12 research outputs found
Extending Context-Sensitivity in Term Rewriting
We propose a generalized version of context-sensitivity in term rewriting
based on the notion of "forbidden patterns". The basic idea is that a rewrite
step should be forbidden if the redex to be contracted has a certain shape and
appears in a certain context. This shape and context is expressed through
forbidden patterns. In particular we analyze the relationships among this novel
approach and the commonly used notion of context-sensitivity in term rewriting,
as well as the feasibility of rewriting with forbidden patterns from a
computational point of view. The latter feasibility is characterized by
demanding that restricting a rewrite relation yields an improved termination
behaviour while still being powerful enough to compute meaningful results.
Sufficient criteria for both kinds of properties in certain classes of rewrite
systems with forbidden patterns are presented
Loops under Strategies ... Continued
While there are many approaches for automatically proving termination of term
rewrite systems, up to now there exist only few techniques to disprove their
termination automatically. Almost all of these techniques try to find loops,
where the existence of a loop implies non-termination of the rewrite system.
However, most programming languages use specific evaluation strategies, whereas
loop detection techniques usually do not take strategies into account. So even
if a rewrite system has a loop, it may still be terminating under certain
strategies.
Therefore, our goal is to develop decision procedures which can determine
whether a given loop is also a loop under the respective evaluation strategy.
In earlier work, such procedures were presented for the strategies of
innermost, outermost, and context-sensitive evaluation. In the current paper,
we build upon this work and develop such decision procedures for important
strategies like leftmost-innermost, leftmost-outermost,
(max-)parallel-innermost, (max-)parallel-outermost, and forbidden patterns
(which generalize innermost, outermost, and context-sensitive strategies). In
this way, we obtain the first approach to disprove termination under these
strategies automatically.Comment: In Proceedings IWS 2010, arXiv:1012.533
Termination of Rewriting with and Automated Synthesis of Forbidden Patterns
We introduce a modified version of the well-known dependency pair framework
that is suitable for the termination analysis of rewriting under forbidden
pattern restrictions. By attaching contexts to dependency pairs that represent
the calling contexts of the corresponding recursive function calls, it is
possible to incorporate the forbidden pattern restrictions in the (adapted)
notion of dependency pair chains, thus yielding a sound and complete approach
to termination analysis. Building upon this contextual dependency pair
framework we introduce a dependency pair processor that simplifies problems by
analyzing the contextual information of the dependency pairs. Moreover, we show
how this processor can be used to synthesize forbidden patterns suitable for a
given term rewriting system on-the-fly during the termination analysis.Comment: In Proceedings IWS 2010, arXiv:1012.533
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
Methods for Proving Termination of Rewriting-based Programming Languages by Transformation
AbstractDespite the remarkable development of the theory of termination of rewriting, its application to high-level (rewriting-based) programming languages is far from being optimal. This is due to the need for features such as conditional equations and rules, types and subtypes, (possibly programmable) strategies for controlling the execution, matching modulo axioms, and so on, that are used in many programs and tend to place such programs outside the scope of current termination tools. The operational meaning of such features is often formalized in a proof theoretic manner by means of an inference system rather than just by a rewriting relation. The corresponding termination notions can also differ from the standard ones. During the last years we have introduced and implemented different notions and transformation techniques which have been proved useful for proving and disproving termination of such programs by using existing tools for proving termination of (variants of) rewriting. In this paper we provide an overview of our main contributions
On-demand Evaluation by Program Transformation1 1Work partially supported by CICYT TIC2001-2705-C03-01 and MCYT grants HA2001-0059 and HU2001-0019.
AbstractStrategy annotations are used in eager programming languages (e.g., OBJ2, OBJ3, CafeOBJ, and Maude) for improving efficiency and/or reducing the risk of nontermination. Syntactically, they are given either as lists of natural numbers or as lists of integers associated to function symbols whose (absolute) values refer to the arguments of the corresponding symbol. A positive index forces the evaluation of an argument whereas a negative index means “evaluation on-demand”. Recently, we have introduced a formal description of the operational meaning of such on-demand strategy annotations which improves previous formalizations that were lacking satisfactory computational properties. In this paper, we introduce an automatic, semantics-preserving program transformation which produces a program (without negative annotations) which can be then correctly executed by typical OBJ interpreters. Moreover, to demonstrate the practicality of our ideas, the program transformation has been implemented (in Haskell) and we compare the evaluation of transformed programs with the original ones on a set of representative benchmarks
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
Context-Sensitive Dependency Pairs Framework
We show how to develop a dependency pair framework for proving termination of context-sensitive rewriting.Gutiérrez Gil, R. (2008). Context-Sensitive Dependency Pairs Framework. http://hdl.handle.net/10251/13625Archivo delegad
Towards a Framework for Proving Termination of Maude Programs
Maude es un lenguaje de programación declarativo basado en la lógica de reescritura
que incorpora muchas características que lo hacen muy potente. Sin
embargo, a la hora de probar ciertas propiedades computacionales esto conlleva
dificultades. La tarea de probar la terminación de sistemas de reesctritura
es de hecho bastante dura, pero aplicada a lenguajes de programación reales
se concierte en más complicada debido a estas características inherentes. Esto
provoca que métodos para probar la terminación de este tipo de programas
requieran técnicas específicas y un análisis cuidadoso. Varios trabajos han intentado
probar terminación de (un subconjunto de) programas Maude. Sin
embargo, todos ellos siguen una aproximación transformacional, donde el programa
original es trasformado hasta alcanzar un sistema de reescritura capaz
de ser manejado con las técnicas y herramientas de terminación existentes. En
la práctica, el hecho de transformar los sistemas originales suele complicar la
demostración de la terminación ya que esto introduce nuevos símbolos y reglas
en el sistema. En esta tesis, llevamos a cabo el problema de probar terminación
de (un subconjunto de) programas Maude mediante métodos directos.
Por un lado, nos centramos en la estrategia de Maude. Maude es un lenguaje
impaciente donde los argumentos de una función son evaluados siempre
antes de la aplicación de la función que los usa. Esta estrategia (conocida como
llamada por valor) puede provocar la no terminación si los programas no
están escritos cuidadosamente. Por esta razón, Maude (en concreto) incorpora
mecanismos para controlar la ejecución de programas como las anotaciones
sintácticas que están asociadas a los argumentos de los símbolos. En reescritura,
esta estrategia sería conocida como reescritura sensible al contexto
innermost (RSCI).
Por otro lado, Maude también incorpora la posibilidad de declarar atributos.Alarcón Jiménez, B. (2011). Towards a Framework for Proving Termination of Maude Programs [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11003Palanci