Lazy rewriting on eager machinery

Abstract

The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting.

Termination of Lazy Rewriting Revisited

“…As in [3] and [11] we are concerned with left-linear lazy rewrite systems in this work. General assumption: Throughout the paper we assume that all lazy rewrite systems are left-linear 3 and finite.…”

“…This means that in the evaluation of an expression, the result of certain subexpressions is not computed until it is known that the particular result is actually needed. A very similar idea is used in lazy rewriting ( [3]) where the reduction of certain subterms is delayed as long as possible (cf. also [1], [8], and [10]).…”

“…Lazy rewriting was initially introduced by [3] in a graph rewriting setting (although the basic underlying idea is much older, cf. e.g.…”

“…They can be found in the technical report version of this paper[17] 3. Nevertheless, for clarity we will mention this assumption in the main results.…”

An Account of Implementing Applicative Term Rewriting

“…One uses innermost rewriting, the other just-in-time (JITty) rewriting [17]. The latter is a strategy close to lazy rewriting [7] (i.e. rewriting (sub)terms only when needed).…”