Basic completion strategies as another application of the Maude strategy language

Abstract

The two levels of data and actions on those data provided by the separation between equations and rules in rewriting logic are completed by a third level of strategies to control the application of those actions. This level is implemented on top of Maude as a strategy language, which has been successfully used in a wide range of applications. First we summarize the Maude strategy language design and review some of its applications; then, we describe a new case study, namely the description of completion procedures as transition rules + control, as proposed by Lescanne.

Model checking strategy-controlled systems in rewriting logic

“…Controlling deduction procedures based on a given set of rules is one of the paradigmatic use cases for strategies, following the principle of separation of concerns enunciated in the motto Algorithm = Logic + Control [Kow79]. The Knuth-Bendix and other equational completion procedures in Section 6.5 are a complete redesign of a previous specification [VM11] that used the Maude-based prototype of the strategy language, which was based in turn on previous work by Lescanne [Les90]. The novelty of our specification is that it fixes a set of Maude rules for the four alternative completion procedures, and only the recursive strategies that apply them vary from one to another.…”

“…Lescanne [Les90] described various such procedures as a combination of transition rules + control, and implemented them in CAML. Completion procedures were also implemented in ELAN [KM95], at the Maude metalevel [CM97], and even using the Maude strategy language [VM11]. However, the separation between rules and control is not clearly enforced in these works, since the rules are adapted to the specific data structure of each method.…”

“…However, the separation between rules and control is not clearly enforced in these works, since the rules are adapted to the specific data structure of each method. In this section, we propose an improvement of [VM11] in which a single fixed set of rules is used to express the different specific procedures as stateful strategies. These strategies are specified in separate strategy modules on top of the same system module COMPLETION, as shown in Figure 6.6.…”

Compositional Specification in Rewriting Logic

“…Using this technique, a base system, specified with all its non-deterministic capabilities, can be put under the control of different strategy-components to achieve different results. This is the idea used in Lescanne (1989); Clavel and Meseguer (1997); Verdejo and Martí-Oliet (2012) to implement Knuth-Bendix-like completion as a basic set of correct rules on which different strategies are applied to get different actual procedures. Again, the same idea is used in Bachmair et al .…”

Parameterized Strategies Specification in Maude

“…The strategy language is based in its authors experience with strategies in Maude and in previous strategy languages like ELAN [2] and Stratego [5]. It has already been exploited in the specification of algorithms, inference systems, and language semantics: Milner's CCS [12], the ambient calculus [12], the semantics of the parallel functional language Eden [9], equational logic completion procedures [16], a proof calculus for membrane systems [1], etc. These examples are likely to be expressed and generalized using control parameterization with strategies, whose implementation was not available at that time.…”