D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165--210, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....axiomatization of full abstractness presented in Section 5.1 and on Corollary 5.2 and Theorem 5.3. 3. On top of the observational logic institution, structured observational specifications can be defined by applying the institution independent specification building operators introduced in [37] and similarly in [6] Since the observational logic institution satisfies the amalgamation property, one can compute, following the construction in [6] for each structured observational specification, a normal form which consists (in general) of a basic observational specification restricted to ....

....would be satisfied as well. The proof of this fact relies on the infinitary axiomatization of reachability presented in Section 5.2 and on Corollary 5.10 and Theorem 5.11. 3. Of course, we can also build structured constructor based specifications by using the specification building operators of [37] or [6] and one can compute normal forms accordingto [6] 4. The functors #Obs associated to constructor based signatures # Obs can be extended to an institution encoding (see [39] which maps the institution of constructor based logic to the institution of standard first order logic. A ....

D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165--210, 1988.

....i.e. it is constructive as well as descriptive. Another unusual feature is the use of information hiding in specifications and the resulting behavioral (i.e. black box ) notion of sat isfaction for views. Similar basic laws for composing specifications were first proved in [GM82] and later in [ST88]. Material from the present paper appeared in [Tra97] and its full version may be found at www.cs.ucsd.edu users goguen ps will.ps.gz, which includes all the proofs omitted here. The next section describes some foundational concepts that are used throughout the paper. This is followed by two ....

Sannella, D. and Tarlecki, A. Specifications in an Arbitrary Institution. Information and Control, 76:165--210, 1988. Earlier version in Proceedings, International Symposium on the Semantics of Data Types, Lecture Notes in Computer Science, Volume 173, Springer, 1985.

....can be tuned as desired to cope with various programming features of interest by selecting the appropriate variation of algebra and signature. This flexibility has been formalized via the notion of institution [GB92] and related work on the theory of specifications and formal program development [ST88a,ST97,BH93] Casl is an algebraic specification language to describe Casl structures : many sorted algebras with subsorts, partial operations and predicates. Structures are classified by Casl signatures, which give sort names (with their sub sorting relation) partial total operation names, and ....

D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation 76:165--210 (1988).

....Cerioli and Meseguer [CM97] Cerioli [Cer93] Tarlecki [Tar96a] Mossakowski [Mos96] study relationships and translations between institutions. Much interesting work using institutions has been done by Tarlecki [Tar84, Tar86a, Tar86b, Tar86c, Tar87, Tar96a] and by Sannella and Tarlecki [ST86, ST87, ST88]. 1 On leave from Fundamentals of Computing, Faculty of Mathematics, University of Bucharest, Romania. As suggested by Goguen and Burstall [GB92] an institution can be regarded as a functor from its category of signatures to some special category. This more categorical view allows us to show ....

Donald Sannella and Andrzej Tarlecki. Specifications in an arbitrary institution. Information and Control, 76:165--210, 1988.

....achieving this is to require that no new observations are introduced for old sorts when composing systems via signature morphisms. Thus the observational logic institution provides a suitable framework for instantiating the institution independent specification building operators introduced in [18], hence for defining structured observational specifications. 3 The Constructor Based Logic Institution Reachability concepts are used to describe the underlying data manipulated by a program. For this purpose, a standard approach is to declare a distinguished subset OP Cons of the operation ....

....provide the necessary ingredients for defining an institution (cf. 5] which is called the constructor based logic institution. As in the observational case this institution provides a suitable framework for instantiating the institution independent specification building operators introduced in [18], hence for defining structured constructor based specifications. 8 4 A First Comparison The observational logic institution presented in Section 2 and the constructorbased logic institution presented in Section 3 were developed step by step in a totally analogous way. Indeed there is a close ....

D.T. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165--210, 1988.

