:- set_prolog_flag(verbose,silent).
:- prompt(_, '').
:- use_module(library(readutil)).
 
:- set_prolog_flag(occurs_check,true).
:- op(500,xfy,$).
 
% STLC type system specification
 
type(C,var(X),       T) :- first(X:T,C).
type(C,lam(X,E),A -> B) :- type([X:A|C], E,  B).
type(C,X $ Y,        B) :- type(C,X,A -> B), type(C,Y,A).
 
first(K:V,[K1:V1|_]) :- K = K1, V=V1.
first(K:V,[K1:_|Xs]) :- K\==K1, first(K:V, Xs). % no cut but use var cmp
 
main:-
	process,
	halt.
 
type_and_print(C,E,T) :- type(C,E,T), print(E : T).
 
process:-
    /* your code goes here */
	type_and_print([],lam(x,var(x)),_), nl,
	type_and_print([],lam(x,lam(y,var(y)$var(x))),_), nl,
	true.
 
:- main.

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