| 1. |
- Armstrong, Alasdair, et al.
(author)
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Kleene Algebra
- 2013
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In: Archive of Formal Proofs. - 2150-914X.
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Journal article (peer-reviewed)
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| 2. |
- Armstrong, Alasdair, et al.
(author)
-
Program Analysis and Verification Based on Kleene Algebra in Isabelle/HOL
- 2013
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In: Interactive Theorem Proving. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642396335 ; , s. 197-212
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Conference paper (peer-reviewed)abstract
- Schematic Kleene algebra with tests (SKAT) supports the equational verification of flowchart scheme equivalence and captures simple while-programs with assignment statements. We formalise SKAT in Isabelle/HOL, using the quotient type package to reason equationally in this algebra. We apply this formalisation to a complex flowchart transformation proof from the literature. We extend SKAT with assertion statements and derive the inference rules of Hoare logic. We apply this extension in simple program verification examples and the derivation of additional Hoare-style rules. This shows that algebra can provide an abstract semantic layer from which different program analysis and verification tasks can be implemented in a simple lightweight way.
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| 3. |
- Armstrong, Alasdair, et al.
(author)
-
Programming and automating mathematics in the Tarski-Kleene hierarchy
- 2014
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In: Journal of Logical and Algebraic Methods in Programming. - : Elsevier BV. - 2352-2208. ; 83:2, s. 87-102
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Journal article (peer-reviewed)abstract
- We present examples from a reference implementation of variants of Kleene algebras and Tarski's relation algebras in the theorem proving environment Isabelle/HOL. For Kleene algebras we show how models can be programmed, including sets of traces and paths, languages, binary relations, max-plus and min-plus algebras, matrices, formal power series. For relation algebras we discuss primarily proof automation in a comprehensive library and present an advanced formalisation example.
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| 4. |
- Gomes, Victor B. F., et al.
(author)
-
Kleene Algebras with Domain
- 2016
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In: Archive of Formal Proofs. - 2150-914X.
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Journal article (peer-reviewed)
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