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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 ..."
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Cited by 31 (16 self)
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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
Matching Power
 Proceedings of RTA’2001, Lecture Notes in Computer Science, Utrecht (The Netherlands
, 2001
"... www.loria.fr/{~cirstea,~ckirchne,~lliquori} Abstract. In this paper we give a simple and uniform presentation of the rewriting calculus, also called Rho Calculus. In addition to its simplicity, this formulation explicitly allows us to encode complex structures such as lists, sets, and objects. We pr ..."
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Cited by 30 (20 self)
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www.loria.fr/{~cirstea,~ckirchne,~lliquori} Abstract. In this paper we give a simple and uniform presentation of the rewriting calculus, also called Rho Calculus. In addition to its simplicity, this formulation explicitly allows us to encode complex structures such as lists, sets, and objects. We provide extensive examples of the calculus, and we focus on its ability to represent some object oriented calculi, namely the Lambda Calculus of Objects of Fisher, Honsell, and Mitchell, and the Object Calculus of Abadi and Cardelli. Furthermore, the calculus allows us to get object oriented constructions unreachable in other calculi. In summa, we intend to show that because of its matching ability, the Rho Calculus represents a lingua franca to naturally encode many paradigms of computations. This enlightens the capabilities of the rewriting calculus based language ELAN to be used as a logical as well as powerful semantical framework. 1
Rewriting calculus with(out) types
 Proceedings of the fourth workshop on rewriting logic and applications
, 2002
"... The last few years have seen the development of a new calculus which can be considered as an outcome of the last decade of various researches on (higher order) term rewriting systems, and lambda calculi. In the Rewriting Calculus (or Rho Calculus, ρCal), algebraic rules are considered as sophisticat ..."
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Cited by 22 (13 self)
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The last few years have seen the development of a new calculus which can be considered as an outcome of the last decade of various researches on (higher order) term rewriting systems, and lambda calculi. In the Rewriting Calculus (or Rho Calculus, ρCal), algebraic rules are considered as sophisticated forms of “lambda terms with patterns”, and rule applications as lambda applications with pattern matching facilities. The calculus can be customized to work modulo sophisticated theories, like commutativity, associativity, associativitycommutativity, etc. This allows us to encode complex structures such as list, sets, and more generally objects. The calculus can either be presented “à la Curry ” or “à la Church ” without sacrificing readability and without complicating too much the metatheory. Many static type systems can be easily pluggedin on top of the calculus in the spirit of the rich typeoriented literature. The Rewriting Calculus could represent a lingua franca to encode many paradigms of computations together with a formal basis used to build powerful theorem provers based on lambda calculus and efficient rewriting, and a step towards new proof engines based on the CurryHoward isomorphism. 1
Parallelizing the Phylogeny Problem
 In Supercomputing '95
, 1994
"... The problem of determining the evolutionary history of species in the form of phylogenetic trees is known as the phylogeny problem. We present a parallelization of the character compatibility method for solving the phylogeny problem. Abstractly, the algorithm searches through all subsets of characte ..."
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Cited by 8 (3 self)
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The problem of determining the evolutionary history of species in the form of phylogenetic trees is known as the phylogeny problem. We present a parallelization of the character compatibility method for solving the phylogeny problem. Abstractly, the algorithm searches through all subsets of characters, which may be traits like opposable thumbs or DNA sequence values, looking for a maximal consistent subset. The notion of consistency in this case is the existence of a particular kind of phylogenetic tree called a perfect phylogeny tree. The two challenges to achieving an efficient implementation are load balancing and efficient sharing of information to enable pruning. In both cases, there is a tradeoff between communication overhead and the quality of the solution. For load balancing we use a distributed task queue, which has imperfect load information but avoids centralization bottlenecks. To prune the search space, we use the following property: If a perfect phylogeny tree does not ...
A Term Equality Problem Equivalent to Graph Isomorphism
 Information Processing Letters
, 1994
"... We demonstrate that deciding if two terms containing otherwise uninterpreted associative, commutative, and associativecommutative function symbols and commutative variablebinding operators are equal is polynomially equivalent to determining if two graphs are isomorphic. The reductions we use provi ..."
