type_of(return(Values), _, [Arity]) :- length(Values, Arity).

type_of(if(Then, Else), Env, T) :-
  type_of(Then, Env, T1),
  type_of(Else, Env, T2),
  union(T1, T2, T).

type_of(fun([]), _, [] -> []).
type_of(fun([Args->Body|Cdr]), Env, TArity->TBody) :-
  length(Args, TArityCar),
  type_of(Body, Env, TBodyCar),
  type_of(fun(Cdr), Env, TArityCdr->TBodyCdr),
  union([TArityCar], TArityCdr, TArity),
  union(TBodyCar, TBodyCdr, TBody).

union2(S1, S2, U) :-
  is_list(S1),
  is_list(S2),
  union(S1, S2, U).
union2(S1, (S2, Var), (U2, Var)) :-
  is_list(S1),
  is_list(S2),
  union(S1, S2, U1),
  lowpass(U1, Var, U2).
union2((S1, Var), S2, X) :-
  is_list(S1),
  is_list(S2),
  union2(S2, (S1, Var), X).
union2((S1, Var1), (S2, Var2), X) :-
  is_list(S1),
  is_list(S2),
  Var1 >= Var2, !,
  union2(S1, (S2, Var2), X).
union2((S1, Var1), (S2, Var2), X) :-
  is_list(S1),
  is_list(S2),
  Var1 < Var2,
  union2(S2, (S1, Var1), X).

lowpass([], _, []).
lowpass([H|T], Cutoff, X) :-
  H >= Cutoff,
  lowpass(T, Var, X).
lowpass([H|T], Cutoff, [H|L]) :-
  H < Cutoff,
  lowpass(T, Var1, L).