Kleene Algebra with Tests and Demonic Refinement Algebras

Alasdair Armstrong, Victor B. F. Gomes 🌐 and Georg Struth 🌐

January 23, 2014

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

We formalise Kleene algebra with tests (KAT) and demonic refinement algebra (DRA) in Isabelle/HOL. KAT is relevant for program verification and correctness proofs in the partial correctness setting. While DRA targets similar applications in the context of total correctness. Our formalisation contains the two most important models of these algebras: binary relations in the case of KAT and predicate transformers in the case of DRA. In addition, we derive the inference rules for Hoare logic in KAT and its relational model and present a simple formally verified program verification tool prototype based on the algebraic approach.

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BSD License

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Session KAT_and_DRA

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× 
@article{KAT_and_DRA-AFP,
  author  = {Alasdair Armstrong and Victor B. F. Gomes and Georg Struth},
  title   = {Kleene Algebra with Tests and Demonic Refinement Algebras},
  journal = {Archive of Formal Proofs},
  month   = {January},
  year    = {2014},
  note    = {\url{https://isa-afp.org/entries/KAT_and_DRA.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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