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 lambda calculus with a bottom 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.Comment: In Proceedings ITRS 2016, arXiv:1702.0187

Automorphisms of types in certain type theories and representation of finite groups

“…Retractions were considered as well, together with isomorphisms or separately. See, for example, Bruce and Longo (1985), Stirling (2013) and Coppo et al (2016) ‡ .…”