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Cited by 6 (1 self)
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We demonstrate that deciding if two terms containing otherwise uninterpreted associative, commutative, and associativecommutative function symbols and commutative variablebinding operators are equal is polynomially equivalent to determining if two graphs are isomorphic. The reductions we use provide insight into this result and suggest polynomial time special cases. Key Words: Automatic Theorem Proving, Computational Complexity, Equality Reasoning, Graph Isomorphism. 1 Introduction Decision procedures for equality play an important role in automated theorem proving. We examine the complexity of a specific problem in equality reasoning: determining if two terms, which possibly contain associative, commutative, and associativecommutative (AC) functions and commutative variablebinding operators (that is, adjacent operators may be swapped) are equal. We prove that this problem is polynomially equivalent to deciding if two graphs are isomorphic. The exact complexity of graph isomorphi...
Combining Computer Algebra and Rule Based Reasoning
 Integrating Symbolic Mathematical Computation and Arti Intelligence. Proceedings of AISMC2, volume 958 of LNCS
, 1995
"... : We present extended term rewriting systems as a means to describe a simplification relation for an equational specification with a builtin domain of external objects. Even if the extended term rewriting system is canonical, the combined relation including builtin computations of `ground term ..."
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Cited by 4 (2 self)
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: We present extended term rewriting systems as a means to describe a simplification relation for an equational specification with a builtin domain of external objects. Even if the extended term rewriting system is canonical, the combined relation including builtin computations of `ground terms' needs neither be terminating nor confluent. We investigate restrictions on the extended term rewriting systems and the builtin domains under which these properties hold. A very important property of extended term rewriting systems is decomposition freedom. Among others decomposition free extended term rewriting systems allow for efficient simplifications. Some interesting algebraic applications of canonical simplification relations are presented. 1 Introduction There has always been mutual interest in the areas of computer algebra and term rewriting systems as can be seen for example from the calls of papers of the main conferences in the two areas (ISSAC and RTA resp.) which each...
Preserving Confluence for Rewrite Systems with Builtin Operations
 In Workshop on Conditional and (Typed) Term Rewriting Systems
, 1994
"... . We consider combinations of term rewriting with builtin operations which compute objects of some external domain from ground terms. Combining a canonical term rewriting system with a computation relation does in general not lead to a canonical simplification relation. We show how a canonical simp ..."
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Cited by 2 (2 self)
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. We consider combinations of term rewriting with builtin operations which compute objects of some external domain from ground terms. Combining a canonical term rewriting system with a computation relation does in general not lead to a canonical simplification relation. We show how a canonical simplification system can be constructed for such rewrite systems with builtin operations. Decomposition free simplification systems never need to look at the internal structure of external objects and thus a previous computation never needs to be undone. For some interesting equational specifications the construction of decomposition free canonical simplification systems succeeds. Our construction of canonical simplification systems relies on simulating combined rewriting and computing by pure term rewriting. This allows us to use the wealth of all rewrite techniques and tools to investigate and manipulate these structures. 1 Introduction Canonical term rewriting systems are an elegant and po...
Parallelizing the Phylogeny Problem
, 1994
"... The problem of determining the evolutionary history of species in the form of phylogenetic trees is known as the phylogeny problem. We present a parallelization of the character compatibility method for solving the phylogeny problem. Abstractly, the algorithm searches through all subsets of char ..."
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The problem of determining the evolutionary history of species in the form of phylogenetic trees is known as the phylogeny problem. We present a parallelization of the character compatibility method for solving the phylogeny problem. Abstractly, the algorithm searches through all subsets of characters, which may be traits like opposable thumbs or DNA sequence values, looking for a maximal consistent subset. The notion of consistency in this case is the existence of a particular kind of phylogenetic tree called a perfect phylogeny tree. The two challenges to achieving an efficient implementation are load balancing and efficient sharing of information to enable pruning. In both cases, there is a tradeoff between communication overhead and the quality of the solution. For load balancing we use a distributed task queue, which has imperfect load information but avoids centralization bottlenecks. For sharing pruning information, we use a distributed trie, which also avoids centralization but maintains incomplete information. We evaluate This work was performed primarily at the University of California, Berkeley, supported in part by the grants given below. y This work was supported in part by the Advanced Research Projects Agency of the Department of Defense monitored by the Office of Naval Research under contract DABT6392C0026, by the Department of Energy grant DEFG0394ER25206, by the National Science Foundation as a Research Initiation Award (number CCR9210260), and as an Infrastructure Grant (number CDA8722788), The information presented here does not necessarily reflect the position or the policy of the Government and no official endorsement should be inferred. 1 several implementations of the trie, the best of which achieves speedups of 50 on...