Clocked lambda calculus

An Introduction to the Clocked Lambda Calculus

We give a brief introduction to the clocked λ-calculus, an extension of the classical λ-calculus with a unary symbol τ used to witness the β-steps. In contrast to the classical λ-calculus, this extension is infinitary strongly normalising and infinitary confluent. The infinitary normal forms are enriched Lévy–Longo Trees, which we call clocked Lévy–Longo Trees. 1998 ACM Subject Classification D...

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...

Discriminating Lambda-Terms Using Clocked Boehm Trees

As observed by Intrigila [16], there are hardly techniques available in the λ-calculus to prove that two λ-terms are not β-convertible. Techniques employing the usual Böhm Trees are inadequate when we deal with terms having the same Böhm Tree (BT). This is the case in particular for fixed point combinators, as they all have the same BT. Another interesting equation, whose consideration was sugg...

The algebraic lambda calculus

We introduce an extension of the pure lambda-calculus by endowing the set of terms with a structure of vector space, or more generally of module, over a xed set of scalars. Terms are moreover subject to identities similar to usual pointwise de nition of linear combinations of functions with values in a vector space. We then study a natural extension of beta-reduction in this setting: we prove i...

Notes on Lambda Calculus