Retractions in intersection types

Abstract

This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a λ-calculus with a ⊥ constant. The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one. Moreover, the characterisation of retraction in the standard intersection types is discussed.