the combinatory logic analogue of rice's theorem says that there is no complete nontrivial predicate. a "predicate" is a combinator that, when applied, returns either t or f. a predicate n is "nontrivial" if there are two arguments "a" and "b" such that n "a" = t and n "b" = f. a combinator n is "complete" if and only if n"m" has a normal form for every argument "m". the analogue of rice's theorem then says that every complete predicate is trivial. the proof of this theorem is rather simple.