Refinement in a language with procedures and modules
Refinement in a language with procedures and modules
Our goal is to make the logic and language generally applicable. We therefore base our language on a general class of typed formula languages, demanding only the existence of simple constructs such as conjunction, negation and renaming, together with a consistent predicate semantics. The term language of HOL forms a language in our class.
We construct from our class of formula languages a class of wide-spectrum languages supporting commands (including local variables), operation environments (providing support for procedural abstraction) and modules (providing support for data abstraction). We extend also the predicate semantics to a monotonic predicate transformer semantics for substitutions, from which we define extended domains for environments, modules and substitutions with procedural abstraction. We consider also the extension of the refinement ordering on predicate transformers to environments and modules. Our semantics is novel in not relying on an initial syntactic substitution or explicit variable environments to overcome problems associated with clashes between local and global state variables.
Having fully considered refinement in the semantic domain, we present a consistent calculus of refinement for commands, environments and modules. We present an implementation of the calculus as an extension to the HOL theorem prover, demonstrating the refinement analogues of HOL rules, conversions, tactics and tacticals.
University of Southampton
Pratten, Christopher Henry John
1996
Pratten, Christopher Henry John
Pratten, Christopher Henry John
(1996)
Refinement in a language with procedures and modules.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Our goal is to make the logic and language generally applicable. We therefore base our language on a general class of typed formula languages, demanding only the existence of simple constructs such as conjunction, negation and renaming, together with a consistent predicate semantics. The term language of HOL forms a language in our class.
We construct from our class of formula languages a class of wide-spectrum languages supporting commands (including local variables), operation environments (providing support for procedural abstraction) and modules (providing support for data abstraction). We extend also the predicate semantics to a monotonic predicate transformer semantics for substitutions, from which we define extended domains for environments, modules and substitutions with procedural abstraction. We consider also the extension of the refinement ordering on predicate transformers to environments and modules. Our semantics is novel in not relying on an initial syntactic substitution or explicit variable environments to overcome problems associated with clashes between local and global state variables.
Having fully considered refinement in the semantic domain, we present a consistent calculus of refinement for commands, environments and modules. We present an implementation of the calculus as an extension to the HOL theorem prover, demonstrating the refinement analogues of HOL rules, conversions, tactics and tacticals.
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Published date: 1996
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Local EPrints ID: 460140
URI: http://eprints.soton.ac.uk/id/eprint/460140
PURE UUID: 45335e3c-1f37-497f-a204-e78afe649139
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Date deposited: 04 Jul 2022 18:00
Last modified: 04 Jul 2022 18:00
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Author:
Christopher Henry John Pratten
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