeinfo(Q,tc_fun(C,A)),typeinfo(R,C)),A)),B)))),
a4 ).
clause(
forall([A, B, C, P, Q, R],
or( equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBC,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(B,tc_fun(A,C)))),typeinfo(P,tc_fun(A,tc_fun(B,C)))),tc_fun(B,tc_fun(A,C))),typeinfo(Q,B)),tc_fun(A,C)),typeinfo(R,A)),C),typeinfo(hAPP(typeinfo(hAPP(typeinfo(P,tc_fun(A,tc_fun(B,C))),typeinfo(R,A)),tc_fun(B,C)),typeinfo(Q,B)),C)))),
a5 ).
clause(
forall([A, X, Y],
or( not(hBOOL(typeinfo(hAPP(typeinfo(hAPP(typeinfo(fequal,tc_fun(A,tc_fun(A,tc_bool))),typeinfo(X,A)),tc_fun(A,tc_bool)),typeinfo(Y,A)),tc_bool))),
equal(typeinfo(X,A),typeinfo(Y,A)))),
a6 ).
clause(
forall([A, X, Y],
or( not(equal(typeinfo(X,A),typeinfo(Y,A))),
hBOOL(typeinfo(hAPP(typeinfo(hAPP(typeinfo(fequal,tc_fun(A,tc_fun(A,tc_bool))),typeinfo(X,A)),tc_fun(A,tc_bool)),typeinfo(Y,A)),tc_bool)))),
a7 ).