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Investigating Z
, 2000
"... In this paper we introduce and investigate an improved kernel logic ZC for the specification language Z. Unlike the standard accounts, this logic is consistent and is easily shown to be sound. We show how a complete schema calculus can be derived within this logic and in doing so we reveal a high de ..."
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Cited by 11 (4 self)
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In this paper we introduce and investigate an improved kernel logic ZC for the specification language Z. Unlike the standard accounts, this logic is consistent and is easily shown to be sound. We show how a complete schema calculus can be derived within this logic and in doing so we reveal a high degree of logical organisation within the language. Finally, our approach eschews all nonstandard concepts introduced in the standard approach, notably object level notions of substitution and entities which share properties both of constants and variables. We show, in addition, that these unusual notions are derivable in ZC and are, therefore, unnecessary innovations. Keywords: Specification language Z; Logic and semantics of specification languages. 1 Introduction In this paper we introduce and investigate an improved kernel logic ZC for the specification language Z, a logic in which, in particular, we can derive a schema calculus: a logic for the entire range of schema expressions permit...
A Logic for the Schema Calculus
, 1998
"... In this paper we introduce and investigate a logic for the schema calculus of Z. The schema calculus is arguably the reason for Z's popularity but so far no true calculus (a sound system of rules for reasoning about schema expressions) has been given. Presentations thus far have either failed to pro ..."
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Cited by 7 (4 self)
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In this paper we introduce and investigate a logic for the schema calculus of Z. The schema calculus is arguably the reason for Z's popularity but so far no true calculus (a sound system of rules for reasoning about schema expressions) has been given. Presentations thus far have either failed to provide a calculus (e.g. the draft standard) or have fallen back on informal descriptions at a syntactic level (most text books). Alongside the calculus we introduce a derived equational logic which enables us to formalise properly the informal notions of schema expression equality to be found in the literature.
Constructive Foundations for Z
, 1997
"... . The specification language Z is based on classical logic and extensional set theory. These are mathematical choices which are largely independent of Z and its calculus of schemata. This paper explores the possibilities of replacing classical logic with intuitionistic logic and extensional set t ..."
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Cited by 4 (4 self)
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. The specification language Z is based on classical logic and extensional set theory. These are mathematical choices which are largely independent of Z and its calculus of schemata. This paper explores the possibilities of replacing classical logic with intuitionistic logic and extensional set theory with intensional set theory, and some of the consequences of these changes for principles of program development. 1 Introduction The language Z ([3], [2], [4] among many others) is perhaps the most widely used and studied specification language at present. The fact that it was developed in conjunction with large practical applications (see pp. 23 of [5] for example) is probably responsible for it providing very general mechanisms (e.g. the schema calculus) for structuring and organising specifications which have proved to be useful in a wide variety of settings and for a wide variety of purposes. In this paper we take a fresh look at the Z language and suggest an alternative mathem...
Revising Z: Part II  logical development
, 1999
"... . This is the second of two related papers. In "Revising Z: Part I  logic and semantics" (this journal) we introduced a simple specification logic ZC comprising a logic and a semantics (in ZF set theory). We then provided an interpretation for (a rational reconstruction of) the specification langua ..."
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Cited by 3 (1 self)
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. This is the second of two related papers. In "Revising Z: Part I  logic and semantics" (this journal) we introduced a simple specification logic ZC comprising a logic and a semantics (in ZF set theory). We then provided an interpretation for (a rational reconstruction of) the specification language Z within ZC . As a result we obtained a sound logic for Z, including the basic schema calculus. In this paper we extend the basic framework with more sophisticated features (including schema operations) and we mount a critique of a number of concepts used in Z. We further demonstrate that the complications and confusions which these concepts introduce can be avoided without compromising expressibility. Keywords: Specification language Z; Logics and semantics of specification languages 1. Introduction In the earlier companion paper [HR99] we introduced a specification system ZC , a typed set theory incorporating the notion of a schema type and we established a number of metamathematical...
Six theories of operation refinement for partial relation semantics Moshe Deutsch
, 2002
"... In this paper we analyse total correctness operation refinement on a partial relation semantics for specification. In particular we show that three theories: a relational completion approach, a prooftheoretic approach and a functional models approach, are all equivalent. This result holds whether or ..."
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Cited by 2 (0 self)
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In this paper we analyse total correctness operation refinement on a partial relation semantics for specification. In particular we show that three theories: a relational completion approach, a prooftheoretic approach and a functional models approach, are all equivalent. This result holds whether or not preconditions are taken to be minimal or fixed conditions for establishing the postcondition. Keyword: Specification Language; Specification Logic; Refinement; 1