Journal ArticleDOI
Data refinement, call by value and higher order programs
TLDR
Using 2-categorical laws of algorithmic refinement, soundness of data refinement for stored programs and hence for higher order procedures with value/result parameters is shown.Abstract:
Using 2-categorical laws of algorithmic refinement, we show soundness of data refinement for stored programs and hence for higher order procedures with value/result parameters. The refinement laws hold in a model that slightly generalizes the standard predicate transformer semantics for the usual imperative programming constructs including prescriptions.read more
Citations
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Proof of Correctness of Data Representations (Reprint).
TL;DR: A powerful method of simplifying the proofs of program correctness is suggested; and some new light is shed on the problem of functions with side-effects.
Book ChapterDOI
Exploring Summation and Product Operators in the Refinement Calculus
Ralph-Johan Back,Michael Butler +1 more
TL;DR: This paper formalises product and summation operators for predicate transformers in the higher order logic approach to the refinement calculus of Back and von Wright, and examines various algebraic properties of these operators.
Book ChapterDOI
Data-Refinement for Call-By-Value Programming Languages
Yoshiki Kinoshita,John Power +1 more
TL;DR: A category theoretic framework for data-refinement in call-by-value programming languages by generalising the notion of logical relation to one of lax logical relation, so that binary lax logical relations compose.
Journal ArticleDOI
Soundness of data refinement for a higher-order imperative language
TL;DR: Using a set-theoretic model of predicate transformers and ordered data types, a semantics for an Oberon-like higher-order imperative language with record subtyping and procedure-type variables and parameters is given.
Book ChapterDOI
Towards squiggly refinement algebra
TL;DR: Results on exponents and recursion on inductive data types are proved, sufficient for carrying out a polytypic derivation that has been given as a substantial example for functions and relations.
References
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Book
Basic concepts of enriched category theory
TL;DR: Lack, Ross Street and Wood as discussed by the authors present a mathematical subject classification of 18-02, 18-D10, 18D20, and 18D21 for mathematics subject classification.
Book
Programming from specifications
TL;DR: This second edition features substantial restructuring of earlier material, streamlining the introduction of programming language features; simplified presentation of procedures, parameters and recursion; an expanded chapter on data refinement, giving the much simpler laws that specialize to functional abstractions.
OtherDOI
Basic concepts of enriched category theory
TL;DR: In this paper , the authors give a selfcontained account of basic category theory as described above, assuming as prior knowledge only the most elementary categorical concepts, and treating the ordinary and enriched cases together from Chapter 3 on.
Journal ArticleDOI
Proof of correctness of data representations
TL;DR: In this paper, a powerful method of simplifying the proofs of program correctness is suggested; and some new light is shed on the problem of functions with side-effects, and a new method for simplifying program correctness proofs is proposed.
Book
Topology via Logic
TL;DR: In this paper, Affirmative and refutative assertions are made for the point logic and spectral algebraic locales, and the definitions of the topology of the spectral lattice are discussed.