W.M. Turski and T.S.E. Maibaum. The Specification of Computer Programs. Addison-Wesley, London, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... ontologies [12, 13] This paper will study a particular kind of change, namely refinement (and its opposite process, abstraction) These concepts are known from the area of software engineering, together with the underlying concept of a conservative extension, where they play a prominent role [16]. Conservativity of extension guarantees that the details added in the development process of software speci fications are non corrupting (the exact meaning will be discussed in a subsequent section) More pertinent for modern software systems is the fact that the conservative extension ....

....purpose. An important aspect of this methodology is its view of what it means for one specification S to be a refinement of another S. One interpretation of this relationship, for instance, is that S is an implementation of S, so S has more detail than S. Influential work by Turski and Maibaum [16] advocated the idea that this be modelled in two steps: i) regard S and S as logical theories, and (ii) let S be a conservative extension of S. Formally we say that S (where S C S ) is a conservative extension of S if the formulae that follow from S and can be expressed in the language of S are ....

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W.M. Turski and T.S.E. Maibaum. The Specification of Computer Programs. Addison-Wesley 1987.

....of this paper is to amplify those remarks. What is Specification Fundamentally, a specification must attempt to capture the relation between the computer system and the real world, for that relation is what gives meaning to the electronic bit manipulations. In the words of Maibaum and Turski [8], the specification binds together a program and its application. Of course, the real world is ultimately informal, so that no formal system can ever truly bind to it. Nonetheless, in writing our specification we should attempt to formalize as best we can the application domain, that is to say ....

....over S . 5 Conclusions The ideas presented here plainly have several radical differences from the conventional view of Z as set out in Brien and Nicholls [1] To mention first one of the less obvious, we have adopted rather fundamentally the idea of specification as theory presentation ([8]) Hence, whatever you think makes a good semantics of theories (and we have implicitly used categorical logic and classifying toposes) should also be the semantics for specifications. This provides an broad mathematical rationale for the semantic account. A second difference from the Z standard ....

W. Turski and T. Maibaum. The Specification of Computer Programs. AddisonWesley, 1987.

....in progress but the availability of a theory that is coherent, complete in some sense and satisfying, is some way off. Defn. An S type program is an executable model of a formal theory termed its specification [8] Defn. An S type program is also termed an implementation of the specification [17,18]. Defn. For an S type program to be correct, all the properties stated or implied by its specification are properties of the program. Defn. Verification is a demonstration that a program satisfies its specification, that it is correct. Note 1 Interest in S type programs reflects a belief that ....

Turski WM and Maibaum T, The Specification of Computer Programs, Addison Wesley, London, 1987, p. 278

.... ontologies [12, 13] This paper will study a particular kind of change, namely refinement (and its opposite process, abstraction) These concepts are known from the area of software engineering, together with the underlying concept of a conservative extension, where they play a prominent role [16]. Conservativity of extension guarantees that the details added in the development process of software specifications are non corrupting (the exact meaning will be discussed in a subsequent section) More pertinent for modern software systems is the fact that the conservative extension criterion ....

....An important aspect of this methodology is its view of what it means for one specification S # to be a refinement of another S. One interpretation of this relationship, for instance, is that S # is an implementation of S, so S # has more detail than S. Influential work by Turski and Maibaum [16] advocated the idea that this be modelled in two steps: i) regard S and S # as logical theories, and (ii) let S # be a conservative extension of S. Formally we say that S # (where S # S # ) is a conservative extension of S if the formulae that follow from S # and can be expressed in the ....

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W.M. Turski and T.S.E. Maibaum. The Specification of Computer Programs. Addison-Wesley 1987.

....comparison on 1. Introduction 4 different database systems. Finally, two dimensional tables are N ary relations. N ary relations sometimes make it very difficult to compute across networks. The algebra of n ary relations is not as simple and intuitive as Thski s rules for binary relations [15]. 1.2.3 How to Use Binary Relations Any information stored as an N ary relation can be viewed as a set of binary relations. For instance, from the relation (product name, product ID, price) we can determine a few binary relations, such as (product name, product ID) and (product ID, price) The ....

W. M. Thski and T. S. E. Maibaum. The Specification of Computer Programs. Addison-Wesley Publishing Company, 1987.

....ordering on functions to obtain higher recall. We could use different transformation functions and or define different orderings on function signatures that would tradeoff precision and recall. Also, more generally, we could define orderings on specifications; viewing specifications as theories [20], for example, we could use theory inclusion as an ordering relation. We also observe that were we to have higher order unification with equality then we would have a more expressive specification language. Work on combining first order Horn clause logic with equality, e.g. as in Eqlog [5] is a ....

W. M. Turski and T. S. E. Maibaum. The Specification of Computer Programs. Addison-Wesley, 1987. 19

....to be shown to constitute a category whose morphisms correspond to property preserving translations between their languages. These translations or mappings are also known as interpretations between theories, and have been used to model relationships between abstract and concrete specifications [25], or to model mappings between different notions of software architecture [23] We adopt a temporal logic with a (global) discrete linear time structure similar to those used in [21] since this allows easier assessment of the support for modular specification that is described. We also use the ....

W. M. Turski and T. S. E. Maibaum. The Specification of Computer Programs. Addison-Wesley, 1987. This article was processed using the L A T E X macro package with LLNCS style

....from smaller theories [3, 7, 30] A theory morphism translates the language of one theory into the language of another theory in a way that preserves theorems. Theory morphisms underlie several aspects of software development, including specification refinement and datatype implementation [5, 27, 30, 51], the binding of parameters in parameterized theories [9, 15] algorithm design [22, 43, 52] and data structure design [32] There has been work on techniques for composing implementations in a way that reflects the structure of the source specification [3, 30] however these composition ....

