M. Clavel and J. Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July  Home/Search   Document Details and Download   Summary   Related Articles   Check

....efforts (CafeOBJ [12] ELAN [1] Maude [9] In particular, Maude supports executable specifications in rewriting logic and is efficiently implemented. Maude is also equipped with the important feature of meta control mechanism on computations through user definable internal execution strategies [10,8]. Since 2 categories are one of the most natural frameworks for interpreting the semantics of a rewriting system, a conservative mapping from double categories to 2 categories can provide a good theoretical basis for the implementation of tile systems. The comparison between tl and rl is carried ....

M. Clavel and J. Meseguer, Internal strategies in a reflective logic, in Proc. CADE-14 Workshop on Strategies in Automated Deduction, 1--12 (1997).

....type inside the logic on which a very open and extensible module algebra can be defined. ffl Internal strategies: thanks to reflection, execution strategies can be expressed inside rewriting logic, where they are formally defined and executed by rewrite rules that operate on metalevel entities [9, 10]. ffl Formal environments: using reflection, it becomes very easy to specify and build formal environments, providing theorem proving and formal analysis support for a logically based specification or programming language [10] 6 Categories Everywhere The theory of general logics [39] extends ....

.... and executed by rewrite rules that operate on metalevel entities [9, 10] ffl Formal environments: using reflection, it becomes very easy to specify and build formal environments, providing theorem proving and formal analysis support for a logically based specification or programming language [10]. 6 Categories Everywhere The theory of general logics [39] extends the theory of institutions [18] and is related to other notions proposed in the literature, including [2, 47, 11, 48, 37, 45, 14, 13, 21] see [42] for a discussion of work in this area) All these approaches, beginning with ....

Manuel G. Clavel and Jos'e Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July 1997), pages 1--12, 1997.

....permuting interfaces) As a result, the mapping becomes effective provided that the rewriting engine is able to filter rewriting computations . To achieve this filtering, we make use of the reflective capabilities [13, 14, 10] of the Maude language [12, 11] to define suitable internal strategies [15], which allow the user to control the computation and to collect the possible results [6] In this paper we give a survey of some basic internal strategies, and we show how they can be applied to obtain executable specifications for a rich class of process calculi. To give an example of the ....

....of a basic reflective kernel, that is some basic functionality provided by the universal theory U . The Maude implementation supports metaprogramming of strategies via a module transforming operation which maps a module T to another module META LEVEL[T] that is a definitional extension of U [15]. For simplicity, we adopt here a simpler version of the metalevel. In particular the following operations are defined: meta reduce(t) takes the metarepresentation t of a term t and evaluates as follows: a) first t is converted to the term it represents; b) then this term is fully reduced ....

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M. Clavel and J. Meseguer. Internal Strategies in a Reflective Logic. In: B. Gramlich, and H. Kirchner, Eds., Proc. of the CADE-14 Workshop on Strategies in Automated Deduction, Townsville, Australia, 1--12 (1997).

....and in its translation. This could be summarized by saying that the rewriting engine must be able to filter rewriting computations . To overcome this difficulty, we make use of the reflective capabilities [17, 18] of the rewriting logic language Maude [15] to define suitable internal strategies [19], which help the user control the computation and collect (some of) the possible (correct) results. The key point is that the internal strategies defined here for simulating tile systems can also be thought of as general meta strategies for rewriting systems in general. We have experimented with ....

....basis of several language implementation efforts [7, 30, 15] In particular, the language Maude [15, 52] developed at SRI International, is based on rewriting logic and is efficiently implemented. Maude comes also equipped with the important feature of userdefinable internal execution strategies [19] which allow the meta control of rewriting computations. This is very important because a correct embedding of double categories into 2 categories heavily depends on the execution of suitable (internal) rewriting strategies. To build a bridge from tiles to ordinary 2 cells we make use of a recent ....

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M. Clavel, and J. Meseguer. Internal Strategies in a Reflective Logic. In: B. Gramlich, and H. Kirchner, Eds., Proc. of the CADE-14 Workshop on Strategies in Automated Deduction, Townsville, Australia. 1997. pp 1--12.

....only in correct tile computations. Indeed, we need suitable meta strategies to control the possible nondeterminism contained in a tile specification and also in its translation. To overcome this difficulty, we make use of the reflective capabilities of Maude to define suitable internal strategies [14,12,13,10], that can help the user to control the rewritings and to collect (some of) the possible (correct) results. The key point is that the internal strategies defined here for simulating tile systems can also be thought of as general meta strategies for nondeterministic rewriting systems. We have ....

M.G. Clavel, and J. Meseguer. Internal Strategies in a Reflective Logic. In: B. Gramlich, and H. Kirchner, Eds., Proc. of the CADE-14 Workshop on Strategies in Automated Deduction, Townsville, Australia, 1--12 (1997).

....tupling, projecting or permuting interfaces) As a result, the mapping becomes effective provided that the rewriting engine is able to filter computations . To achieve this, in [5] we make use of the reflective capabilities [11, 8] of the Maude language [9] to define suitable internal strategies [10, 12], which allow the user to control the computation and to collect the possible results. In this paper we give a survey of some basic internal strategies, and we show how they can be applied to obtain executable specifications for a rich class of process calculi. To give an example of the ....

