R. M. Burstall and J. A. Goguen. The semantics of CLEAR, a specification language. In Proc. Advanced Course in Abstract Software Specification, number 86 in Lecture Notes in Computer Science, pages 292-- 332, Copenhagen, 1980. Springer Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in our case, equational and rewrite theories that operate on other such theories as their data. By observing that we can not only reify theories, but also views among them, this 12 Clavel et al. includes the more traditional parameterized programming capabilities in the Clear OBJ tradition [4,11] as a particular instance. The difference is that in that tradition theories are metalevel entities not accessible at the object level of the logic, since this is only possible in an explicitly reflective logical context. What reflection accomplishes is to open up to the user the metalelevel of ....

Rod Burstall and Joseph Goguen. The semantics of Clear, a specification language. In Dines Bjorner, editor, Proceedings of the 1979.

....from data type definitions. Furthermore parameterization comes naturally with specification languages, no matter whether they are operational, axiomatic (algebraic) or algorithmic ( EM90] A non exhaustive list of specification languages using parameterization is Alphard ( WLS76] Sha81] CLEAR([BG80]) ACT ONE ( EM85] and OBSCURE ( LL87] LL90] All these languages differ substantially in the methods used for implementing, resp. specifying, data structures and operations. In this paper we take an abstract approach and present an idealized language for expressing modules. The language ....

R. M. Burstall and J. A. Goguen. Semantics of CLEAR, a specification language. In D. Bjorner, editor, Abstract Softare Specifications, pages 292--332, Springer LNCS, vol. 86, 1980.

....the last two decades, algebraic specification has frequently been used to study denotational semantics of functional [6, 55] and imperative [7] languages. Algebraic specification languages inherently provide algebraic semantics and thus mathematical objects denoting syntactical constructs (c.f. [8, 27, 21, 12, 5, 57, 25]) Algebraic semantics are also used in the field of abstract state machines to formalize the machine model underlying an operational semantics [31] Based on this approach, Gurevich shows such a semantics for the C programming language [32] In the context of algebraic specification languages, a ....

R. M. Burstall and J. A. Goguen. The semantics of CLEAR, a specification language. In Proceedings of the 1979.

....oriented, the second one is given by the behavioural specification of objects which is more faithful to the principle of state encapsulation. Powerful module system The principles of the CafeOBJ module system are inherited from OBJ which builds on ideas first implemented by the language Clear [2, 3]. CafeOBJ has several kinds of imports, parameterised programming (also allowing integration of CafeOBJ specifications with executable code in a lower level language) views, and module expressions. Powerful type system The type system that allows subtypes based on order sorted algebra [22, 15] ....

....for rewriting logic [27] in the second case. 5 Programming in the Large In this section we are concerned with the semantics of the module interconnection system. CafeOBJ module interconnection system follows the principles of the OBJ module system which are inherited from earlier work on Clear [3]. Consequently our semantics is based on institutions employing the theory developed in [9] In the actual case of CafeOBJ this institutional semantics is instantiated to the CafeOBJ cube, however its essential core can be presented at the level of institutions thus avoiding the particular details ....

[Article contains additional citation context not shown here]

Rod Burstall and Joseph Goguen. The semantics of Clear, a specification language. In Dines Bjorner, editor, Proceedings, 1979.

....operate on other such theories as their data. By observing that, using rewriting logic reflection, we can reify not only theories, but also views that is, theory interpretations between them, this includes the more traditional parameterized programming capabilities in the Clear OBJ tradition [23, 67] as a particular instance. The difference is that in that tradition theories are metalevel entities not accessible at the object level of the logic, since this is only possible in an explicitly reflective logical context. What reflection accomplishes is to open up to the user the metalevel of the ....

R. Burstall and J. Goguen. The semantics of Clear, a specification language. In D. Bjorner, editor, Proceedings of the

....and system modules and some predefined modules are implemented in C , giving rise to a sublanguage called Core Maude. This is extended by special syntax for object oriented specifications, and by a rich module algebra of parameterized modules and module composition in the Clear OBJ style [10, 32] giving rise to the Full Maude language. All of Full Maude has been formally specified in Core Maude [23, 22] This formal specification about 7,000 lines is in fact its implementation, which is available in the Maude web page (http: maude.csl.sri.com) Our experience in this regard is very ....

R. Burstall and J. A. Goguen. The semantics of Clear, a specification language. In D. Bjorner, editor, Proceedings of the

....there are horizontal theory composition operations at each level. The structuring and composition are formalized in terms of mappings between reasoning theories. Therefore, our work is in the spirit of putting theories together by means of theory mappings as advocated by Burstall and Goguen [7], that is widely used in algebraic specifications [2] In order to simplify the presentation, we treat a restricted subcase of horizontal composition that is none the less adequate for interesting examples. A more general treatment in terms of pushouts of order sorted theories [16, 22, 23] can be ....