.... of a general logic, and to generalize the Clear like operations to institutions [17,18] These ideas have had a great theoretical and practical im pact: see the bibliographies [3,16] the survey [24] and for sample references on logic independent specification building operations, e.g. [27,10,2,25]. Typically, theory composition operations begin with theories structured in some way for example, a diagram and result in an unstructured, or less structured, specification as their result for example, a colimit. That is, structured theories are often flattened when being composed. There ....

D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76(2/3):165--210, 1988.

.... EQ defined in Example 5, for D being class of all inclusions in the category of algebraic signatures, does not have the weak D amalgamation property (see Appendix B for details) 2 4 Specifications In the rest of the paper we will work with specifications similar to specifications defined in [ST 88] As in [ST 88] we assume that software systems described by specifications are adequately represented by models of institutions. This means that a specification must describe a signature and a class of models over this signature. We call this class the class of models of the specification. ....

.... in Example 5, for D being class of all inclusions in the category of algebraic signatures, does not have the weak D amalgamation property (see Appendix B for details) 2 4 Specifications In the rest of the paper we will work with specifications similar to specifications defined in [ST 88] As in [ST 88] we assume that software systems described by specifications are adequately represented by models of institutions. This means that a specification must describe a signature and a class of models over this signature. We call this class the class of models of the specification. For any ....

D. Sannella, A. Tarlecki. Specifications in an Arbitrary Institution. Information and Computation, volume 76, pages 165--210, 1988.

....achieving this is to require that no new observations are introduced for old sorts when composing systems via signature morphisms. Thus the observational logic institution provides a suitable framework for instantiating the institution independent specification building operators introduced in [18], hence for defining structured observational specifications. 3 The Constructor Based Logic Institution Reachability concepts are used to describe the underlying data manipulated by a program. For this purpose, a standard approach is to declare a distinguished subset OP Cons of the operation ....

....provide the necessary ingredients for defining an institution (cf. 5] which is called the constructor based logic institution. As in the observational case this institution provides a suitable framework for instantiating the institution independent specification building operators introduced in [18], hence for defining structured constructor based specifications. 4 A First Comparison The observational logic institution and the constructor based logic institution were developed step by step in a totally analogous way. Indeed there is a close correspondence between all notions of the ....

D.T. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165--210, 1988.

....for specifications; in fact, this was a major motivation [5, 27, 29] among many papers on this topic, we mention [18, 33] and [56] which all add inclusion systems to institutions. Much other interesting work with institutions has been done by Tarlecki [62, 63, 64, 65, 67] Sannella and Tarlecki [58, 59, 60], Cerioli [7] Mossakowski [45] and Diaconescu [19, 14, 15] among others; 67] in particular is an important paper with goals and results similar to those of this paper. Burstall and Diaconescu [4] generalize hiding from algebra to an arbitrary institution, and apply this to both many sorted ....

....iff the functor Mod : Sign Cat op preserves the pushouts 7 , i.e. it takes pushouts in Sign to pullbacks in Cat. Xi The term semiexactness was introduced in [18] as a weakening of exactness, which says that Mod preserves general colimits; exactness seems to have first appeared in [60], and was used by Tarlecki [63] on abstract algebraic institutions and by Meseguer [43] on general logics. Although many sorted logics tend to be exact, their unsorted variants tend to be only semiexact. The category of theories, Th, inherits many properties from Sign. One of the most important of ....

Donald Sannella and Andrzej Tarlecki. Specifications in an arbitrary institution. Information and Control, 76:165--210, 1988.

....which is allows one to split theories into different parts while preserving as much proof work as possible. 7. Related Works There is a countless number of work concerned with the definition and the semantics of structured (or compound) theories and how to use this structure in proof search (e.g. [4, 16, 7, 9, 17, 11]) 17] for instance, consider proof search in a structured theory presentation. They present a basic machinery of a language of structured theory presentations that allows one to put logics together in the same way as the structured theory presentations provides the machinery for putting ....

D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76(2/3):165--210, 1988.

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D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165-210, 1988.

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D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165--210, 1988.

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D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation 76:165--210 (1988).

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D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation 76:165--210 (1988).

