Perpetual Reductions inλ-Calculus

Perpetual Reductions in *-Calculus

This paper surveys a part of the theory of ;-reduction in *-calculus which might aptly be called perpetual reductions. The theory is concerned with perpetual reduction strategies, i.e., reduction strategies that compute infinite reduction paths from *-terms (when possible), and with perpetual redexes, i.e., redexes whose contraction in *-terms preserves the possibility (when present) of infinit...

The Longest Perpetual Reductions in Orthogonal

We consider reductions in Orthogonal Expression Reduction Systems (OERS), that is, Orthogonal Term Rewriting Systems with bound variables and substitutions, as in the-calculus. We design a strategy that for any given term t constructs a longest reduction starting from t if t is strongly normalizable, and constructs an innnite reduction otherwise. The Conservation Theorem for OERSs follows easil...

Semantical Analysis of Perpetual Strategies in -calculus ?

Perpetual strategies in-calculus are analyzed from a semantical perspective. This is achieved using suitable denotational models, computationally adequate with respect to the observational (operational) equivalence, p , induced by perpetual strategies. A necessary and suucient condition is given for an !-algebraic lattice, isomorphic to the space of its strict continuous self-maps, to be comput...

In -calculus and Type Theory Preface Viii Contents Preface V Introduction 1 1 Perpetual Reductions in -calculus 11 2 Weak and Strong Normalization in Type Theory 71

it can apparently happen that someone, without much exact learning and with little of the information collected by earlier generations in his head, that such an individual, passing his days like other artists in the creation of more or less fantastic pictures, can one day feel ripen in himself a conscious wish to use his imaginary images to approach innnity as purely and as closely as possible....

Property-Dependent Reductions for the Modal Mu-Calculus