Computing More Specific Versions of Conditional Rewriting Systems

Abstract

Abstract. Rewrite systems obtained by some automated transformation often have a poor syntactic structure even if they have good properties from a semantic point of view. For instance, a rewrite system might have overlapping left-hand sides even if it can only produce at most one constructor normal form (i.e., value). In this paper, we propose a method for computing "more specific" versions of deterministic conditional rewrite systems (i.e., typical functional programs) by replacing a given rule (e.g., an overlapping rule) with a finite set of instances of this rule. In some cases, the technique is able to produce a non-overlapping system from an overlapping one. We have applied the transformation to improve the systems produced by a previous technique for function inversion with encouraging results (all the overlapping systems were successfully transformed to non-overlapping systems).

A Finite Representation of the Narrowing Space

“…Among the possible applications, one can consider the use of extended narrowing trees and success set equations to better understand the program's control flow, to analyze weak termination [13], to detect subtrees that will never produce a computed answer as in Example 1 (which could be useful, e.g., in the context of the more specific transformation recently introduced in [22]), and so forth. This work opens many possibilities for future work.…”

“…For instance, one can use them to better understand the program's control flow, to analyze weak termination, 3 to detect subtrees that will never produce a computed answer (which is useful, e.g., in the context of the more specific transformation recently introduced in [22]), and so forth. In this paper, we present the building blocks for designing such techniques.…”

On Transforming Narrowing Trees into Regular Tree Grammars Generating Ranges of Substitutions

“…The narrowing relation [27,14] mainly extends rewriting by replacing matching with unification. This paper follows the formalization in [22], while we use the rule (x…”

“…When we consider two (or more) narrowing derivations S 1 i * σ 1 ,R T 1 and S 2 i * σ 2 ,R T 2 , we assume that VRan(σ 1 ) ∩ VRan(σ 2 ) = / 0. Innermost narrowing is a counterpart of constructor-based rewriting (cf [22]…”

“…). Following[22], we define constructor-based conditional rewriting on goal clauses as follows: for a goal clauseS = U & s t & S with U ∈ T ({ , &}), we write S c → R T if there exist a non-variable position p of (s t), a rule → r ⇐ C in R, and a constructor substitution σ such that (s t)| p is basic, (s t)| p = σ , and T = U & σC & (s t)[σ r] p & S .…”