From Conditional to Unconditional Rewriting

Abstract

Abstract. An automated technique to translate conditional rewrite rules into unconditional ones is presented, which is suitable to implement, or compile, conditional rewriting on top of much simpler and easier to optimize unconditional rewrite systems. An experiment performed on world's fastest conditional rewriting engines shows that speedups for conditional rewriting of an order of magnitude can already be obtained by applying the presented technique as a front-end transformation.

Computationally Equivalent Elimination of Conditions

“…The transformation in [Ros04] requires the rewrite engine to support some simple contextual rewriting strategies, namely an if( , , ) eager on the condition and an equal? eager on both arguments.…”

“…The bracket clears the failed conditions on the path to the top: σ(x 1 , .., {x i }, .., x arity(σ) , y 1 , .., y m ) → {σ(x 1 , .., x i , .., x arity(σ) , true, .., true)} It is shown in [Ros04] that the transformation is sound and that operational termination is preserved and implies completeness and preservation of ground confluence, that is, computational equivalence. Left linearity needs not be assumed.…”

“…Left linearity needs not be assumed. Although most modern rewrite systems support the rewrite strategies required by the transformation in [Ros04], we argue that imposing restrictions on the order of evaluation makes a rewrite engine less friendly w.r.t parallelism and more complex; in some sense, contextual strategies can be seen as some sort of conditional rules: apply the rule if the context permits. Our transformation basically integrates Rosu's { } operation within Viry's transformation, which allows us to also eliminate the need to carry a substitution.…”

“…Odd/Even [Ros04]. Let us consider natural numbers with 0 and successor s, constants true and false and the following on purpose inefficient conditional rules defining odd and even operators on natural numbers:…”

“…Rewriting of a given term in a CTRS may not terminate for two reasons [Ros04]: the reduction of the condition of a rule does not terminate, or there are some rules that can be applied infinitely often on the given term. In rewrite engines, the effect in both situations is the same: the system loops forever or crashes running out of memory.…”