Donald Sannella and Andrzej Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Sigma will denote a s oriented S sorted signature which can be equally represented by the set of operator symbols foe1; oerg, r 1, where 8i 1 i r; oei has type hwi; si where wi 2 S and wi = wi 1 ; wi n i with n i 0. Let us now see an example (which were inspired by [ST95] illustrating all these previous definitions. Example 5 The set of sorts will be the following: S = fshape; suitg. 72 Let us define a S Theta S indexed set Sigma by: Sigma = f Sigma ffl;shape ; Sigma ffl;suit ; Sigma shape;shape ; Sigma shape suit;suit g in which: Sigma ffl;shape = ....

D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge University Press, (to appear) 1995.

....such a framework describe the intended models via the use of axioms and of an extra logical notion, stating which (non necessarily proper) subclass of the algebras satisfying the axioms has to be taken in account. A number of survey of the field of algebraic specifications have been produced, e.g. [328, 402, 842, 942] In [841] Sannella and Tarlecki provide a summary overview of the model theoretic foundations of program specification and formal software development, with emphasis on the basic motivations behind the technicalities presented elsewhere rather than on providing new results. Loose Semantics The ....

....as a means of using algebraic technology in the programming of parallel computers. The approach was sketched and compared with other parallel programming models in [464, 468, 465] and [624] relates Sapphire to Standard ML. Program development in Sapphire supports the methodology advocated in [842]. A sequential prototype compiler now exists for the language, and a parallellising version is expected to be available in 1997. 4.1.3 Theoretical Background Termination of rewrite systems. Proving termination of rewrite systems is an important issue. A promising method is based on ....

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D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge University Press, 1996. To appear. \Phi.

....The result shows that no confusion is equivalent to a variation of the property of hierarchy consistency that makes use of conditional equations. Support tools In this area some work has been done in Barcelona in automated theorem proving. In particular, in our previous work [4] and [5] we have shown that ordering and equality constraints can indeed be extremely useful in theorem proving with first order (constrained) clauses with equality. More precisely, by means of equality constrained clauses, we proved the completeness of basic superposition: a restricted form of ....

....T. Rus and G. Scollo (eds) Springer Workshops in Computing (1993) 211 218. 4] Robert Nieuwenhuis and Albert Rubio. Basic superposition is complete. In B. KriegBr uckner, editor, European Symposium on Programming, LNCS 582, pages 371 390, Rennes, France, February 26 28, 1992. Springer Verlag. [5] Robert Nieuwenhuis and Albert Rubio. Theorem proving with ordering constrained clauses. In Deepak Kapur, editor, 11th International Conference on Automated Deduction, LNAI 607, pages 477 491, Saratoga Springs, New York, USA, June 15 18, 1992. Springer Verlag. 6] Fernando Orejas, Marisa ....

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D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge University Press, in preparation.

....[58] where the emphasis is almost entirely on syntax and formal systems of rules, and semantic models are absent or regarded as of secondary importance. The past 25 years has seen a great deal of research on the theory and practice of algebraic specification. Overviews of this material include [5,9,13,41,68,69,76]. Developments on the foundational side have been balanced by work on applications, but despite a number of success stories, industrial adoption has so far been limited. The current proliferation of algebraic specification languages is seen as a significant obstacle to the dissemination and use of ....

Donald Sannella and Andrzej Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear.

....[35] where the emphasis is almost entirely on syntax and formal systems of rules and semantic models are absent or regarded as of secondary importance. The past 25 years has seen a great deal of research on the theory and practice of algebraic specification. Overviews of this material include [47,6,8,23,41,3,42]. Developments on the foundational side have been balanced by work on applications, but despite a number of success stories, industrial adoption has so far been limited. The proliferation of algebraic specification languages is seen as a significant obstacle to the dissemination and use of these ....

Donald Sannella and Andrzej Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear. 43

....between an algebra or program and a specification. An idea oriented presentation of almost all of this material, with examples, can be found in [ST97] and this presentation is based on that. See [ST88] SST92] BST99] and the references in [ST97] for a more technical presentation. Someday [ST ] will contain a unified presentation of the whole picture and at that point everybody reading this must immediately go out and buy it. Until then, other starting points for learning about algebraic specification are [Wir90] LEW96] and [AKK99] 2 Simple refinement Given a specification SP , the ....

D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear.

....[Gor86] When multiple institutions are applied in the construction of a single system, some way of relating the institutions to each other is required. There are several ways of relating institutions; the one that seems most relevant for this purpose is the concept of institution semi morphism [ST94] (cf. semi institution morphisms in [ST88] Informally, an institution semi morphism maps the models of one institution to those of another; the direction of the map is from the richer , more detailed institution to the poorer , less detailed and hence more abstract one. This model translation ....

D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear (1994).

....syntax and formal systems of rules while semantic models are absent or regarded as of secondary importance. The past 25 years has seen a great deal of research on the theory and practice of algebraic specification. Overviews of this material include [Wir90] BKLOS91] LEW96] ST97] AKK99] and [ST ]. Developments on the foundational side have been balanced by work on applications, but despite a number of success stories, industrial adoption has so far been limited. The proliferation of This research was supported by the ESPRIT funded CoFI Working Group. algebraic specification ....

