Results 1  10
of
14
Rewrite Strategies in the Rewriting Calculus
 WRS 2003
, 2003
"... This paper presents an overview on the use of the rewriting calculus to express rewrite strategies. We motivate first the use of rewrite strategies by examples in the ELAN language. We then show how this has been modeled in the initial version of the rewriting calculus and how the matching power of ..."
Abstract

Cited by 18 (7 self)
 Add to MetaCart
This paper presents an overview on the use of the rewriting calculus to express rewrite strategies. We motivate first the use of rewrite strategies by examples in the ELAN language. We then show how this has been modeled in the initial version of the rewriting calculus and how the matching power of this framework facilitates the representation of powerful strategies.
A rewriting calculus for cyclic higherorder term graphs
 in "2nd International Workshop on Term Graph Rewriting  TERMGRAPH’2004
, 2004
"... graphs ..."
A DomainSpecific Language for Incremental and Modular Design of LargeScale VerifiablySafe Flow Networks (Preliminary Report)
"... We define a domainspecific language (DSL) to inductively assemble flow networks from small networks or modules to produce arbitrarily large ones, with interchangeable functionallyequivalent parts. Our small networks or modules are “small ” only as the building blocks in this inductive definition ( ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We define a domainspecific language (DSL) to inductively assemble flow networks from small networks or modules to produce arbitrarily large ones, with interchangeable functionallyequivalent parts. Our small networks or modules are “small ” only as the building blocks in this inductive definition (there is no limit on their size). Associated with our DSL is a type theory, a system of formal annotations to express desirable properties of flow networks together with rules that enforce them as invariants across their interfaces, i.e., the rules guarantee the properties are preserved as we build larger networks from smaller ones. A prerequisite for a type theory is a formal semantics, i.e., a rigorous definition of the entities that qualify as feasible flows through the networks, possibly restricted to satisfy additional efficiency or safety requirements. This can be carried out in one of two ways, as a denotational semantics or as an operational (or reduction) semantics; we choose the first in preference to the second, partly to avoid exponentialgrowth rewriting in the operational approach. We set up a typing system and prove its soundness for our DSL. 1
Matching modulo superdevelopments application to secondorder matching
 In 13th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning  LPAR’06
, 2006
"... Abstract. To perform higherorder matching, we need to decide the βηequivalence on λterms. The first way to do it is to use simply typed λcalculus and this is the usual framework where higherorder matching is performed. Another approach consists in deciding a restricted equivalence based on fini ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Abstract. To perform higherorder matching, we need to decide the βηequivalence on λterms. The first way to do it is to use simply typed λcalculus and this is the usual framework where higherorder matching is performed. Another approach consists in deciding a restricted equivalence based on finite superdevelopments. We consider higherorder matching modulo this equivalence over untyped λterms for which we propose a terminating, sound and complete matching algorithm. This is in particular of interest since all secondorder βmatches are matches modulo superdevelopments. We further propose a restriction to secondorder matching that gives exactly all secondorder matches.
From functional programs to interaction nets via the Rewriting Calculus
 WRS 2006 PRELIMINARY VERSION
, 2006
"... We use the ρcalculus as an intermediate language to compile functional languages with patternmatching features, and give an interaction net encoding of the ρterms arising from the compilation. This encoding gives rise to new strategies of evaluation, where patternmatching and ‘traditional ’ βre ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We use the ρcalculus as an intermediate language to compile functional languages with patternmatching features, and give an interaction net encoding of the ρterms arising from the compilation. This encoding gives rise to new strategies of evaluation, where patternmatching and ‘traditional ’ βreduction can proceed in parallel without overheads.
