Eliminating Proofs from Programs

AbstractThis paper presents a step in the development of an operational approach to program extraction in type theory. In order to get a program from a lambda term, the logical parts need to be removed. This is done by a reduction relation →ε. We study the combination of β-reduction and ε-reduction, both in the setting of simply typed lambda calculus and for pure type systems. In the general setting the properties confluence, subject reduction, and strong normalization are studied