Burstall, R. and Goguen, J. "The Semantics of Clear, a Specification Language". In Lecture Notes in Computer Science, Spring Verlag, 1980. Proc. of Advanced Course on Abstract Software Specifications  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to the .lse of attributions, so th,t the semantic ambiguities and some of the inadequacies of semantics networks [4] are resolved. Omega is based on descriptions, which are a generalization of the notion of type as used in programming languages [26, 16, 12] and in program specification fbrmalisms [5, 10]. Descriptions are also closely related to sets, indeed their semantics is given in term of sets of individuals. Omega is a calculus of descriptions rather then a calculus of predicates as ordinary logic. l]e concept of dcscriptk)n in logic, and in particular (4 ,leftnile descrctions, can be ....

Burstall, R. and Goguen, J. "The Semantics of Clear, a Specification Language". In Lecture Notes in Computer Science, Spring Verlag, 1980. Proc. of Advanced Course on Abstract Software Specifications

....specifications Property oriented approaches are often based on abstract data types and the most popular approaches are based on algebraic semantics . Algebraic specifications denote indeed a lot of different specification languages (LARCH [GH86] ASL [SW83] Wir86] PLUSS [Gau92] CLEAR [BG80][San84] OBJ [FGJM85] ACT ONE ACT TWO [EM85] and an incredible number of different specification theories. The paradigm of algebraic specifications is rather a 1 Consistency is not decidable in general but there are usually usable sufficient conditions to ensure consistency. 4 way of ....

Burstall R.M., Goguen J.A. : "The semantics of CLEAR, a specification language." Advanced Course on Abstract Software Specifications, Copenhagen, Springer-Verlag LNCS 86, p.292-332, 1980.

....be instantiated with specific programs. In WRIGHT [1] role instantiation has to obey a compatibility requirement (expressed via a refinement relation) which in COMMUNITY is again captured via morphisms. Hence, role instantiation can be performed in much the same way as in algebraic specifications [3] through a fitting morphism. An example of instantiation is the following: producer consumer read produce send send sval sval ready ready get get rval rval b b reader writer with programs reader and writer defined as follows: program reader is ### val : elem, ready : bool #### r : ....

....the expressive power of the proposed notion of connector, namely in relation to notions of parameterisation closer to algebraic specifications. There are several forms of parameterisation that have been proposed in the literature [17] In this paper, we take what has been called the Clear style [3]. Parameterisation in this simple style can be characterised by a morphism (connecting the formal parameter to the body of the parameterised specification) Like for connectors, the instantiation of the parameter is established via a (fitting) morphism from the formal to the actual parameter. The ....

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. R.Burstall and J.Goguen, "The Semantics of CLEAR, a Specification Language", in Proc. Advanced Course on Abstract Software Specification, LNCS 86, SpringerVerlag

....operation over the parameter type is required. A typical example of this would be the definition of a polymorphic type of ordered lists of a, where we should require that any possible instance of a is equipped with an ordering relation. Conversely, algebraic) specification languages (see e.g. BG 80] traditionally provide generic or parameterized constructs without this kind of limitations. The idea is that generic constructs are parameterized by specifications (i.e. sorts, operations and even axioms) and not just by sorts. However, in these languages, if one wants to use an instance of a ....

#Burstall, R.M.; Goguen, J.A.: "The semantics of Clear, a specification language", Proc. Copenhagen Winter School on Abstract Software Specification, Springer LNCS 86, pp. 292-332, 1980.

....rle as standard inheritance in O O design. A similar conclusion can also be found in [Gog 91] This relationship is one of the bases of Glider, the specification language of the ICARUS project. Being specific, Glider is an algebraic specification language following the tradition of Clear [BG 77, BG 80] Its basic construction is the Cluster for defining new types and operations. As usual, clusters may be parameterized. The logic underlying Glider is, essentially, first order partial logic. However, the language provides some additional constructions that increase its expressive power, such as ....

....T, including a sort of interest t and a set of operations Op. Furthermore, let us assume that T is an extension of clusters T1, Tn. Then the semantics of T is defined as follows: At the specification level Let (S , Ax ) be the result of putting together (technically, a colimit, as in [BG 80] the presentations denoted by T1, Tn and let C be the result of putting together the corresponding sets of constraints, then the meaning of T, T] Spec , consists of the presentation (S, Ax Ax) where S is the signature obtained enriching S by the new sort t and operations, i.e. S = ....

