This paper surveys a part of the theory ofβ-reduction inλ-calculus which might aptly be
calledperpetual reductions. The theory is concerned withperpetual reduction strategies, ie …

All traditional implementation techniques for functional languages fail to avoid useless
repetition of work. They are not" optimal" in their implementation of sharing, often causing a …

The identification of the needed redexes in a term is an undecidable problem. We introduce
a (partially decidable) type assignment system, which distinguishes certain redexes called …

Standardization is a fundamental notion for connecting programming languages and
rewriting calculi. Since both programming languages and calculi rely on substitution for …

BL Presents a fresh perspective on the role of calculus in computer science In contrast to
other books on this topic, which have all been written by logicians, this book is written from …

Publisher Summary This chapter discusses lambda calculus and explains how this system is
able to capture all computable functions. Once a reduction strategy is chosen, the behavior …

We describe lambda calculus reduction strategies, such as call-by-value, call-by-name,
normal order, and applicative order, using big-step operational semantics. We show how to …

For orthogonal term rewriting systems Q. Huet and J.-J. Lévy have introduced the property of
'strong sequentiality'. A strongly sequential orthogonal term rewriting system admits an …

The following theorem of Huet and Lévy forms the basis of all results on optimal reduction
strategies for orthogonal term rewriting systems: every term not in normal form contains a …

In this paper, we propose to extend the Barendregt Cube by generalisingβ-reduction and by
adding definition mechanisms. Generalised reduction allows contracting more visible …