% encoding type judgments

% This definition is from chapter 33 of _Programming languages: application
% and interpretation_, by Shriram Krishnamurthi.

type(_, numConst, num).
type(_, boolConst, bool).
type(TEnv, if(Test, Then, Else), Tau) :- type(TEnv, Test, bool),
                                         type(TEnv, Then, Tau),
                                         type(TEnv, Else, Tau).
type([bind(V, Tau) | _], var(V), Tau).
type([bind(_, _) | TEnvRest], var(V), Tau) :- type(TEnvRest, var(V), Tau).
type(TEnv, fun(Var, Body), arrow(Tau1, Tau2)) :- 
    type([bind(Var, Tau1) | TEnv], Body, Tau2).
type(TEnv, app(Fun, Arg), Tau2) :- type(TEnv, Fun, arrow(Tau1, Tau2)),
                                   type(TEnv, Arg, Tau1).