Right and left invertibility in $\lambda - \beta $-calculus

Infinitary Lambda Calculus Innnitary Lambda Calculus

In a previous paper we have established the theory of transsnite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of innnitary rewriting, the BB ohm model of the lambda calculus can be seen as an innnitary term model. In contrast to term rewriting, there are several diierent possible notions of innnite term, whic...

Rewriting Modulo \beta in the \lambda\Pi-Calculus Modulo

The λ Π-calculus Modulo is a variant of the λ -calculus with dependent types where β -conversion is extended with user-defined rewrite rules. It is an expressive logical framework and has been used to encode logics and type systems in a shallow way. Basic properties such as subject reduction or uniqueness of types do not hold in general in the λ Π-calculus Modulo. However, they hold if the rewr...

Encoding Left Reduction in the Lambda-Calculus with Interaction Nets

Modularity in lambda calculus

The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the rst-order predicate logic. In this paper we prove that the variety of lambda abstraction algebras is not congruence modular and that the lattice of lambda theories is not modular.

The lambda mechanism in lambda calculus and in other calculi

A comparison of Landin’s form of lambda calculus with Church’s shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the arguments are indexed numerically. We call this the “lambda mechanism” and show how it can be used in other calculi. In first-order predicate logic it can be ...