Extensional and Intensional Strategies

TLDR: In this article, a general definition of abstract strategies is presented, which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system.

Abstract: This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system. We then move to a more intensional definition supporting the abstract view but more operational in the sense that it describes a means for determining such a set. We characterize the class of extensional stra tegies that can be defined intensionally. We also give some hints towards a logical characterization of intensional strategies and propose a few challenging perspectives.