R. M. Burstall and J. A. Goguen. The semantics of Clear, a specification language. In Proc.

....itself. Therefore, the ideas in the present paper are part of this overall reflective and modifiable design. We now explain in more detail how the Clear OBJ operations and the transformation of object oriented modules are defined. 1. 1 Module Hierarchies and Parameterized Programming As in Clear [2], OBJ [13,17] and other specification languages in that tradition, the abstract syntax for writing specifications in Maude can be seen as given by module expressions, where the notion of module expression is understood as an expression that defines a new module out of previously defined modules ....

....form of this structure for the example. NAT (sort Nat to Nat3) NAT3 2. 3 Flattening The flattening of the normalized structure is accomplished following the tradition of the Clear OBJ family of languages, in which specification structuring is based on the categorical concept of colimit [2,11,12]. However, instead of considering the category of specifications and specification morphisms [2] flattening is understood as a colimit in the category of specifications and inclusions of specifications. The colimit of a diagram in this category coincides with the set theoretic union of the ....

[Article contains additional citation context not shown here]

Rod Burstall and Joseph Goguen. The semantics of Clear, a specification language. In Dines Bjrner, editor, Proceedings of the

....complexity of large systems at all levels, including specifications and code. Category theory provides an excellent foundation for studying structured specifications and their composition. A key contribution in the late seventies and early eighties was made by Burstall and Goguen with the Clear [4] specification language, that proposed taking colimits of theories as a systematic way of putting theories together . Clear was based on many sorted equational logic, but its categorical semantics was in fact logic independent. This led Goguen and Burstall to propose the notion of institution as ....

.... we often want to associate to the inclusion of a parameter theory into the body of a parameterized specification a freeness constraint, requiring that the models of the body are free extensions of the models of the parameter; more generally, one can similarly consider other notions of constraint [26,4,28,18,15]. In practice, the need for keeping and using structure is both recognized and supported by a number of languages and systems such as, for example, languages in the Clear OBJ tradition [4,19,9,6] SPECWARE [30] and CASL [8] Although a number of concepts and techniques have been suggested both ....

[Article contains additional citation context not shown here]

R. Burstall and J. Goguen. The semantics of Clear, a specification language. In D. Bjrner, editor, Proceedings of the

....techniques in the OBJ3 style [37] Moreover, Maude provides useful basic support for modularity by allowing the definition of module hierarchies, that is, acyclic graphs of module importations. Parameterized modules, theories, and views are the basic building blocks of parameterized programming [10,37,26,23]. As in OBJ, a theory 5 defines the interface of a parameterized module, that is, the structure and properties required of an actual parameter. The instantiation of the formal parameters of a parameterized module with actual parameter modules requires a view from the formal interface theory to ....

R. Burstall and J. A. Goguen. The semantics of Clear, a specification language. In D. Bjrner, editor, Proceedings of the

.... user definable internal strategy languages, that typically extend the module META LEVEL, can be used to change the (default) operational semantics of Maude for system modules; ffl Dur an and Meseguer [15] have explained how Maude s parameterized programming style in the Clear and OBJ tradition [5,17] can be internalized in Maude in an extension of META LEVEL and enriched with new modes of parameterization, new methods of program composition, and new ways of defining views of other program modules; and ffl Maude s (default) syntax for programs can be re defined in an extension of META LEVEL, ....

R. Burstall and J. Goguen. The semantics of Clear, a specification language. In D. Bjrner, editor, Proceedings of the

....designate some parts of a specification as formal parameters. The specification abstraction obtained is called parameterized and can subsequently be instantiated with actual specifications fitting the formal ones. Parameterized specifications were first used in the specification language CLEAR [2]. Since then, plenty of approaches were developed with different semantics or abstraction and instantiation mechanisms. Among them, probably best known are the CLEAR style parameterized specifications, the ASL style parameterized specifications [17] the ACT ONE style parameterized ....

R. Burstall and J. Goguen. The semantics of CLEAR, a specification language. In Proceedings of Advance Course on Software Specification, volume 86 of LNCS, pages 292--332, 1980.

....problem) Specifications, just as programs, can be large and unwieldy making them difficult to understand or reason about. Specification languages with facilities for structuring specifications have been developed to cope with the large specifications which may arise in practice (see for example [GB80, EM85, EM90, FJ90, San89]) From a clean structuring of a specification we may, for example, see the consequences of our definitions and axioms more readily. This is not only important from the perspective of the specification writer but also of the many parties who may come to rely on the specification during the course ....

