Extensional and Intensional Strategies

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 strategies that can be defined intensionally. We also give some hints towards a logical characterization of intensional strategies and propose a few challenging perspectives.

A rewriting point of view on strategies

“…Another view of rewriting is to consider it as an abstract relation on structural objects. An Abstract Reduction System (ARS) [19,15,6] −−→ a n or a 0 π − → a n , where n ∈ N. The source of π is a 0 and its domain Dom(π) = {a 0 }. The target of π is a n and applying π to a 0 gives the singleton set {a n }, which is denoted π • a 0 = {a n }.…”

“…Abstract strategies are defined in [15] and in [6] as follows: for a given ARS A , an abstract strategy ζ is a subset of the set of all derivations (finite or not) of A . The notions of domain and application are generalized as follows: Dom(ζ ) = π∈ζ Dom(π) and ζ • a = {b | ∃π ∈ ζ such that a π − → b} = {π • a | π ∈ ζ }.…”

Strategic Port Graph Rewriting: An Interactive Modelling and Analysis Framework

“…Reduction strategies define which (sub)expression(s) should be selected for evaluation and which rule(s) should be applied (see [20,8] for general definitions). Strategies are present in programming languages such as Clean [25], Curry [18], and Haskell [19] and can be explicitly defined to rewrite terms in languages such as ELAN [7], Stratego [32], Maude [22] or Tom [4].…”

A Strategy Language for Graph Rewriting

“…We denote it S R , G Q P , or simply S, G Q P when R is obvious. The formal semantics of a graph program is given below, using an Abstract Reduction System [40,26,12]. The idea is to build a set of rewrite derivations out of S, G Q P according to the strategy S (i.e., a derivation tree).…”

“…Reduction strategies define which (sub)expression(s) should be selected for evaluation and which rule(s) should be applied (see [26,12] for general definitions). These choices affect fundamental properties of computations such as laziness, strictness, completeness, termination and efficiency, to name a few (see, e.g., [43,41,28]).…”