Burstall, R.M., Goguen, J.A. The semantics of Clear, a speci cation language. In Proceedings, 1978 Copenhagen Winter School on Abstract Software Development, Springer-Verlag, Lecture Notes in Computer Science 86, 1980, 292-332.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... how user de nable internal strategy languages, that typically extend the module META LEVEL, can be used to change the (default) operational semantics of Maude for system modules; 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 de ning views of other program modules; and Maude s (default) syntax for programs can be re de ned in an extension of META LEVEL, so ....

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

....theory of rewriting logic with new data types and new functions. In this way, one can reason formally about the correctness of metaprogramming constructions by analyzing their associated rewrite theories. In particular, Maude s parameterized programming style in the Clear and OBJ tradition [7,22] becomes internalized in the logic as a very useful metaprogramming style that can now be extended with new modes of parameterization of theories, new methods of program composition, and new ways of de ning views of other program modules [18] Thus, Maude opens the meta reasoning of the ....

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

....components of most speci cation languages. Module operations belong to the metalevel of the logic in question, that is, they can be seen as functions taking theories and returning other theories as results. This is in fact the idea behind a number of approaches, beginning with the Clear language [5], and further developed in the module expressions in OBJ [34] ACT ONE [26] ACT TWO [27] the module algebra by Bergstra, Heering, and Klint in [2] Larch [35] CASL [15] and a vast body of related research [30,4] Preprint submitted to Theoretical Computer Science 12 January 2001 In general, ....

....theories, views, and modules, and the module operations of Full Maude. The general notion of structured theory is introduced in [23,18] as a way of considering structured theories as rst class citizens, so that the structure of each theory is preserved when theories are combined. As in Clear [5] and SPECWARE [44] the categorical notion of diagram is used for giving semantics to structured theories. One can specialize the concept to a hierarchy of theories by requiring that the diagram scheme is a nite poset and that all the arrows in the diagram are inclusions in an appropriate ....

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

....functional and system modules and some prede ned modules are implemented in C , giving rise to a sublanguage called Core Maude. This is extended by special syntax for object oriented speci cations, and by a rich module algebra of parameterized modules and module composition in the Clear OBJ style [9, 32], as described in [26, Chapter 3] and in [14] giving rise to the Full Maude language. All of Full Maude has been formally speci ed in Core Maude [27, 15, 26] This executable formal speci cation a Maude speci cation of about 7,000 lines is in fact its implementation in the Maude 1.00 system. Our ....

....of this structure for the example. NAT3 NAT (sort Nat to Nat3) # # ## 7.1. 2 Flattening The attening of the normalized structure is accomplished following the tradition of the Clear OBJ family of languages, in which speci cation structuring is based on the categorical concept of colimit [9, 25, 30]. However, instead of considering the category of speci cations and speci cation morphisms [9] attening is understood as a colimit in the category of speci cations and inclusions of speci cations. The colimit of a diagram in this category coincides with the set theoretic union of the theories in ....

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

....the jargon of computer science are import (in logical terms: combination of theories) export (restricting the signature of a theory) and renaming. The results are presented in an algebraic fashion. 1. 1 Relation with Other Work Operators on modules and their semantics have been studied in e.g. [1] (in the context of CLEAR) 5] in the context of PLUSS) 3] and [4] using category theory) 16] using model class semantics) Our main source of inspiration has been [2] where the approach is similar to Wirsing s in [16] extended to theory semantics and countable model semantics. The role ....

R.M. Burstall and J.A. Goguen, The semantics of CLEAR, a specication language, in: Abstract software specications, LNCS 86, Springer-Verlag (1980) 292-332

....rules: SP ; SP 0 SP 0 ; SP 00 SP ; SP 00 SP 1 ; SP 0 1 : SP n ; SP 0 n op(SP 1 ; SP n ) op(SP 0 1 ; SP 0 n ) where op is an arbitrary (monotonic) SBO. The above rules are known as vertical composability and horizontal composability respectively (see [GB 80, ST 97] Another interesting task is to present within our framework some standard examples of universal logics (cf. Tar 95] in which we will represent simpler logics in order to reuse for them strategies known worked out for stronger universal logics. Theorem 7.1 together with Theorem 3.9 ....

J. A. Goguen, R. M. Burstall. The semantics of Clear, a specication language. Proc.

....We are particularly interested in a module algebra framework in which theories with loose semantics and modules with initial semantics coexist, giving rise to a uniform setting. We like to view a module or theory as a more general form of a structured theory, possibly with initiality constrains [15, 1, 10, 9] on parts of its structure. In this setting, we want to be able to support parameterized theories and also parameterized views, allowing in this way the structuring of these entities as well. Traditionally, the semantics of module operations is given in terms of attened modules, assuming that ....

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

....proposition is immediate for all versions of assertional re nement we have discussed so far. Proposition 4.4 Assertional re nement is compositional: if A is re ned by B and B is re ned by C then A is re ned by C. 2 This is so called vertical composition. What is called horizontal composition [6] may be de ned in a setting with parameterised speci cations which we do not have. 5 Behavioural Re nement In the previous section we have focused on re nement in terms of validity of assertions. Next we shall introduce re nement in terms of simulation of behaviour. This turns out to be more ....

J.A Goguen and R. Burstall. The semantics of CLEAR, a specication language. In Abstract Software Specication, number 86 in Lect. Notes Comp. Sci., pages 292-332. Springer, Berlin, 1980.

....many practical examples that motivate parameterization, for instance, storing structures like stacks, lists, and queues, which are parameterized with respect to the elements to be stored. In the literature one can nd two major approaches to parameterization, the so called pushout approach (e.g. [BG80,EM85]) and that based on the calculus (e.g. SST92,Wir90] see also Chapter 8 for a discussion of both approaches) The drawback of the former approach is that it does not easily generalize to abstraction over arbitrary higher order variables. The need for higher order parameterization arises ....

