The aim of this article is double. From one side we survey the knowledge we have acquired
these last ten years about the lattice of all λ-theories (equational extensions of untyped λ …

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 …

Λ μ-calculus is an extension of Parigot's λμ-calculus which (i) satisfies Separation theorem: it
is Böhm-complete,(ii) corresponds to CBN delimited control and (iii) is provided with a …

Abstract We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the
first notion of infinitary higher-order rewriting. The systems defined are sufficiently general …

Parigot's λμ-calculus (Parigot, 1992 [1]) is now a standard reference about the computational
content of classical logic as well as for the formal study of control operators in functional …

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 …

Böhm-Like Trees for Rewriting Page 1 VU Research Portal Bohm-Like Trees for Rewriting
Ketema, J. 2006 document version Publisher's PDF, also known as Version of record Link to …

We introduce a coinductive definition of infinitary term rewriting. The setup is surprisingly
simple, and has in contrast to the usual definitions of infinitary rewriting, neither need for …

We define infinitary combinatory reduction systems (iCRSs). This provides the first extension
of infinitary rewriting to higher-order rewriting. We lift two well-known results from infinitary …

There are two themes in this note. The first is how to derive new fixed point combinators from
given ones. Here we extend the derivation principle leading to the Böhm sequence of fpc's …