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  On Hoare logic, Kleene algebra, and types (1999) [3 citations — 2 self]

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by Dexter Kozen
Computer Science Department, Cornell University
http://www.cs.cornell.edu/kozen/papers/typedHoare.ps
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Abstract:

We show that propositional Hoare logic is subsumed by the type calculus of typed Kleene algebra augmented with subtypes and typecasting. Assertions are interpreted as typecast operators. Thus Hoare-style reasoning with partial correctness assertions reduces to typechecking in this system. 1

Citations

318 Towards a theory of type structure – Reynolds
285 Propositional dynamic logic of regular programs – Fischer, Ladner - 1979
260 Proofs and Types – Girard, Taylor, et al. - 1989
258 Representation of events in nerve nets and finite automata – Kleene - 1956
213 Constructive mathematics and computer programming – Martin-Löf - 1979
187 Regular Algebra and Finite Machines – Conway - 1971
184 Une extension de l’interprétation de Gödel à l’analyse, et son application à l’élimination des coupures dans l’analyse et la théorie des types – Girard
110 A completeness theorem for Kleene algebras and the algebra of regular events – Kozen - 1994
84 Soundness and Completeness of an Axiom System for Program Verification – Cook - 1978
81 Proofs as programs – Bates, Constable - 1985
65 Methods and logics for proving programs – Cousot - 1999
58 Kleene algebra with tests – Kozen - 1997
28 A practical decision method for propositional dynamic logic – Pratt - 1978
25 On Hoare logic and Kleene algebra with tests – Kozen - 2000
17 Kleene algebra with tests: Completeness and decidability – Kozen, Smith - 1996
9 Kleene algebra with tests and commutativity conditions – Kozen - 1996
6 Ten years of hoare logic: A survey---part 1 – Apt - 1981
6 Predicate transformer semantics – Manes - 1992
5 Typed Kleene algebra – Kozen - 1998
1 Themes in the development of programming logics circa 1963--1987 – Constable - 1988
1 Types in mathematics, logic, and programming – Constable - 1998
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