Retracts in simply type lambda beta eta -calculus

Abstract

Retractions existing in all models of simply typed lambda -calculus are studied and related to other relations among types, such as isomorphisms, surjections, and injections. A formal system to deduce the existence of such retractions is shown to be sound and complete with respect to retractions definable by linear lambda -terms. Results aiming at a system complete with respect to the provable retractions tout court are established.<>