Results on formal stepwise design in Z

Deutsch, Moshe; Henson, Martin C.; Reeves, Steve

doi:10.1109/apsec.2002.1182973

Cited by 7 publications

(24 citation statements)

References 12 publications

(18 reference statements)

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“…Having established this characterisation in a general simulation-based setting (complementing our investigation of implementation-based operation-refinement in [11,12]), there are two immediate questions arising naturally: first and foremost, is this a valid theory of refinement? and, if it is, what is its relationship to the normative theory that we established in [8,9,7]?…”

Section: Discussionmentioning

confidence: 98%

“…Our second characterisation of data-refinement constitutes a generalisations of the approach we have taken for operation-refinement in [11] and [12]. In a similar manner, we consider specifications as sets of implementations and then define refinement in terms of this notion.…”

Section: Preamblementioning

confidence: 98%

“…In a similar manner to our counterpart investigation of operation-refinement in [11,12], one of the directions of implication, in each of the equivalence proofs below, requires the use of the axiom of choice (e.g. [15, ch.15]).…”

Section: Two Equivalent Theories In Each Of the Simulation Techniquesmentioning

confidence: 98%

“…This paper provides a generalisation, to data refinement, of an approach we investigated for operation-refinement in [11,12]. There, in the spirit of constructive theories of program development, e.g.…”

Section: Introductionmentioning

confidence: 98%

“…in [11,12]) as well as data-refinement (e.g. in [8,9,7]), answering various questions raised by the technical machinery; in particular, precisely explaining the extent to which this approach is canonical and the extent to which it is arbitrary.…”

Section: Introductionmentioning

confidence: 99%

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An alternative approach to handling nondeterminism in model-oriented data-refinement

Deutsch

Henson

2005

12th Asia-Pacific Software Engineering Conference (APSEC'05)

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This paper investigates data-refinement by forward and backward simulations for model-oriented specifications whose semantics is given by partial relations. The most well-known example of such a semantics is that for Z. The standard model-theoretic characterisation of refinement is a relational approach based on totalisation and lifting. We contrast this, and relate it to, a new approach inspired by various concepts in algebraic paradigms and Type Theory (adapted into a framework based on classical logic) for handling nondeterminism and underspecification in datarefinement. We provide a new characterisation of refinement based on extracting a set of (deterministic) "implementations", each of which models the specification in question. We examine a means by which data simulations interact with this notion and demonstrate that each of the ensuing simulation-based theories is equivalent to the corresponding standard relational characterisation of refinement.

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