Syntactic analysis of η-expansions in Pure Type Systems

Abstract

By a detailed analysis of the interaction between β -reduction → β and η -expansion → η ̄ in the simply typed λ -calculus, a modular and purely syntactic proof method is devised in order to derive strong normalization of the combined reduction → β η ̄ from that of → β and → η ̄ . It is shown how this technique extends to β -normalizing functional Pure Type Systems with Barthe’s formulation of η -expansion.