Correct and Complete (Positive) Strategy Annotations for OBJ

AbstractStrategy annotations are used in several rewriting-based programming languages to introduce replacement restrictions aimed at improving efficiency and/or reducing the risk of nontermination. Unfortunately, rewriting restrictions can have a negative impact on the ability to compute normal forms. In this paper, we first ascertain/clarify the conditions ensuring correctness and completeness (regarding normalization) of computing with strategy annotations. Then, we define a program transformation methodology for (correct and) complete evaluations which applies to OBJ-like languages

Termination of rewriting strategies: a generic approach

We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying narrowing and abstracting steps. The induction principle is applied through the abstraction mechanism, where terms are replaced by variables representing any of their normal forms. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. Abstraction constraints can be used to control the narrowing mechanism, well known to easily diverge. The generic method is then instantiated for the innermost, outermost and local strategies.Comment: 49 page

Rewriting Strategies and Strategic Rewrite Programs

International audienceThis survey aims at providing unified definitions of strategies, strategic rewriting and strategic programs. It gives examples of main constructs and languages used to write strategies. It also explores some properties of strategic rewriting and operational semantics of strategic programs. Current research topics are identified

Rewriting Strategies and Strategic Rewrite Programs (Updated version)

This survey aims at providing unified definitions of strategies , strategic rewriting and strategic programs. It gives examples of main constructs and languages used to write strategies. It also explores some properties of strategic rewriting and operational semantics of strategic programs. Current research topics are identified

Innermost Termination of Context-Sensitive Rewriting

Innermost context-sensitive rewriting (CSR) has been proved useful for modeling the computational behavior of programs of algebraic languages like Maude, OBJ, etc, which incorporate an innermost strategy which is used to break down the nondeterminism which is inherent to reduction relations. Furthermore, innermost termination of rewriting is often easier to prove than termination. Thus, under appropriate conditions, a useful strategy for proving termination of rewriting is trying to prove termination of innermost rewriting. This phenomenon has also been investigated for context-sensitive rewriting. Up to now, only few transformation-based methods have been proposed and used to (specifically) prove termination of innermost CSR. Powerful and e cient techniques for proving (innermost) termination of (unrestricted) rewriting like the dependency pair framework have not been considered yet. In this work, we investigate the adaptation of the dependency pair framework to innermost CSR. We provide a suitable notion of innermost context-sensitive dependency pair and show how to extend and adapt the main notions which conform the framework (chain, termination problem, processor, etc.). Thanks to the innermost context-sensitive dependency pairs, we can now use powerful techniques for proving termination of innermost CSR. This is made clear by means of some benchmarks showing that our techniques dramatically improve over previously existing transformational techniques, thus establishing the new state-of-the-art in the area. We have implemented them as part of the termination tool MU-TERM.Alarcón Jiménez, B.; Lucas, S. (2011). Innermost Termination of Context-Sensitive Rewriting. http://hdl.handle.net/10251/1079

Applications and extensions of context-sensitive rewriting

[EN] Context-sensitive rewriting is a restriction of term rewriting which is obtained by imposing replacement restrictions on the arguments of function symbols. It has proven useful to analyze computational properties of programs written in sophisticated rewriting-based programming languages such asCafeOBJ, Haskell, Maude, OBJ*, etc. Also, a number of extensions(e.g., to conditional rewritingor constrained equational systems) and generalizations(e.g., controlled rewritingor forbidden patterns) of context-sensitive rewriting have been proposed. In this paper, we provide an overview of these applications and related issues. (C) 2021 Elsevier Inc. All rights reserved.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Applications and extensions of context-sensitive rewriting. Journal of Logical and Algebraic Methods in Programming. 121:1-33. https://doi.org/10.1016/j.jlamp.2021.10068013312

Function Calls at Frozen Positions in Termination of Context-Sensitive Rewriting

Context-sensitive rewriting (CSR) is a variant of rewriting where only selected arguments of function symbols can be rewritten. Consequently, the subterm positions of a term are classified as either active, i.e., positions of subterms that can be rewritten; or frozen, i.e., positions that cannot. Frozen positions can be used to denote subexpressions whose evaluation is delayed or just forbidden. A typical example is the if-then-else operator whose second and third arguments are not evaluated until the evaluation of the first argument yields either true or false. Imposing replacement restrictions can improve the termination behavior of rewriting-based computational systems. Termination of CSR has been investigated by several authors and a number of automatic tools are able to prove it. In this paper, we analyze how frozen subterms affect termination of CSR. This analysis helps us to improve our context-sensitive dependency pair (CS-DP) framework for automatically proving termination of CSR. We have implemented these improvements in our tool MU-TERM. The experiments show the power of the improvements in practice.Gutiérrez Gil, R.; Lucas Alba, S. (2015). Function Calls at Frozen Positions in Termination of Context-Sensitive Rewriting. http://hdl.handle.net/10251/5075

Equational logic and rewriting

International audienceIn this survey, we do not address higher order logics nor type theory, but rather restrict to first-order concepts. We focus on equational logic and its relation to rewriting logic and we consider their impact on automated deduction and programming languages

Innermost Termination of Context-Sensitive Rewriting

Innermost context-sensitive rewriting (CSR) has been proved useful for modeling the computational behavior of programs of algebraic languages like Maude. We adapt the Dependency Pairs Framework to innermost CSR since, up to now, only few transformation-based techniques have been proposed, thus, establishing the new state-of-the-art in the area.Alarcón Jiménez, B. (2008). Innermost Termination of Context-Sensitive Rewriting. http://hdl.handle.net/10251/13630Archivo delegad