An Introduction to the Clocked Lambda Calculus

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...

Highlights in infinitary rewriting and lambda calculus

We present some highlights from the emerging theory of infinitary rewriting, both for first-order term rewriting systems and λ-calculus. In the first section we introduce the framework of infinitary rewriting for first-order rewrite systems, so without bound variables. We present a recent observation concerning the continuity of infinitary rewriting. In the second section we present an excursio...

An introduction to functional programming through lambda calculus

Modular Construction of Fixed Point Combinators and Clocked Boehm Trees

Fixed point combinators (and their generalization: looping combinators) are classic notions belonging to the heart of λ-calculus and logic. We start with an exploration of the structure of fixed point combinators (fpc’s), vastly generalizing the well-known fact that if Y is an fpc, Y (SI) is again an fpc, generating the Böhm sequence of fpc’s. Using the infinitary λ-calculus we devise infinitel...

On graphic lambda calculus and the dual of the graphic beta move

This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move. While the graphic beta move corresponds to beta reduction in untyped lambda...