Toward a General Theory of Names, Binding and Scope
, 2005
"... Highlevel formalisms for reasoning about names and binding such as de Bruijn indices, various flavors of higherorder abstract syntax, the Theory of Contexts, and nominal abstract syntax address only one relatively restrictive form of scoping: namely, unary lexical scoping, in which the scope of a ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Highlevel formalisms for reasoning about names and binding such as de Bruijn indices, various flavors of higherorder abstract syntax, the Theory of Contexts, and nominal abstract syntax address only one relatively restrictive form of scoping: namely, unary lexical scoping, in which the scope of a (single) bound name is a subtree of the abstract syntax tree (possibly with other subtrees removed due to shadowing). Many languages exhibit binding or renaming structure that does not fit this mold. Examples include binding transitions in the #calculus; unique identifiers in contexts, memory heaps, and XML documents; declaration scoping in modules and namespaces; anonymous identifiers in automata, type schemes, and Horn clauses; and pattern matching and mutual recursion constructs in functional languages. In these cases, it appears necessary to either rearrange the abstract syntax so that lexical scoping can be used, or revert to firstorder techniques. The purpose
The simplytyped pure pattern type system ensures strong normalization
 Proc. of TCS’04
, 2004
"... Abstract Pure Pattern Type Systems (P 2 T S) combine in a unified setting the capabilities of rewriting and λcalculus. Their type systems, adapted from Barendregt’s λcube, are especially interesting from a logical point of view. Strong normalization, an essential property for logical soundness, ha ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract Pure Pattern Type Systems (P 2 T S) combine in a unified setting the capabilities of rewriting and λcalculus. Their type systems, adapted from Barendregt’s λcube, are especially interesting from a logical point of view. Strong normalization, an essential property for logical soundness, had only been conjectured so far: in this paper, we give a positive answer for the simplytyped system. The proof is based on a translation of terms and types from P 2 T S into the λcalculus. First, we deal with untyped terms, ensuring that reductions are faithfully mimicked in the λcalculus. For this, we rely on an original encoding of the pattern matching capability of P 2 T S into the λcalculus. Then we show how to translate types: the expressive power of System Fω is needed in order to fully reproduce the original typing judgments of P 2 T S. We prove that the encoding is correct with respect to reductions and typing, and we conclude with the strong normalization of simplytyped P 2 T S terms. 1
The graph rewriting calculus : confluence and expressiveness
 in "9th Italian conference on Italian Conference on Theoretical Computer Science  ICTCS 2005
"... Abstract. Introduced at the end of the nineties, the Rewriting Calculus (ρcalculus, for short) is a simple calculus that uniformly integrates termrewriting and λcalculus. The ρgcalculus has been recently introduced as an extension of the ρcalculus, handling structures with cycles and sharing. Th ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. Introduced at the end of the nineties, the Rewriting Calculus (ρcalculus, for short) is a simple calculus that uniformly integrates termrewriting and λcalculus. The ρgcalculus has been recently introduced as an extension of the ρcalculus, handling structures with cycles and sharing. The calculus over terms is naturally generalized by using unification constraints in addition to the standard ρcalculus matching constraints. This leads to a termgraph representation in an equational style where terms consist of unordered lists of equations. In this paper we show that the (linear) ρgcalculus is confluent. The proof of this result is quite elaborated, due to the nontermination of the system and to the fact that we work on equivalence classes of terms. We also show that the ρgcalculus can be seen as a generalization of firstorder termgraph rewriting, in the sense that for any termgraph rewrite step a corresponding sequence of rewritings can be found in the ρgcalculus. 1
Superdeduction at Work
"... Abstract Superdeduction is a systematic way to extend a deduction system like the sequent calculus by new deduction rules computed from the user theory. We show how this could be done in a systematic, correct and complete way. We prove in detail the strong normalization of a proof term language that ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract Superdeduction is a systematic way to extend a deduction system like the sequent calculus by new deduction rules computed from the user theory. We show how this could be done in a systematic, correct and complete way. We prove in detail the strong normalization of a proof term language that models appropriately superdeduction. We finaly examplify on several examples, including equality and noetherian induction, the usefulness of this approach which is implemented in the lemuridæ system, written in TOM. 1