Turski, W. M., and Maibaum, T. E. The Specification of Computer Programs. Addison-Wesley, Wokingham, England, 1987.

....sciences [shr90] The basis for axiomatic theory development as epitomised by Euclidean geometry and used for many centuries in the mathematical and physical sciences is well established. So is the application of formal methods and of the many representations and logics in computer science [tur87]. Success in the investigation will require access to the appropriate knowledge, understanding and experience to all these approaches through the co ordinated work of an international team with expertise in the various related fields. 8. Final Remarks The research hypothesis is that the software ....

Turski WM and Maibaum T, The Specification of Computer Programs, Addison Wesley, London, UK, 1987, p. 278

....8X(t 6= X) 2 S, then t = err 2 S. D. If : A 2 S, then A 2 S (D. If : A B) 2 S, then A; B 2 S (D. If A B 2 S, then either :A 2 S or B 2 S (D. 8) If :8XA(X) 2 S and :8XA(X) 6j 9X(X = t 0 ) for some term t 0 , then, for some term t, A(t) 9X(X = t) 2 S. 24 Turski and Maibaum [TM87], p. 175, write: It seems that the crucial requirement to establish the (Modularization Theorem) is that the Craig Interpolation Lemma holds in the linguistic system. See also [Vel93] 25 In our definition of a model set, we follow the conventions in [Gum79a] pp. 37 38, and [Gum84] p. ....

Wladyslaw M. Turski and Thomas S. E. Maibaum. The Specification of Computer Programs. Addison-Wesley, Workingham, England, 1987.

....on classes. These predicates are expressed in terms of the operators 2 (always) 3 (eventually) and flflfl (next) To reason about such properties, the logic for Object Z needs to be extended to include rules for these operators. This could be done as in the Appendix of Turski and Miabaum[12] which describes the extension of predicate logic to include the modal operators 2 and 3 . 2 is introduced by the distribution axiom and rule of necessitation ( Distribution ) 2 (p ) q) 2 p ) 2 q) p ( Necessitation ) 2 p and 3 is defined in terms of 2 as follows. 2 p , 3: p ....

W.M. Turski and T.S.E. Maibaum. The Specification of Computer Programs. AddisonWesley, 1987.

....the usual terminology and notation for logical concepts, for which the reader is referred to standard textbooks ( End72, Sho67] 2 Constructs for introducing new sorts A specification describes (properties of) some objects expressed in some specific language. Following the logical approach ([Vel87, TM87]) we shall formulate the specifications within the formalism of first order logic. Thus, a specification is an axiomatic presentation of a theory in many sorted first order logic and the properties described by such specification are the consequences of the presentation. The semantics of the ....

....is not extensively studied. The four constructs examined correspond to natural constructions of new sets. Three of them have found their way as data structuring constructs in programming languages [Hoa74] The quotient construct is of importance in developing and verifying correct implementations [TM87, Vel87]. In [VM94] we have analised them as parameterised formal specifications of data types. In logical terms, each parameterised specification amounts to a presentation of a theory in the extended language which is a conservative extension of its parameter (a presentation of the theory of the old ....

W.M. Turski and T.S.E. Maibaum. The Specification of Computer Programs. Addison-Wesley Publishing Company, 1987.

.... which can be abstracted to axioms introducing the new sorts and capturing (some of) the socalled representation invariants [20, 23] With this abstraction in mind, we are ready to describe this situation in terms of formal specifications, ie, logical theories presented by (finite sets of) axioms [44, 41]. One expands the language of the concrete specification T by adding symbols to correspond to the abstract ones in S, perhaps together with some auxiliary symbols, and extends T to M by adding extension axioms which are sentences in the extended language. Since one does not want to disturb the ....

....one theory interpretation i ff :S M and a conservative extension e ff :T M, which share a common target M, called the mediating specification. An implementation ff = hi ff ; e ff i of S on T is depicted as an implementation triangle below, and is often called a canonical implementation step [41]. S M ff T i ff e ff ff In stepwise development, it is highly desirable to be able to compose refinement steps in a natural way. Given an implementation ff, of S on T 1 followed by an implementation fi of T 1 on T 2 , one would like to compose these implementations in an easy and natural ....

W. M. Turski and T. S. E. Maibaum. The Specification of Computer Programs. Addison-Wesley, 1987.

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Turski, W.M. and Maibaum, T.S.E. (1987) The Specification of Computer Programs. Addison-Wesley, Wokingham.

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W.M. Turski and T.S.E. Maibaum. The Specification of Computer Programs. Addison-Wesley, London, 1987.

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Turski, W., Maibaum, T.: The Specification of Computer Programs. AddisonWesley (1987)

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W.M. Turski and T.S.E. Maibaum. The Specification of Computer Programs. Addison-Wesley, London, 1987.

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Turski, W., and T. Maibaum, Specification of Computer Programs, Addison-Wesley Longman Publishing, Boston, 1987.

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TURSKI, W.M. and MAIBAUM, T.: 'The Specification of Computer Programs', Addison Wesley, London, 1987, p. 278)

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Turski WM and Maibaum T, The Specification of Computer Programs, Addison Wesley, UK, 1987, 278 pps.

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W. M. Turski, T.S.E. Maibaum, "The Specification of Computer Programs ", Addison-Wesley, 1987.

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Turski, W. M., and Maibaum, T. S. E, 1987, "The Specification of Computer Programs", Addison-Wesley.

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Turski WM, and Maibaum T, The Specification of Computer Programs, Addison Wesley, London, 1987, p. 278

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W.Turski and T.Maibaum, The Specification of Computer Programs, Addison-Wesley 1987

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Turski WM, and Maibaum T, The Specification of Computer Programs, Addison Wesley, London, 1987, p. 278

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