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Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations
| Title: | Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations |
| Author: | Walter Guttmann |
| Submission date: | 2021-10-12 |
| Abstract: | We study models of state-based non-deterministic sequential computations and describe them using algebras. We propose algebras that describe iteration for strict and non-strict computations. They unify computation models which differ in the fixpoints used to represent iteration. We propose algebras that describe the infinite executions of a computation. They lead to a unified approximation order and results that connect fixpoints in the approximation and refinement orders. This unifies the semantics of recursion for a range of computation models. We propose algebras that describe preconditions and the effect of while-programs under postconditions. They unify correctness statements in two dimensions: one statement applies in various computation models to various correctness claims. |
| BibTeX: |
@article{Correctness_Algebras-AFP,
author = {Walter Guttmann},
title = {Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations},
journal = {Archive of Formal Proofs},
month = oct,
year = 2021,
note = {\url{https://isa-afp.org/entries/Correctness_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
| Depends on: | MonoBoolTranAlgebra, Stone_Kleene_Relation_Algebras, Subset_Boolean_Algebras |
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