R. Burstall and J. Goguen. Putting theories together to make specifications. In Proc. 5th Intl. Joint Conf. on Artificial Intelligence, pages 1045--1058, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Rod Burstall on prototype designs for modules in Hope [MAC81] and on theoretical investigations with Ravi Sethi and Gordon Plotkin [MAC82, MAC84] that were motivated by those designs. The module designs for Hope were in turn influenced by the Clear specification language of Burstall and Goguen [BUR77]. Many hours of discussion with Luca Cardelli helped to solidify the ideas, and a limited prototype of modules implemented by Cardelli in Pose 3 of his ML system [CAR83a] has made it possible to gain valuable experience programming with modules. This paper is a companion to Robin Milner s proposal ....

R. M. Burstall and J. A. Goguen, Putting theories together to make specifications, Proc. 5th lnt. Joint Conf on Artificial Intelligence, Cambridge, Mass., August, 1977, pp. 1045-1058.

....axioms may be removed if they do not contribute to assertions about symbols that are imported. A dependency analysis algorithm could, in principle, identify and remove such dead code . of just those predicates and functions we require corresponds to Burstall and Goguen s derive operation [Burstall and Goguen, 1977] which is used to build al gebraic theories from others. Our overall approach with knowledge patterns is similar to the use of theories and morphisms in the formal specification of software (e.g. Goguen, 1986, Srinivas and Jutrig, 1995, Williamson et at. 2000] and part of our goal is to ....

....1995, Williamson et at. 2000] and part of our goal is to motivate, simplify, and apply it in the context of knowledge engineering. As these authors have shown, category theory, applied to algebraic theories, provides a formal basis for this approach. To apply this to logic, Burstall and Goguen [Burstall and Goguen, 1977] show how a first order logic theory can be understood as a many sorted al gebraic theory (comprising a set of sorts, a set of op erators over those sorts, and a set of laws that those operators must satisfy) by: introducing truth values as a sort, and two no argument operators (constants) ....

Burstall, R. M. and Goguen, J. A. (1977). Putting theories together to make specifications. In IJCAI-77, pages 1045-1058.

....(here termed signatures) of declarations and axioms. In Veritas, the declarations may be datatypes (eg, nat = 0jnat ) definitions (eg, 2 ) ordinary declarations (eg, n: nat) axioms (eg, hyp: n 0) or pairs of these. The treatment of signatures in Veritas is motivated by Clear [BG78]; the aim is to support formal verification in the large . Signatures are first class objects, fully on a par with typed terms. There is an empty signature and three methods of constructing new signatures: ffl A signature may be extended by adjoining a declaration. ffl Two signatures may be ....

R. M. Burstall and J. A. Goguen, Putting theories together to make specifications, Proc 5th IJCAI, pp1045-58, 1978.

....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] ....

Rod Burstall and Joseph Goguen. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977.

....(see e.g. SW83] EM85] GH93] CoFI96] SW99] is the provision of specification building operations for building large specifications in a structured fashion from smaller and simpler ones. This was pioneered by Burstall and Goguen in their seminal work on the Clear specification language [BG77] BG80] Less usual in specification languages are features for describing the modular structure of software systems under development. This paper is about the facilities for this that are provided in Casl, the new Common Algebraic Specification Language [ABK 01] CoFI01b] that has been ....

R. Burstall and J. Goguen. Putting theories together to make specifications. Proc. 5th Intl. Joint Conf. on Artificial Intelligence, Cambridge, 1045--1058 (1977).

....implementation, and what constitutes proof of correctness. Our examples come from both the functional style and imperative (state changing) style of theory. Finally, we explore how one implementation can be transformed to another. 0 Introduction A classic paper by Burstall and Goguen in 1977 [2] taught us to think about data types used in computer programs as logical theories, presented by axioms, whose properties can be explored by logical deduction. The following year, a paper by Guttag and Horning [4] developed the idea further, showing us the algebraic properties of data types ....

....the left nor associates to the right, but means a = b b = c . A mixture of continuing operators can be used; for example, a b c means a b b c . For further details on notation and basic theories please consult [5] or [6] 2 Theories Here is a little theory presented in a style similar to [2] and [4] Theory0: names: chain, start, link, isStart signatures: start: chain link: chainchain isStart: chainbool axioms: isStart start c: chain isStart (link c) Theory0 introduces four new names into our vocabulary. The signatures section tells us something about the role these names ....