R.M. Burstall and J.A. Goguen. The semantics of clear, a specication language. In D. Bjorner, editor, Proc. Copenhagen Winter School on Abstract Software Specication, volume 86 of Lecture Notes in Computer Science, pages 292-332. Springer, 1980.

....and well formed) speci cation text a signature and a class of models. In general the semantics is compositional w.r.t. the speci cationbuilding primitives. Note that some algebraic speci cation languages have a presentation semantics (cf. e.g. Act One [15] or a theory semantics (cf. e.g. Clear [8]) but in these cases also we can consider that we are provided with a model semantics [29] As regards Tool the situation is less clear. However, if we think of the most used tools, such as e.g. rewrite engines, theorem provers, proof checkers, etc. we may consider as well that we are provided ....

R.M. Burstall and J.A. Goguen. The semantics of Clear, a specication language. In Advance Course on Abstract Software Specications, pages 292-332. SpringerVerlag L.N.C.S. 86, 1980.

....renamed and retagged to avoid con icts with the constants in T 0 . 0 is an interpretation of thy(T) in thy(T 00 ) which extends . For further details, see [7] This notion of theory instantiation is closely related to the notion of theory instantiation proposed by Burstall and Goguen [2]; in both approaches a theory is instantiated via an interpretation. However, in our approach, any theory can be instantiated with respect to any of its subtheories. In the Burstall Goguen approach, only parameterized theories can be instantiated and only with respect to the explicit parameter ....

R. Burstall and J. Goguen. The semantics of Clear, a specication language. In Advanced Course on Abstract Software Specications, volume 86 of Lecture Notes in Computer Science, pages 292-332. Springer-Verlag, 1980.

.... of T in T 0 is a translation from the expressions of T to the expressions of T 0 which preserves the validity of sentences (see [6, 8, 18] Given T T 0 , an instance of T 0 via an interpretation of T in a theory U is the result of using to instantiate T in T 0 with U (see [2, 13]) The following are the basic ingredients of the method. A user de ned mce type is represented as a model conservative extension (T ; T 0 ) where T and T 0 are generally as abstract as possible) T T 0 must be shown before can be added to the set of supported mce types. By the Model ....

....notion of the instance of a theory under an interpretation where new machinery is created only if it is not already present in the target theory of the interpretation. 2 Our notion of a theory instantiation is closely related to the notion of theory instantiation proposed by Burstall and Goguen [2, 12, 13]; in both approaches a theory is instantiated via an interpretation. However, in our approach, any theory can be instantiated with respect to any of its subtheories. In the Burstall Goguen approach, only parameterized theories can be instantiated and only with respect to the explicit parameter ....

R. Burstall and J. Goguen. The semantics of Clear, a specication language. In Advanced Course on Abstract Software Specications, volume 86 of Lecture Notes in Computer Science, pages 292-332. SpringerVerlag, 1980.

....version of the axiomatic method lies o the main path of previous work in mechanized theorem proving. The little theories idea is, however, a familiar ingredient in work on speci cation languages, probably rst introduced by Burstall and Goguen [2] It was a central tenet of work on Clear [3, 4], and it was also a motivating idea in Larch [16] The idea is also an ingredient in more recent work on logical frameworks [18] In the logical frameworks context, however, it appears in an unusual guise in which not just theories but also logics may be combined. It is not clear whether this ....

R. Burstall and J. Goguen. The semantics of Clear, a specication language. In Advanced Course on Abstract Software Specications, volume 86 of Lecture Notes in Computer Science, pages 292-332. SpringerVerlag, 1980.

....of speci cations with independence of any logic formalism. The notion was de ned as a slight abstraction of the notion of institution [22] de ned, some years before, by Goguen and Burstall with similar aims. That idea was connected with the design of the Clear speci cation language [10]. In particular, Clear was de ned as providing operations for structuring speci cations independently of the underlying logic. Speci cation frames are indexed categories that satisfy some additional structural properties: De nition 3.1. A speci cation frame SF is a pair (Spec; Mod) where ....

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

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Burstall, R.M., Goguen, J.A. The semantics of Clear, a speci cation language. In Proceedings, 1978 Copenhagen Winter School on Abstract Software Development, Springer-Verlag, Lecture Notes in Computer Science 86, 1980, 292-332.

....This theorem was rst proved in the original version of [18] We will later relate the Satisfaction Condition to the encapsulation of modules, and in Section 4. 1, we will see that it is an important part of the formalisation of logical system called an institution by Burstall and Goguen [6, 17, 18]. 2.5 Other Topics Section 3.1 assumes familiarity with basic order sorted algebra, as given for example in [22] For simplicity of exposition, this paper will rst treat the many sorted case, and then treat the order sorted case more brie y afterwards. Some examples assume familiarity with some ....

....paper, it is especially signi cant that the notions of module, generic (parameterised) module, sum (combination) of modules, importation (inheritance) of modules, etc. can all be de ned (using colimits of speci cations) over any institution whose signatures admit colimits (details are given in [6, 18, 10]) This includes all the institutions that interest us, such as hidden sorted equational logic over over a xed and D. The following result (from [18] supports this approach, and is also used in Section 7. Theorem 21: If the category Sign of signatures of an institution I has all ( nite) ....

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

No context found.

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

No context found.

R. M. Burstall and J. A. Goguen. The semantics of Clear, a specication language. In ########### ## ######## ###### ## ######## #####################, pages 292-332. Springer-Verlag, Lecture Notes in Computer Science, 1980.

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