....of a basic reflective kernel, that is some basic functionality provided by the universal theory U . The Maude implementation supports metaprogramming of strategies via a module transforming operation which maps a module T to another module META LEVEL[T] that is a definitional extension of U [12]. For simplicity, we adopt here a simpler version of the metalevel. In particular, the following operations are defined: meta reduce(t) and meta apply(t,l,n) meta reduce(t) takes the metarepresentation t of a term t and evaluates as follows: a) t is converted to the term it represents; b) this ....

M. Clavel and J. Meseguer, Internal Strategies in a Reflective Logic, in Proc. of the CADE-14 Workshop on Strategies in Automated Deduction, 1--12 (1997).

....substitution oe. As the universal theory U that it implements in a built in fashion, META LEVEL can also support a reflective tower with an arbitrary number of levels of reflection. Reflection can be exploited in many useful ways. One important area of application is internal rewriting strategies [34, 35, 29], that is, strategies to guide the rewriting process whose semantics can be defined inside the logic by rewrite rules at the metalevel. Since rewrite theories need not be Church Rosser and may not terminate, they can in general be executed in many different ways, yielding widely different ....

....META LEVEL by semantic equations and semantic rules, that define in rewriting logic the precise rewriting semantics for each of the constructors building up strategy expressions in our strategy language of choice. Several simple, yet powerful, strategy languages of this kind are discussed in [32, 35, 29, 31]. The idea of expressing strategies with rewrite rules and some reflective properties have also been adopted by more recent work on ELAN [17, 82] The ELAN system [79, 20] has been the first rewriting logic language providing good user support for strategies, in what might now be called an ....

M. Clavel and J. Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July

....terminating. Furthermore, some rules in R may have additional variables on their righthand sides, yet another source of nondeterminism. For this reason, sequential implementations of rewriting logic typically support rewriting strategies that let the user specify how the rules should be applied [169,82,22,83,17,319,65]. Such strategies can be defined in metalevel theories by reflection, as already indicated, or they may be part of a strategy language supported by a language implementation. However, one should not forget that rewriting logic is an intrinsically concurrent formalism, that can be used directly for ....

Manuel Clavel and Jos'e Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction, pages 1--12, Townsville, Australia, July 1997.

....that builds in key functionality for the universal theory U . In particular, both functional and system modules are represented as terms of sort Module. As pointed out in [8] and demonstrated in a number of substantial applications such as theorem proving tools and translations between logics [10,3,7], the reflective features of Maude support a novel style of metaprogramming with very powerful module combining and module transforming operations that surpass those of traditional parameterized programming and can greatly advance software reusability and adaptability. 1 Supported by DARPA ....

Manuel Clavel and Jos'e Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July

.... to the sustained efforts of many researchers, particularly in the ELAN, Pisa, Stanford, and Maude teams, there is by now very extensive evidence supporting the claim that rewriting logic is indeed a 5 Clavel et al. very flexible and simple semantic framework [21,23,24,4] and logical framework [20,18,34,19,3,32,6,14,7,10]. Moreover, object oriented design languages, architectural description languages, and languages for distributed components also have a natural semantics in rewriting logic [35,25,33,27,28] What is common to all these applications is that the models of computation, logics, or languages are ....

M. Clavel and J. Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July

....advanced, with a beta release in the first quarter of 1998 and a first distributable version planned for December 1998. It has very high performance, reaching about 600,000 logical inferences per second on real applications on a Pentium Pro computer. The following papers have been published [21, 89, 60, 87, 9, 8, 31, 18, 28, 19, 67, 72, 76, 71, 88, 74, 52, 25, 16, 68, 7, 6, 84] Ongoing Work Use of the event model for Maude as a basis for mappings between Maude and Rapide and for the use of Rapide tools in combination with Maude architectural specifications will be investigated. In collaboration with Cheng at U. Michigan, OMT notations will be formalized in Maude and ....

Manuel Clavel and Jose Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July 1997), pages 1--12, 1997.

.... Thanks to the sustained efforts of many researchers, particularly in the ELAN, Pisa, Stanford, and Maude teams, there is by now very extensive evidence supporting the claim that rewriting logic is indeed a very flexible and simple semantic framework [37, 40, 42, 6] and logical framework [32, 29, 62, 30, 2, 55, 8, 16, 10, 12]. Moreover, object oriented design languages, CHAPTER 1. INTRODUCTION 7 architectural description languages, and languages for distributed components also have a natural semantics in rewriting logic [63, 34, 57, 47, 48] see Section 2.8.2 for more discussion on the use of reflection in logical and ....

....computation can be efficiently carried out at the object level. An example of this kind of combined descent is given in Section 3.3. More generally, we should view descent functions as basic strategies, that can be used as fundamental building blocks to define internal strategy languages [16, 10], in which they can be combined with each other and with more complex strategies at several levels of reflection to perform efficiently sophisticated metalevel computations (see section 2.6) 2.5.2 The Module META LEVEL In Maude, key functionality of a metalevel theory M with several descent ....