.... the modules facilities already present in Standard ML to structure specifications [San89, ST89] Specifications in Extended ML are of parameterised program modules, rather than the more usual parameterised specifications (of programs) found in other algebraic specification languages, for example, [GB80, EM85, EM90]. Program development is by stepwise refinement (described below) from algebraic specifications of a (parameterised) module s interfaces. We briefly overview the salient features of both the Extended ML specification language and the program development methodology below. 2.1 Structures, ....

J. A. Goguen and R. M. Burstall. The Semantics of Clear, A Specification Language. In Abstract Software Specifications, LNCS 86. Springer-Verlag, 1980.

....more detail on institutions and specification frames) Institutions were invented by Goguen and Burstall as a means to describe, at an abstract level, logical systems that can be used for specification or other purposes. The idea was connected with the design of the Clear specification language [4]. In particular, Clear was defined as providing operations for structuring specifications independently of the underlying logic (institution) Technically, an institution is defined in terms of four parts: the category of signatures , i.e. the available classes of symbols for writing ....

#R.M. Burstall, J.A. Goguen, The semantics of Clear, a specification language, in Proc. Copenhagen Winter School on Abstract Software Specification, Springer LNCS 86, pp. 292-332, 1980.

.... 16] Interpretation between theories has been formalized in a categorial framework by Maibaum and Fiadeiro in [10] and category theory was also used to define an abstract specification theory for refining specifications by Ury and Gergely in [15] Earlier work by Burstall, Goguen and Sannella in [1, 2, 12] used the construction of colimits for diagrams during theory building. By using based theory morphisms, they extended theories by including the diagram of the extension in the extended theory. In [3] Goguen has presented an axiomatisation of the notion of extension as inclusion between ....

R. M. Burstall and J. A. Goguen. The semantics of Clear, a specification language. In Abstract Software Specifications, LNCS 86. Springer-Verlag, 1979.

....giving semantics to canons. In his approach, a constraint designates a part of a specification that is to be interpreted initially (or to be more accurate, freely) This kind of constraint has been called a data or free generating constraint. They were the basis of the semantic definition of CLEAR [184] and of other specification languages [334] More recently, in [815] the combined use of initial and terminal constraints for the specification of data types on one hand and of behavior classes on the other hand has been suggested. Till now terminal and initial constraints have been used ....

....satisfaction relation. 956] provides a unified formal description of four relevant specification frameworks based on the notion of institution. Institutions were introduced to define the semantics of specification languages independently from the underlying algebraic formalism (examples are CLEAR [184], ASL [837] OBSCURE [604] and PLUSS [93] It is also possible to discuss fundamental concepts such as free constructions [896, 897] observational equivalence [845] refinement [62, 846] and composability of implementation steps [859] in this context. Defining a wide spectrum language in this ....

[Article contains additional citation context not shown here]

R. M. Burstall and J. A. Goguen. The semantics of CLEAR, a specification language. In Proc. Advanced Course on Abstract Software Specifications, pages 292--332. Springer LNCS 86, 1980.

....and GEQ(oe) is the corresponding restriction of EQ(oe) Proposition 2.13 1. EQ and GEQ are logical systems with inclusions. 2. Sig EQ has pushouts along inclusions (in fact, is co complete) Proof EQ(oe : Sigma Sigma 0 ) is a CR morphism because of the Satisfaction Lemma [BG80] Similarly for GEQ. Pushouts in Sig EQ are defined as in [GB84b] In a similar manner we can present first order logic with equality. The logical system FOEQ has the same signatures as EQ (we take equality to be the only predicate) and for any many sorted algebraic signature Sigma, ....

....some symbols (for example, auxiliary function symbols needed to finitely axiomatize some other function) and perhaps renaming the rest. The operations used are almost the same as those in [SB83] union is inessentially different) The theory building operations of the specification language CLEAR [BG80] may be defined in terms of these primitives. A few concrete examples should help to clarify the motivation behind structured theory presentations. See [BG81] SB83] and Section 4 for further examples. We will consider structured theory presentations over the logic EQ defined in Section 2. ....

[Article contains additional citation context not shown here]

R. Burstall and J. Goguen. The semantics of CLEAR, a specification language. In Proceedings of Advanced Course on Abstract Software Specifications, pages 292--332, SpringerVerlag, Copenhagen, 1980.