D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear.

.... is quite general, as both the structural requirements imposed implicitly (like the functoriality of translations of sentences and reducts of models along signature morphisms) and explicitly (the satisfaction condition) are rather obvious and are indeed satisfied by the usual logical systems (see [ST9 ] for further detailed analysis) Here are a few examples: The institution EQ of equational logic: Signatures are the usual many sorted algebraic signatures; sentences are (universally quantified) equations with translation along a signature morphism defined essentially by replacing the operation ....

....semantic interpretation than more poor models of the institution I. An institution semi morphism fl: I 0 semi I extracts then simpler I signatures out of more complex I 0 signatures and simpler I models out of more complex I 0 models. Let us sketch two examples (omitting the details [ST9 ]) fl FOEQ EQ : FOEQ semi EQ: This archetypical institution semi morphism extracts algebraic signatures out of first order signatures (by throwing away predicate symbols) and then algebras out of first order structures (by disregarding the interpretation of predicates) fl PLNG PFOEQ : PLNG ....

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Sannella, D., Tarlecki, A.: Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear; see http://zls.mimuw.edu.pl/~tarlecki/book/index.html.

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D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge University Press. To appear.

....this paper can be viewed merely as a presentation of a necessary but preliminary work preceding a more subtle and technically involved but similar treatment of parchments (perhaps with some notion of context) and various mappings between them corresponding to various mappings between institutions. [ST9 ], Mos95] provide some initial results in this direction. ....

D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear; see http://zls.mimuw.edu.pl/~tarlecki/book/index.html.

....various infinitary and higher order logics, logical systems for partial, regular, continuous, order sorted algebras, etc, may be presented as institutions and typically equipped with standard entailment systems. We refer to [ Tarlecki, 1998 ] for details of a few standard examples and to [ Sannella and Tarlecki, 1999 ] for many more, including non standard examples presenting for instance a semantic view of a simple programming language as an institution. 2.1 Institutions with extra structure The notion of institution is very general and imposes only very light requirements on the logical system to be ....

Donald Sannella and Andrzej Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge University Press, 1999. To appear.

....Extended ML (EML) specification framework [San 91, KST 96] Since the emphasis here is on motivation and intuition, citations to the literature refer the interested reader to papers where complete technical details may be found. These topics are also covered in detail in a forthcoming monograph [ST 9 ] For readers who prefer even less detail, the material in Sections 3.1, 8.1 and 9.1 may be skipped on first reading. 1 The logical framework The overall aim of work on algebraic specification is to provide semantic foundations for the development of programs that are correct with respect to ....

....of equations Phi entails an equation , written Phi j= if every algebra that satisfies all the equations in Phi also satisfies . Here is a simple example, where a signature is accompanied by a list of equational axioms, presented using a hopefully self explanatory notation: sorts nat ; list opns 0 : nat succ : nat nat nil : list cons : nat Theta list list head : list nat tail : list list axioms 8x:nat : 8l:list : head(cons(x; l) x 8x:nat : 8l:list : tail (cons(x; l) l For example now: 8x:nat : 8l:list : head(cons(x; l) x; 8x:nat : 8l:list : tail (cons(x; l) l ....

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D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear (199?).

....clearly our current views on the role of behavioural equivalence in the development process. Since the emphasis here is on motivation and intuition, we refer the interested reader to the papers we have published on these and related topics over the last few years and to a forthcoming monograph [ST 93] for the corresponding technical details. 1 To appear in Proc. 19th Intl. Colloq. on Automata, Languages and Programming, Vienna. Springer LNCS (1992) 1 The logical framework The overall aim of work on algebraic specification is to provide semantic foundations for the development of ....

D. Sannella and A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear (1993?).

.... is quite general, as both the structural requirements imposed implicitly (like the functoriality of translations of sentences and reducts of models along signature morphisms) and explicitly (the satisfaction condition) are rather obvious and are indeed satisfied by the usual logical systems (see [ST9 ] for further detailed analysis) Here are a few examples: The institution EQ of equational logic: Signatures are the usual many sorted algebraic signatures; sentences are (universally quantified) equations with translation along a signature morphism defined essentially by replacing the operation ....

....interpretation than more poor models of the institution I. An institution semi morphism fl : I 0 semi I extracts then simpler I signatures out of more complex I 0 signatures and simpler I models out of more complex I 0 models. Let us sketch two examples (omitting the details [ST9 ]) fl FOEQ EQ : FOEQ semi EQ: This archetypical institution semi morphism extracts algebraic signatures out of first order signatures (by throwing away predicate symbols) and then algebras out of first order structures (by disregarding the interpretation of predicates) fl PLNG PFOEQ : PLNG ....

[Article contains additional citation context not shown here]

Sannella, D., Tarlecki, A.: Foundations of Algebraic Specifications and Formal Program Development. Cambridge Univ. Press, to appear; see http://zls.mimuw.edu.pl/~tarlecki/book/index.html.

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