A self-dependency constraint in the simply typed lambda calculus

Abstract

We consider a class of terms in the simply typed lambda calculus in which initially, during reduction, and for the potential terms it is never allowed that a variable x is applied to an argument containing x. The terms form a wide class which includes linear terms. We show that corresponding variant of the dual interpolation problem (i.e. the problem in which all expressions can be restricted to terms of this kind) is decidable. Thus the model for this kind of expressions can admit fully abstract semantics and the higher-order matching problem is decidable. © Springer-Verlag Berlin Heidelberg 2005.