Manuel Clavel and Jos'e Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July 1997), pages 1--12, 1997.

.... [3, 4] Reflection supports dynamic evolution and adaptation of components and of system architectures, hierarchical and distributed management of runtime services [17] powerful and extensible module composition operations, and development of formally based analysis and reasoning tools [5]. 2.1 Interoperability Our approach to formal interoperability of software components and architectures is to represent the underlying interaction models and architectural styles as classes of rewriting logic theories meeting specific structural constraints that reflect and enforce the features ....

Manuel G. Clavel and Jos'e Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July 1997), pages 1--12, 1997.

....implementations. For example, since the Maude system is precisely a way to implement any finitely specifiable rewrite theory, this means that the Maude system is in an adequate sense an implementation of the universal theory. Making this explicit in the implementation through a module METALEVEL [10] provides powerful ways of accessing metalevel entities for example modules and proofs at the object level, that is, as first class citizens within the logic itself. The following areas seem particularly promising for exploiting the power of reflection in rewriting logic: Reflective logical ....

....Formal environments Reflection can also be exploited to make the development and interoperation of new formal tools for rewriting logic, and for other logics, much easier. The idea is that, with the help of reflection, such tools can themselves be specified and prototyped in rewriting logic. In [10] we explain in detail how the rules of inference for Knuth Bendix completion can be given strategies corresponding to completion procedures in a completely modular way, not requiring any change whatsoever to the inference rules themselves. As it is well known, the Knuth Bendix completion algorithm ....

Manuel Clavel and Jos'e Meseguer. Internal strategies in a reflective logic. In Bernhard Gramlich and H'el`ene Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction, pages 1--12, Townsville, Australia, July 1997.

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M. Clavel and J. Meseguer. Internal Strategies in a Reflective Logic. In: B. Gramlich, and H. Kirchner, Eds., Proc. of the CADE-14 Workshop on Strategies in Automated Deduction. Townsville, Australia, (1997).

....provided that the rewriting engine is able to select, among all the possible rewriting computations, those interpreting tile logic derivations. For this purpose, we exploit the reflective capabilities [10,11] of the Maude language [9,8] developed at SRI, defining suitable internal strategies [12], which can help the user to collect and analyze the possible computations and results. A key point is that the internal strategies needed to embed tile systems in rewriting logic are for the most part general meta strategies for nondeterministic rewriting systems. We give a precise description of ....

.... to the top of the tree like structure of terms) However, since Maude is a reflective Bruni, Meseguer, and Montanari language, it is possible to overcome this limitation by importing the meta level of some specification, and controlling the computation with suitable (metaprogrammed) strategies [12]. We are mostly interested in strategies for dk nondeterminism. 3.2 A Strategy Kernel Language in Maude Given a logical theory T , a strategy is any computational way of looking for certain proofs of some theorems of T . An internal strategy language is a theory transforming function S that sends ....

M.G. Clavel and J. Meseguer. Internal Strategies in a Reflective Logic. In: B. Gramlich, and H. Kirchner, Eds., Proc. of the CADE-14 Workshop on Strategies in Automated Deduction, Townsville, Australia, 1--12 (1997).

....KBC specifies the subset of rules of inference KBC KB that are needed to check that a terminating rewrite theory R is confluent. Thus, only the rules Simplify, Delete, and Deduce in KB are specified. Further details regarding the complete specification of the inference system KB can be found in [5]. mod KBC is protecting META LEVEL . sorts EquationC EquationCSet Position PositionSet UnifPair ComplPair . subsorts MachineInt Position PositionSet . subsorts EquationC Term EquationCSet . op and : Bool Bool Bool [assoc comm] op or : Bool Bool Bool [assoc comm] op nor : Bool ....

M. Clavel and J. Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction, pages 1--12, Townsville, Australia, July 1997.

....to bring deduction strategies within the field of logic, and to exploit these high level strategies in various domains. In last year s CADE 14 Workshop on Strategies in Automated Deduction, Manuel Clavel presented work by himself and Jose Meseguer on Internal Strategies in a Reflective Logic [11], introducing the basic notions of internal strategy languages and reflective logics, and describing a particular strategy language and an interesting example. Here we summarize some recent developments along the same lines since that time. Maude, the basis for this work, is a logical language ....

....operations that surpass those of traditional parameterized programming and can greatly advance software reusability and adaptability. Internal Strategies. The strategies controlling the rewriting process can be defined by rewrite rules and can be reasoned about inside the logic [10, 11, 5]. Therefore, instead of having a Logic Control introduction of extra logical features, in Maude Control Logic. Here we give a brief overview of some recent developments exploiting the meta level strategy languages of Maude in several application areas. The work most closely related to ours ....

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M. Clavel and J. Meseguer. Internal strategies in a reflective logic. In B. Gramlich and H. Kirchner, editors, Proceedings of the CADE-14 Workshop on Strategies in Automated Deduction (Townsville, Australia, July 1997), pages 1--12, 1997.

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