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R.M.Burstall, J.A.Goguen: "Putting Theories Together to make Specifications", in R.Reddy (ed.): Proceedings of the fifth International Joint Conference on Artificial Intelligence, volume 6 pages 1045-1058, Morgan Kaufman , Cambridge MA, 1977

....which is more closely related to the semantics of unit specifications in Casl. 39 8.4 OBJ3 OBJ3 [32] is an executable specification language, also known as an ultrahigh level programming language. It is institution independent in the sense that it originated as an implementation of Clear [12], which is institutionindependent, for the institution of order sorted conditional equational logic. OBJ3 s mixfix notation for operations was the origin of mixfix notation in Casl and other languages. The same for views, although the features for views in OBJ3 di#er from those in Casl. In an OBJ3 ....

Rod Burstall and Joseph Goguen. Putting Theories Together to Make Specifications. Proc. 5th Intl. Joint Conference on Artificial Intelligence, Cambridge (USA), pages 1045--1058 (1977).

....functions and procedures. The invariant of the representation and the equality interpretation of the implementation may be defined with the data structure, as well as the abstraction function introduced in section 4. In both kinds of universes some structuring mechanisms (in the way of [BuG77]) can be included. The basic one is the use of specifications, which makes all the symbols exported by a specification universe available to its users. There is also a parameterisation facility to define generic universes, coupled with a parameter passing mechanism; formal parameters are defined ....

R.M. Burstall, J.A. Goguen. "Putting Theories together to make Specifications", in Proceedings of 5th International Joint Conference on Artificial Intelligence, Cambridge M.A., 1977.

....initiated. Keywords: formal specification, formal software development, software synthesis and composition, refinement and modularity, categorical models and methods, fibred categories. 1 Introduction One fundamental difference between this form of parameterisation, and previous work (such as [18, 24, 26, 17, 3]) is grounded on that the proposed form of parameterisation accounts to a special kind of cocone in a finitely cocomplete category Pres of specifications and specification morphisms, rather than a single specification morphism. The latter allows to parameterise a specification by a Pres diagram ....

....a refinement calculus for parameterisations of specifications by diagrams is currently on going. 19 6 Conclusion and further work In this paper we introduced and analysed a new notion of parameterisation for logical and algebraic specification, extending previous work on the subject including [18, 13, 26, 25, 3]. The main advantage of this notion of parameterisation is that the parameters can be presented diagrammatically and instantiated along compatible families of parallel instantiating morphisms. The concepts of parallel families of morphisms between specification diagrams, and of diagram ....

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R. Burstall and J. Goguen. Putting theories together to make specifications. In R. Reddy, editor, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058, 1977.

....Kent [Ken99] Ken97] uses a graphical notation called constraint diagrams to express system properties. The diagrams achieve a similar aim to equalisers as used in this paper. The use of operators such as Theta and to construct system descriptions dates back to the specification language clear [Bur77b] which lead to the OBJ family of specification languages [Gog99] which differ from the approach taken in this paper by using a semantic framework based on rewriting terms in order sorted equational logic. A related approach which addresses object oriented system execution is the use of modal ....

Burstall, R. M. & Goguen, J. A.: Putting Theories Together to Make Specifications. In the proceedings of IJCAI '77, 1977.

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Rod Burstall and Joseph Goguen. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977.

....[109] for a more detailed discussion of the educational uses of OBJ. 1. 1 A Brief History of OBJ OBJ was designed in 1976 by Goguen [43] using error algebras to extend algebraic abstract data type theory with error handling and partial functions; this first design also used ideas from Clear [8, 10] for parameterized modules, thus giving birth to parameterized programming. The first implementations of OBJ were done from 1977 to 1979 at UCLA by Joseph Tardo and Joseph Goguen. OBJ0 [45] was based on unsorted equational logic, while OBJT used error algebras plus an image construct for ....

....fixes made at Oxford. Although the syntax of OBJ3 is close to that of OBJ2, it has a different implementation based on a simpler approach to order sorted rewriting [101] and it also provides much more sophisticated parameterized programming. OBJ2 and OBJ3 can be seen as implementations of Clear [8, 10], where the chosen logic is order sorted equational logic. Other implementations of OBJ1 include UMIST OBJ from the University of Manchester Institute of Science and Technology [20] Abstract Pascal from the University of Manchester [105] and MC OBJ from the University of Milan [14] the first ....

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Rod Burstall and Joseph Goguen. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977.

.... Notation for Ada ) for this purpose [DIA83, Tra93b] Although we avoid abstract algebra and category theory, both the module composition facility and its semantics as described in this paper are largely inspired by work done using such formalisms, including the Clear specification language [BG77], and the OBJ [GM96, GWMFJ] system. The approach in this paper differs from that of those languages in providing a constructive module composition facility for an imperative programming language, as contemplated for the CAT and LIL [Gog85] systems, which are ancestors of lileanna. The set ....

Burstall, R. and Goguen, J. Putting Theories Together to Make Specifications. In Proceedings of Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977.

....coinductive assertions for such systems [12] 3. Some Related Work OBJ began around 1974 as a notation for algebraic specification, and soon after was implemented in an interpreter based on term rewriting. Early designs [8] called for a module system like that of the Clear specification language [1], and this first order approach to modularization was later formalized under the name parameterized programming, including default views, to greatly reduce the effort of writing views [9, 11] Parameterized programming was first fully implemented in OBJ3 [14] following partial implementations in ....

....order parameterization. We speculate that the lack of views explains the confusing multiplicity of semantics that have been given for ML higher order functors ( functor is ML terminology for parameterized module) as well as its awkward treatment of sharing. The Clear module system semantics [1] uses the category of theories, where views are the natural notion of morphism for theories, and module composition is given by colimit, inspired by an earlier category theoretic approach to general systems [7] this applies directly to OBJ3. Our semantics of higher order parameterized programming ....

Rod Burstall and Joseph Goguen. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977. 5

....with each data type (so types become algebras instead of simply sets) Rather than generalising to otree(alpha) we could generalise to otree(alpha[ requiring an order relation to exist on the parameter type. This is the approach taken in CLU [25] and in the specification language CLEAR [8]. We really want HOPE modules to have , a collection of types and operators, Just as CLU clusters have parameters. As a further example, refer again to figure 1 and note that the module tree sort does not depend on the fact that otrees are trees, but just on certain properties of insert and ....

Burstall, R.M. and Goguen, J.A. Putting Theories Together to Make Specifications. Proc. 5th Int. Joint Conf. on Artificial Intelligence, Cambridge, Massachusetts, August, 1977, pp. 1045-1058.

....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 ....

Rod Burstall and Joseph Goguen. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977.

....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. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977.

.... I think this paper [6] finally came out very well, and it may not be unfair to say that it gave the first rigorous theory of abstract data types, and laid foundations for the more general field of algebraic specification that was later to emerge in projects like the specification language Clear [1]. We didn t even try to use the controversial slogan. Perhaps it was the strain of that paper, plus some others that we tried to write across the Atlantic while I was at the University of Edinburgh on a Senior Visiting Fellowship, that finally broke up the collaboration. In fact, I was able to ....

Rod Burstall and Joseph Goguen. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Arti4 ficial Intelligence, pages 1045--1058. Department of Computer Science, CarnegieMellon University, 1977.

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R. Burstall and J. Goguen. Putting theories together to make specifications. In Proc. 5th Intl. Joint Conf. on Artificial Intelligence, pages 1045--1058, 1977.

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Rod Burstall and Joseph Goguen. Putting theories together to make specifications. In Raj Reddy, editor, Proceedings, Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058. Department of Computer Science, Carnegie-Mellon University, 1977.

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. R.Burstall and J.Goguen, "Putting Theories Together to Make Specifications", in Proc.

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R. M. Burstall and J. A. Goguen, `Putting theories together to make specifications', Proc. 5th International Joint Conference on Artificial Intelligence, Cambridge, MA, 1977, pp. 1045--1058.

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R.Burstall and J.Goguen, "Putting Theories together to make Specifications", in R.Reddy (ed) Proc Fifth International Joint Conference on Artificial Intelligence, 1977, 1045-1058.

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R.M. Burstall and J.A. Goguen, "Putting Theories Together to Make Specifications," Pmc. 5th International Joint Conference on Anb'cial Intelligence, Cambridge, MA, 1977, 1045-1058.

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R. M. Burstall and J. A. Goguen. Putting theories together to make specifications. Proceedings of the Fifth International Joint Conference on Artificial Intelligence, pages 1045--1058, 1977.

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