Results 1 
6 of
6
ELAN from a rewriting logic point of view
 Theoretical Computer Science
, 2002
"... ELAN implements computational systems, a concept that combines two first class entities: rewrite rules and rewriting strategies. ELAN can be used either as a logical framework or to describe and execute deterministic as well as nondeterministic rule based processes. With the general goal to make pr ..."
Abstract

Cited by 54 (5 self)
 Add to MetaCart
ELAN implements computational systems, a concept that combines two first class entities: rewrite rules and rewriting strategies. ELAN can be used either as a logical framework or to describe and execute deterministic as well as nondeterministic rule based processes. With the general goal to make precise a rewriting logic based semantics of ELAN, this paper has three contributions: a presentation of the concepts of rules and strategies available in ELAN, an expression of rewrite rules with matching conditions in conditional rewriting logic, and finally an enrichment mechanism of a rewrite theory into a strategy theory in conditional rewriting logic.
The Rho Cube
 In Proc. of FOSSACS, volume 2030 of LNCS
, 2001
"... www.loria.fr/{~cirstea,~ckirchne,~lliquori} Abstract. The rewriting calculus, or Rho Calculus (ρCal), is a simple calculus that uniformly integrates abstraction on patterns and nondeterminism. Therefore, it fully integrates rewriting and λcalculus. The original presentation of the calculus was unty ..."
Abstract

Cited by 32 (16 self)
 Add to MetaCart
www.loria.fr/{~cirstea,~ckirchne,~lliquori} Abstract. The rewriting calculus, or Rho Calculus (ρCal), is a simple calculus that uniformly integrates abstraction on patterns and nondeterminism. Therefore, it fully integrates rewriting and λcalculus. The original presentation of the calculus was untyped. In this paper we present a uniform way to decorate the terms of the calculus with types. This gives raise to a new presentation à la Church, together with nine (8+1) type systems which can be placed in a ρcube that extends the λcube of Barendregt. Due to the matching capabilities of the calculus, the type systems use only one abstraction mechanism and therefore gives an original answer to the identification of the standard “λ ” and “Π” abstractors. As a consequence, this brings matching and rewriting as the first class concepts of the Rhoversions of the Logical Framework (LF) of Harper
Rewriting calculus with fixpoints: Untyped and firstorder systems
 In Postproceedings of TYPES, Lecture Notes in Computer Science
, 2003
"... Abstract The rewriting calculus, also called ρcalculus, is a framework embedding λcalculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higherorder mechanisms of the λcalculus and the pattern matching facilities of the rewriting are then bot ..."
Abstract

Cited by 26 (10 self)
 Add to MetaCart
Abstract The rewriting calculus, also called ρcalculus, is a framework embedding λcalculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higherorder mechanisms of the λcalculus and the pattern matching facilities of the rewriting are then both available at the same level. Many type systems for the λcalculus can be generalized to the ρcalculus: in this paper, we study extensively a firstorder ρcalculus à la Church, called ρ stk The type system of ρ stk � allows one to type (object oriented flavored) fixpoints, leading to an expressive and safe calculus. In particular, using pattern matching, one can encode and typecheck term rewriting systems in a natural and automatic way. Therefore, we can see our framework as a starting point for the theoretical basis of a powerful typed rewritingbased language.
The rewriting calculus  Part II
 Journal of the Interest Group in Pure and Applied Logics 9(3), 427498. main.tex; 18/09/2002; 20:09; p.29 30 Quang
, 2001
"... The calculus integrates in a uniform and simple setting rstorder rewriting, calculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T . We have seen in the rst part of this work ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
The calculus integrates in a uniform and simple setting rstorder rewriting, calculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T . We have seen in the rst part of this work the motivations, denitions and basic properties of the calculus. This second part is rst devoted to the use of the calculus for encoding a (conditional) rewrite relation. To this end we extend the calculus with a rst operator whose purpose is to detect rule application failure. This extension allows us to express recursively rule application and therefore to encode strategy based rewriting processes. We then use this extended calculus to give an operational semantics to ELAN programs. We conclude with an overview of ongoing and future works on calculus. Keywords: rewriting, strategy, nondeterminism, matching, rewritingcalculus, lambdacalculus, rule based language. 1 Intro...
unknown title
"... The ρcalculus integrates in a uniform and simple setting firstorder rewriting, λcalculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T. We have seen in the first part of this ..."
Abstract
 Add to MetaCart
The ρcalculus integrates in a uniform and simple setting firstorder rewriting, λcalculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T. We have seen in the first part of this work the motivations, definitions and basic properties of the ρcalculus. This second part is first devoted to the use of an extension of the ρcalculus for encoding a (conditional) rewrite relation. This extension is based on the first operator whose purpose is to detect rule application failure. It allows us to express recursively rule application and therefore to encode strategy based rewriting processes. We then use this extended calculus to give an operational semantics to ELAN programs. We conclude with an overview of ongoing and future works on ρcalculus.
unknown title
"... The ρcalculus integrates in a uniform and simple setting firstorder rewriting, λcalculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T. We have seen in the first part of this ..."
Abstract
 Add to MetaCart
The ρcalculus integrates in a uniform and simple setting firstorder rewriting, λcalculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T. We have seen in the first part of this work the motivations, definitions and basic properties of the ρcalculus. This second part is first devoted to the use of the ρcalculus for encoding a (conditional) rewrite relation. To this end we extend the calculus with a first operator whose purpose is to detect rule application failure. This extension allows us to express recursively rule application and therefore to encode strategy based rewriting processes. We then use this extended calculus to give an operational semantics to ELAN programs. We conclude with an overview of ongoing and future works on ρcalculus.