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D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165-210, 1988.

....can be tuned as desired to cope with various programming features of interest by selecting the appropriate variation of algebra and signature. This flexibility has been formalized via the notion of institution [GB92] and related work on the theory of specifications and formal program development [ST88a,ST97,BH93] However, rather than exploiting the full generality of institutions, to keep things simple and illustrative we will in this paper base our considerations on a very basic logical framework, leaving to a more extensive presentation elsewhere the required generalization and adaptation to ....

.... ) Sig(SP 2 ) and Mod (SP 1 and SP 2 ) Mod (SP 2 ) So, specifications can for instance be basic specifications, given by a signature and a set of axioms (sentences) over this signature; or structured specifications built over the institution we have implicitly introduced above as defined in [ST88a] or structured specifications built using more advanced structuring mechanisms such as those of Casl [ABK 03] 3 Program Development and Refinements In this section we briefly recapitulate our view of the process by means of which software can be formally developed from an algebraic ....

D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation 76:165--210 (1988).

.... Sigma , Sigma . If SP is a flat specification then Mod(behaviour SP w:r:t: and Mod(behaviour SP w:r:t: coincide by Theorem 3.35. But for structured specifications they do not coincide in general. Methods for reasoning about structured specifications see e.g. the inference rules in [ST88a] apply to the second interpretation but appear to be inapplicable to the first. Further research is required to clarify the relationship between abstractor specifications (which generalize easily to structured specifications) and this alternative interpretation of behavioural specifications. ....

D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation 76:165--210 (1988).

....6= parameterised program) specification In Sections 5 and 6, the technical and methodological consequences of extending parameterisation to the higher order case are considered. Section 7 presents a specification formalism built on the institution independent kernel specification language in [ST 88a] which supports the specification of arbitrarily high order parameterised programs, as well as extending the mechanism in [ST 88a] for defining first order parameterised specifications to the higher order case. This section is based on a more extensive presentation of this formalism in [ST 91a] ....

....to the higher order case are considered. Section 7 presents a specification formalism built on the institution independent kernel specification language in [ST 88a] which supports the specification of arbitrarily high order parameterised programs, as well as extending the mechanism in [ST 88a] for defining first order parameterised specifications to the higher order case. This section is based on a more extensive presentation of this formalism in [ST 91a] Finally, Section 8 contains conclusions and some ideas for future work. 2 Preliminaries Throughout the paper we assume that the ....

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Sannella, D. and Tarlecki, A. Specifications in an arbitrary institution. Information and Computation 76, 165--210 (1988).

....operations may essentially be given in an arbitrary institution, so the specification structuring mechanisms of Casl make sense as long as the semantics of basic specifications is based on an institution. This is much as in earlier approaches to specifications in an arbitrary institution, cf. [67], where the semantics of specification building operations is given in terms of the constructions available in an arbitrary institution (with a prominent role played by reduct functors induced by signature morphisms, and by the categorical structure of model classes) The only exception in Casl ....

....structure of model classes) The only exception in Casl to strict institution independence is the way names and their maps (forming signature morphisms) are handled. The standard notion of an institution of [30] and consequently the specification building operations described e.g. in [67], take signature morphisms for granted. With the emphasis in Casl on the use of names of symbols (the same name, same thing principle discussed above) this is not su#cient. Therefore, we work with 19 institutions with symbols [47] which are institutions additionally equipped with a proper ....

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Donald Sannella and Andrzej Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76, pages 165--210, 1988.

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D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165--210, 1988.

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D. Sannella and A. Tarlecki. Specification in an arbitrary institution. Information and Computation, 76:165--210, 1988.

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D. T. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76(2/3):165--210, Feb/Mar 1988.

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D. Sanella and A. Tarlecki. Specifications in an arbitrary institution", Journal of Information and Computation, pages 165--210, 1998

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Donald T. Sannella and Andrzej Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76(2/3):165--210, 1988.

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Donald Sannella and Andrzej Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165--210, 1988.

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