....of specifications with independence of any logic formalism. The notion was defined as a slight abstraction of the notion of institution [24] defined, some years before, by Goguen and Burstall with similar aims. That idea was connected with the design of the Clear specification language [11]. In particular, Clear was defined as providing operations for structuring specifications independently of the underlying logic. Specification frames are indexed categories that satisfy some additional structural properties: Definition 1 A specification frame SF is a pair (Spec; Mod) where ....

Burstall, R.M., Goguen, J.A., The semantics of Clear, a specification language, in: Proc. Copenhagen Winter School on Abstract Software Specification, Springer LNCS 86:292-332, 1980.

....Of course if two base specifications are isomorphic, and if this isomorphism is not part of C 0 , then we will fail to find it. Most existing specification languages give more importance to the construction of a modular specification than to the result of the construction; for example CLEAR [3, 4], ACTONE [6] ASL [14] OBJ2 [7] PLUSS [8, 2] LPG [1] This implies that the only tractable isomorphisms are isomorphisms of structure. We propose to adopt a less syntactic view of modular specification, by representing them as diagrams over the category of base specifications C 0 . This ....

....than terms because irrelevant steps of the construction disappear. We need of course to work in a category of diagrams, and so we associate specification morphisms between modular specifications to diagram morphisms. This approach is similar to that adopted to describe the semantics of CLEAR [4]. Our diagrams correspond to based theories. We need a more general definition for arrows than that of based morphisms, because based morphisms only correspond to inclusions of modular specifications, whereas we want a diagram morphism to correspond to any specification morphism. So we define a ....

R.M. Burstall and J.A. Goguen. The semantics of CLEAR, a specification language. In Proc. Advanced Course on Abstract Software Specification, number 86 in LNCS, pages 292--332. Springer-Verlag, 1980.

.... of M preserving arity, value sort, and the meanings of the attributes assoc, comm, idem, id: idr: to the extent that these attributes are present) such that every equation in T is true of every model of M (thus, a view from one theory to another is called a theory interpretation in logic [9]) The mapping of sorts is expressed with the syntax sort S1 to S1 . sort S2 to S2 . and the mapping of operators is expressed with the syntax op o1 to o1 . op o2 to o2 . Warning: The final blank and period are required. Comments may not appear anywhere inside of views. Thus, ....

Rod Burstall and Joseph Goguen. The semantics of Clear, a specification language. In Dines Bjorner, editor, Proceedings, 1979.

....using many different logical systems suggests generalising to an arbitrary logical system. This requires formalising the notion of logical system. Fortunately, such a formalisation is available in the form of institutions [18] which arose in the semantics of the specification language Clear [2, 3]. The framework of institutions is reviewed in Section 2.1, and then systematically used thereafter. Acknowledgements The approach in this paper evolved out of work on Clear [2, 3, 18] and its semantics; this joint research with Rod Burstall includes the concept of institution and the putting ....

....is available in the form of institutions [18] which arose in the semantics of the specification language Clear [2, 3] The framework of institutions is reviewed in Section 2.1, and then systematically used thereafter. Acknowledgements The approach in this paper evolved out of work on Clear [2, 3, 18] and its semantics; this joint research with Rod Burstall includes the concept of institution and the putting together of theories by colimits to form larger specifications. These ideas were further developed in joint work with Jos e Meseguer on various topics, including OBJ [9, 28] which can be ....

[Article contains additional citation context not shown here]

Rod Burstall and Joseph Goguen. The semantics of Clear, a specification language. In Dines Bjorner, editor, Proceedings,

....for sort constraints is an initial algebra construction reducing the problem to order sorted equational logic. Part III will give an algebraic semantics for parameterized order sorted abstract data types with the related concepts of theory, view and module expression, as in OBJ [14, 15] and Clear [3, 4]. This supports the effective integration of the programming and assertional aspects of OBJ, which make it a wide spectrum language. 1.7 Acknowledgements We thank Prof. Jean Pierre Jouannaud for help with several of the topics discussed here. In particular, he participated in formulating the ....

Rod Burstall and Joseph Goguen. The semantics of Clear, a specification language. In Dines Bjorner, editor, Proceedings,

No context found.

R. M. Burstall and J. A. Goguen. The semantics of CLEAR, a specification language. In Proc. Advanced Course in Abstract Software Specification, number 86 in Lecture Notes in Computer Science, pages 292-- 332, Copenhagen, 1980. Springer Verlag.

No context found.

Burstall, R. M. and Goguen, J. A., The Semantics of Clear, a Specification Language, Proceedings of the

No context found.

R.M. Burstall and J.A. Goguen. The semantics of Clear, a specification language. In D. Bjřrner, editor, Abstract Software Specifications, pages 292--332. Springer Verlag, LNCS 86, 1980.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC