Burstall, R.M., Goguen, J.A. Putting theories together to make speci cations. In Proceedings, Fifth International Conference on Arti cial Intelligence, 1977, 1045-1058.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....u i : X Y i . Then the pushout Z, a simple colimit, con gures a new speci cation out of Y 1 and Y 2 with sharing of a common part X . Many applications of this idea work by choosing a category with the appropriate colimits. For example, a categorical semantics was given by Burstall and Goguen [BG77, BG79] for Clear: a language for writing structured speci cations. A Clear text denotes a many sorted theory; the structuring of theories is expressed by colimits in order to take account of shared sub theories. This has continued in work in the algebraic approach to speci cation [EM90, EFHLP87] and ....

....Diag(C) is somewhat intricate. It is much more evident that the corresponding presheaves are isomorphic: PreShhg; h : X j g = h; g = fhi = PreShhk : X j k = fki 3. Instances The use of colimits to build complex speci cations out of simpler ones dates back to the work of Burstall and Goguen [BG77] on Clear, which is dependent on the underlying logic of the speci cations. Oriat, in [Ori98] has developed the use of diagrams to express these colimits independently of the speci cational logic. Our results of Section 2 show that Oriat s diagrams can equivalently be interpreted in terms of ....

Burstall, R. M. and Goguen, J. A.: Putting Theories Together to Make Specications. Proceedings of the 5th. International Joint Conference on Articial Intelligence, Cambridge, Mass., pp. 1045-1058, 1977.

....which is more closely related to the semantics of unit speci cations in Casl. 39 8.4 OBJ3 OBJ3 [32] is an executable speci cation 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 mix x notation for operations was the origin of mix x 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 Specications. Proc. 5th Intl. Joint Conference on Articial Intelligence, Cambridge (USA), pages 1045-1058 (1977).

....algorithms in all practically relevant cases. Introduction A common feature of present day algebraic speci cation languages (see e.g. Wir86,EM85,GHG 93,CoFI96,SW99] is the provision of operations for building large speci cations in a structured fashion from smaller and simpler ones [BG77]. Much less usual in speci cation languages are features for describing the modular structure of software systems under development. Since mechanisms for structuring speci cations do not and, in fact, cannot serve this purpose [SST92] architectural speci cations have been introduced as a ....

R. M. Burstall and J. A. Goguen. Putting theories together to make speci cations. In Proc. 5th Intl. Joint Conf. on Articial Intelligence, pages 1045-1058, 1977.

....system or body of knowledge is described by a network of theories linked by interpretations. The little theories method is an old idea that has been used in mathematics since the late 1800s and has been advocated in recent years by a number of computer scientists for various purposes (e.g. see [1, 2, 5, 6, 7, 8]) The imps theorem proving system [3] supports the little theories method and contains a large database of traditional mathematics organized as a network of theories. Suppose that an intelligent agent is trying to solve a goal G in a some theory T within a theory network. How can an intelligent ....

R. Burstall and J. Goguen. Putting theories together to make specications. In Proceedings of the Fifth International Joint Conference on Arti- cial Intelligence, pages 1045-1058, 1977.

....IMPS In spite of its utility, the little theories 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 ....

R. Burstall and J. Goguen. Putting theories together to make speci- cations. In Proceedings of the Fifth International Joint Conference on Articial Intelligence, pages 1045-1058, 1977. 17

....in terms of colimits. Correspondence and o print requests to: Steven Vickers (sjv doc.ic.ac.uk) Gillian Hill (gah doc.ic.ac.uk) Department of Computing, Imperial College, London SW7 2BZ, UK. Steven Vickers and Gillian Hill A categorical semantics was given by Burstall and Goguen [BG77, BG79] for Clear: a language for writing structured speci cations. A Clear text denotes a many sorted theory; the structuring of theories is expressed by colimits in order to take account of shared sub theories. This has continued in work in the algebraic approach to speci cation [EM90, EFHLP87] and ....

....if g and 0 g are connected by a zigzag in the diagram D 0 , and this is the de nition of F F 0 . We have therefore proved that colim is equiv faithful. 3. Instances The use of colimits to build complex speci cations out of simpler ones dates back to the work of Burstall and Goguen [BG77] and Oriat [Ori96] has developed the use of diagrams to express these colimits. Our results of Section 2 show that these can equivalently be interpreted in terms of presheaves, but one might very reasonably question what has been achieved by this. Our goal in this section is to show that the ....

Burstall, R. M. and Goguen, J. A.: Putting Theories Together to Make Speci cations. Proceedings of the 5th. International Joint Conference on Articial Intelligence, Cambridge, Mass., pp. 1045-1058, 1977.

....can be speci ed separately and when composed give raise to complex systems. On the process of formalising systems speci cations Burstall and Goguen developed in a paper back in 1977 a new idea of describing individual components of systems by theories and putting them together to specify systems [BG77] This style goes very well with the intention of the object oriented paradigm as is shown in [FM92] where the authors use the same categorical approach for the speci cation of systems of interconnected components. Systems components, namely the objects, are described by 1 This work has been ....

R. Burstall and J. Goguen. Putting Theories Together to Make Specications. In R. Reddy, editor, Proc. Fifth International Joint Conference on Articial Intelligence, pages 1045-1058, 1977.

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Burstall, R.M., Goguen, J.A. Putting theories together to make speci cations. In Proceedings, Fifth International Conference on Arti cial Intelligence, 1977, 1045-1058.

....over inclusive institutions is studied in [9] but its modules do not hide information, and its notion of inclusion system is less general then the present one. This paper is another step in research on parameterized programming, begun in [10, 11] inspired by the Clear module system [3], and further developed in [18] and [9] Bergstra, Heering and Klint [1] axiomatize several operations on modules and prove certain properties, including a normalization theorem; unfortunately, rst order logic is built into their formalism for sentences, which limits the application of their ....

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

....BOBJ, it suces to transform signatures and equations, though the transformations are still rather complex. OBJ began around 1974 as a notation for algebraic speci cation, and was soon implemented as a term rewriting interpreter. Early designs [9] had a rst order module system like that of Clear [1], later formalized as parameterized programming [10] which added default views and simpli ed syntax. Parameterized programming was rst fully implemented in OBJ3 [16] extending earlier versions of OBJ, and it appears in all members of the OBJ family, including CafeOBJ [5] Maude [3] BOBJ ....

....and simpli ed syntax. Parameterized programming was rst fully implemented in OBJ3 [16] extending earlier versions of OBJ, and it appears in all members of the OBJ family, including CafeOBJ [5] Maude [3] BOBJ [14] and the European languages casl [4] and acttwo. Semantics follows that of Clear [1], using a category of theories, with theory morphisms for views, and colimit for module composition, based on ideas from an early category theoretic general systems theory [8] This semantics works over any logical system, using the formalism of institutions [13] Other languages in uenced by ....

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

....over inclusive institutions in studied in [10] but its modules do not hide information, and its notion of inclusion system is less general then the present one. We paper seems a natural next step in research on parameterized programming, as begun in [11, 12] inspired by the Clear module system [3], and further developed in [17] and [10] Bergstra, Heering and Klint [1] axiomatize several operations on modules and prove certain properties, including a normalization theorem; unfortunately, rst order logic is built into their formalism for sentences, which limits the application of their ....

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

No context found.

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

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