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Maude: Specification and Programming in Rewriting Logic
, 2001
"... Maude is a highlevel language and a highperformance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and ..."
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Cited by 205 (64 self)
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Maude is a highlevel language and a highperformance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both userdefinable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and objectoriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude.
Membership Algebra as a Logical Framework for Equational Specification
, 1998
"... This paper proposes membership equational logica Horn logic in which the basic predicates are equations t = t 0 and membership assertions t : s stating that a term t belongs to a sort sas a logical framework in which a very wide range of total and partial equational specification formalisms ..."
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Cited by 172 (54 self)
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This paper proposes membership equational logica Horn logic in which the basic predicates are equations t = t 0 and membership assertions t : s stating that a term t belongs to a sort sas a logical framework in which a very wide range of total and partial equational specification formalisms can be naturally represented. Key features of this logic include: simplicity, liberality and equational character; generality and expressiveness in supporting subsorts, overloading, errors and partiality; and efficient implementability in systems such as Maude. The paper presents the basic properties of the logic and its models, and discusses in detail how many total and partial equational specification formalisms, including ordersorted algebra and partial membership equational logic, can be represented in it, as well as the practical benefits in terms of tool reusability that this opens up for other languages, including CASL.
Stratego: A Language for Program Transformation based on Rewriting Strategies  System Description of Stratego 0.5
 Rewriting Techniques and Applications (RTA’01), volume 2051 of Lecture Notes in Computer Science
, 2001
"... Introduction Program transformation is used in many areas of software engineering. Examples include compilation, optimization, synthesis, refactoring, migration, normalization and improvement [15]. Rewrite rules are a natural formalism for expressing single program transformations. However, using a ..."
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Cited by 161 (12 self)
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Introduction Program transformation is used in many areas of software engineering. Examples include compilation, optimization, synthesis, refactoring, migration, normalization and improvement [15]. Rewrite rules are a natural formalism for expressing single program transformations. However, using a standard strategy for normalizing a program with a set of rewrite rules is not adequate for implementing program transformation systems. It may be necessary to apply a rule only in some phase of a transformation, to apply rules in some order, or to apply a rule only to part of a program. These restrictions may be necessary to avoid nontermination or to choose a specific path in a nonconfluent rewrite system. Stratego is a language for the specification of program transformation systems based on the paradigm of rewriting strategies. It supports the separation of strategies from transformation rules, thus allowing careful control over the application of these rules. As a result of this sepa
Introducing OBJ
, 1993
"... This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OBJ3 is described in detail, with many examples. OBJ is a wide spectrum firstorder functional language that is rigorously based on ..."
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Cited by 138 (30 self)
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This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OBJ3 is described in detail, with many examples. OBJ is a wide spectrum firstorder functional language that is rigorously based on (order sorted) equational logic and parameterized programming, supporting a declarative style that facilitates verification and allows OBJ to be used as a theorem prover.
CAPSL Integrated Protocol Environment
 IN PROC. OF DARPA INFORMATION SURVIVABILITY CONFERENCE (DISCEX 2000), PP 207221, IEEE COMPUTER SOCIETY
, 2000
"... CAPSL, a Common Authentication Protocol Specification Language, is a highlevel language to support security analysis of cryptographic authentication and key distribution protocols. It is translated to CIL, an intermediate language expressing state transitions with termrewriting rules. Connectors a ..."
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Cited by 70 (7 self)
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CAPSL, a Common Authentication Protocol Specification Language, is a highlevel language to support security analysis of cryptographic authentication and key distribution protocols. It is translated to CIL, an intermediate language expressing state transitions with termrewriting rules. Connectors are being written to adapt CIL to supply input to different security analysis tools, including PVS for inductive verification and Maude for modelchecking.
Metalogical Frameworks
, 1992
"... In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the me ..."
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Cited by 58 (17 self)
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In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the metalogic of the object language being implemented. We also reason about the implementation itself, say to know it is correct; this is done in a programming logic. How do all these logics relate? This paper considers that question and more. We show that by taking the view that the metalogic is primary, these other parts are related in standard ways. The metalogic should be suitably rich so that the object logic can be presented as an abstract data type, and it must be suitably computational (or constructive) so that an instance of that type is an implementation. The data type abstractly encodes all that is relevant for metareasoning, i.e., not only the term constructing functions but also the...
