Algorithmic Eta-reduction in Type-theory of Acyclic Recursion

Abstract

We investigate the applicability of the classic eta-conversion in the type-theory of acyclic algorithms. While denotationally valid, classic eta-conversion is not algorithmically valid in the type theory of algorithms, with the exception of few limited cases. The paper shows how the restricted, algorithmic eta-rule can recover algorithmic eta-conversion in the reduction calculi of type-theory of algorithms.