In this paper, an extension of Pure Type Systems (PTS's) to include deenitions is presented and the meta-theory of these PTS's with deenitions is treated in detail. We prove that all the propertiesâ€¦ (More)

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applicationsâ€¦ (More)

In this paper, we use types for ensuring that programs involving streams are well-behaved. We extend pure type systems with a type constructor for streams, a modal operator next and a fixed pointâ€¦ (More)

In this paper we present a set of necessary and sufficient conditions on a set of lambda terms to serve as the set of meaningless terms in an infinitary bottom extension of lambda calculus. So farâ€¦ (More)

We show the existence of an infinitary confluent and normalising extension of the finite extensional lambda calculus with beta and eta. Besides infinite beta reductions also infinite eta reductionsâ€¦ (More)

This is an informal explanation of the main concepts and results of Sev96] 1. We consider typed and untyped lambda calculi. For untyped lambda calculus, we give a new method to prove properties onâ€¦ (More)

We propose an extension of lambda calculus for which the Berarducci trees equality coincides with observational equivalence, when we observe rootstable or rootactive behavior of terms. In oneâ€¦ (More)

Gabbay and Pitts proved that lambda-terms up to alphaequivalence constitute an initial algebra for a certain endofunctor on the category of nominal sets. We show that the terms of the infinitaryâ€¦ (More)