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Burstall, R.M.; Goguen, J.A.: "The semantics of Clear, a specification language", Proc. Copenhagen Winter School on Abstract Software Specification, Springer LNCS 86, pp. 292-332, 1980.

.... next(q) converts next, rest, isEmpty, 2 exempting next(new) rest(new) Unlike the preceding traits in this section, PriorityQueue specifies an abstract data type constructor. In such a trait there is a distinguished sort, sometimes called the type of interest [Guttag 1975] or data sort [Burstall and Goguen 1980]. An abstract data type s operators can be categorized as generators, observers, and extensions (sometimes in more than one way) A set of generators produces all the values of the distinguished sort. The extensions are the remaining operators whose range is the distinguished sort. The observers ....

....and to check, so we have dropped them from the language. In many respects, LSL is distinguished from other specification languages as much by what it doesn t include as by what it does. LSL provides no construct for hiding operators. The hiding constructs of other specification languages [e.g. Burstall and Goguen 1980] allow the introduction of auxiliary operators that don t have to be implemented. These operators are not completely hidden, since they must be read to understand the specification, and they are likely to appear in reasoning based on the specification. The two tiered structure of Larch ....

R.M. Burstall and J.A. Goguen, "Semantics of CLEAR, a Specification Language," Proc. Advanced Course on Abstract Software Specifications, D. Bjorner (ed.), Springer-Verlag Lecture Notes in Computer Science 86, pp. 292--332, 1980.

....ECC. The approach to theory abstraction adopted in this paper (section 5) may be called theories as types , particularly, as Sigma types. Another approach to theory structuring in proof development [SB83] BLuo88] borrows the idea from researches in algebraic specification languages like Clear [BG80]. This later approach may be called theories as values , as there are theory operations to put theories together in structured theory development. Although the type hierarchy in ECC enables us to view Sigma types (hence, theories) as a sort of values, it seems not flexible enough to have ....

R.Burstall and J.Goguen, `The Semantics of CLEAR, a Specification Language', LNCS 86.

....of a required structure (ring in this case) are more complicated, this is desirably useful to make proof development structured. Remark There are several different ways to control structure sharing which appear in programming and specification languages ML [HMM86] Mac86] Pebble [LB88] and Clear [BG80] (see [Bur84] for a simple explanation) Although propositional equality (e.g. Leibniz s equality) can be defined in Constructions, it can not be used to express sharing constraints in the style of ML, as Thierry Coquand pointed out to the author. 2 4.4 Discussion We have shown above that the ....

....to theory abstraction discussed above adopts a view of theories as types . More precisely, abstract theories are expressed as Sigma types. There is another approach to theory structuring [SB83] BLuo88] HST89] borrowing an idea from research in algebraic specification languages like Clear [BG80]. This latter approach may be called theories as values , as there are theory operations to put theories together . In the AUTOMATH project, ideas like telescope of organizing mathematical texts through manipulating contexts were informally studied [dB80] Zuc75] Thanks to a referee for ....

R. Burstall and J. Goguen, `The Semantics of CLEAR, a Specification Language', Lecture Notes in Computer Science 86.

....suitable type theories may be viewed as programming logics in which one can describe and reason about program specification and program development. Program specifications have been studied quite extensively in computer science (for example, algebraic specification languages like Clear [BGog80], Act1 [EFH83] OBJ [FGJM85] and ASL [ST88] In type theory, a specification may be formulated as a type. In particular, Sigma types provide a nice mechanism for describing program specifications. For example, a specification of sorting programs for lists of natural numbers can be expressed as ....

....be used to express information hiding. Three existing ways to handle the problem of structure sharing are simply explained in [Bur84] which are: sharing by equation in Standard ML [HMM86] Mac86] sharing by parameterization in Pebble [BLam84] LB88] and INTRODUCTION 9 sharing by history in Clear [BGog80]. In particular, rich type structures play an essential role in the second style as we shall explain in section 8.3. In interactive theorem proving systems, a notion of theory is needed to structure proof development. Burstall et al. considered how a notion of theory can be used to structure ....

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R. Burstall and J. Goguen, `The Semantics of CLEAR, a Specification Language', Lecture Notes in Computer Science 86.

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Burstall, R. M. and Goguen, J. A. (1980), "The Semantics of Clear, a Specification Language ", in Proc. Advanced Course on Abstract Software Specifications, Lecture Notes in Computer Science , No. 86, Springer-Verlag, (also Report CSR-65-80, Department of Computer Science, University of Edinburgh).

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