Abstract
Kleene algebra with tests (KAT) was introduced as an algebraic structure to model and reason about classic imperative programs, i.e. sequences of discrete actions guarded by Boolean tests.
This paper introduces two generalisations of this structure able to express programs as weighted transitions and tests with outcomes in a not necessary bivalent truth space, namely graded Kleene algebra with tests (GKAT) and Heyting Kleene algebra with tests (HKAT).
On these contexts, in analogy to Kozen’s encoding of Propositional Hoare Logic (PHL) in KAT [10], we discuss the encoding of a graded PHL in HKAT and of its while-free fragment in GKAT.
This work is financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. The second author is also supported by the individual grant SFRH/BPD/103004/2014.
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Gomes, L., Madeira, A., Barbosa, L.S. (2017). On Kleene Algebras for Weighted Computation. In: Cavalheiro, S., Fiadeiro, J. (eds) Formal Methods: Foundations and Applications. SBMF 2017. Lecture Notes in Computer Science(), vol 10623. Springer, Cham. https://doi.org/10.1007/978-3-319-70848-5_17
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