Building Equational Proving Tools by Reflection in Rewriting Logic
 In Cafe: An IndustrialStrength Algebraic Formal Method
, 1998
"... This paper explains the design and use of two equational proving tools, namely an inductive theorem prover  to prove theorems about equational specifications with an initial algebra semantics  and a ChurchRosser checkerto check whether such specifications satisfy the ChurchRosser property. ..."
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Cited by 40 (20 self)
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This paper explains the design and use of two equational proving tools, namely an inductive theorem prover  to prove theorems about equational specifications with an initial algebra semantics  and a ChurchRosser checkerto check whether such specifications satisfy the ChurchRosser property. These tools can be used to prove properties of ordersorted equational specifications in Cafe [11] and of membership equational logic specifications in Maude [7, 6]. The tools have been written entirely in Maude and are in fact executable specifications in rewriting logic of the formal inference systems that they implement.
Process and Term Tile Logic
, 1998
"... In a similar way as 2categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also sideeffects and rewriting synchronization are considered. Since rewriting logic is the semantic basis o ..."
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Cited by 34 (25 self)
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In a similar way as 2categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also sideeffects and rewriting synchronization are considered. Since rewriting logic is the semantic basis of several language implementation efforts, it is useful to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. We extend the results of earlier work by two of the authors, focusing on some interesting cases where the mathematical structures representing configurations (i.e., states) and effects (i.e., observable actions) are very similar, in the sense that they have in common some auxiliary structure (e.g., for tupling, projecting, etc.). In particular, we give in full detail the descriptions of two such cases where (net) processlike and usual term structures are employed. Corresponding to these two cases, we introduce two ca...
Research Directions in Rewriting Logic
, 1998
"... Rewriting logic expresses an essential equivalence between logic and computation. System states are in bijective correspondence with formulas, and concurrent computations are in bijective correspondence with proofs. Given this equivalence between computation and logic, a rewriting logic axiom of the ..."
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Cited by 32 (12 self)
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Rewriting logic expresses an essential equivalence between logic and computation. System states are in bijective correspondence with formulas, and concurrent computations are in bijective correspondence with proofs. Given this equivalence between computation and logic, a rewriting logic axiom of the form t \Gamma! t 0 has two readings. Computationally, it means that a fragment of a system 's state that is an instance of the pattern t can change to the corresponding instance of t 0 concurrently with any other state changes; logically, it just means that we can derive the formula t 0 from the formula t. Rewriting logic is entirely neutral about the structure and properties of the formulas/states t. They are entirely userdefinable as an algebraic data type satisfying certain equational axioms. Because of this ecumenical neutrality, rewriting logic has, from a logical viewpoint, good properties as a logical framework, in which many other logics can be naturally represented. And, computationally, it has also good properties as a semantic framework, in which many different system styles and models of concurrent computation and many different languages can be naturally expressed without any distorting encodings. The goal of this paper is to provide a relatively gentle introduction to rewriting logic, and to paint in broad strokes the main research directions that, since its introduction in 1990, have been pursued by a growing number of researchers in Europe, the US, and Japan. Key theoretical developments, as well as the main current applications of rewriting logic as a logical and semantic framework, and the work on formal reasoning to prove properties of specifications are surveyed.
A Survey of Rewriting Strategies in Program Transformation Systems
 In Workshop on Reduction Strategies in Rewriting and Programming (WRS’01), volume 57 of Electronic Notes in Theoretical Computer Science
, 2001
"... Program transformation is used in a wide range of applications including compiler construction, optimization, program synthesis, refactoring, software renovation, and reverse engineering. Complex program transformations are achieved through a number of consecutive modifications of a program. Transfo ..."
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Cited by 28 (1 self)
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Program transformation is used in a wide range of applications including compiler construction, optimization, program synthesis, refactoring, software renovation, and reverse engineering. Complex program transformations are achieved through a number of consecutive modifications of a program. Transformation rules define basic modifications. A transformation strategy is an algorithm for choosing a path in the rewrite relation induced by a set of rules. This paper surveys the support for the definition of strategies in program transformation systems. After a discussion of kinds of program transformation and choices in program representation, the basic elements of a strategy system are discussed and the choices in the design of a strategy language are considered. Several styles of strategy systems as provided in existing languages are then analyzed.