File: lambda.elpi

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% test Z yields Z=impl(impl A B) (impl A B)

% Type inference for simply typed lambda terms
% Syntax: t ::= appl t t | abs F    where F is a function t -> t
% Syntax: ty ::= impl ty ty

:untyped of (appl T1 T2) B :- of T1 (impl A B), of T2 A.
:untyped of (lam F) (impl A B) :- pi x\ of x A => of (F x) B.

:untyped test Z :- of (lam f\ lam a\ appl f a) Z.

:untyped main :- test Z, Z = impl (impl a b) (impl a b).