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Hoare Logic for Mutual Recursion and Local Variables
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Hoare Logic for Mutual Recursion and Local Variables
David von Oheimb6 
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Technische Universität München, D-80290 München, Germany |
Abstract
We present a (the first?)sou nd and relatively complete Hoare logic for a simple imperative programming language including
mutually recursive procedures with call-by-value parameters as well as global and local variables. For such a language we
formalize an operational and an axiomatic semantics of partial correctness and prove their equivalence. Global and local variables,
including parameters, are handled in a rather straightforward way allowing for both dynamic and simple static scoping. For
the completeness proof we employ the powerful MGF (Most General Formula)a pproach, introducing and comparing three variants
for dealing with complications arising from mutual recursion.
All this work is done using the theorem prover Isabelle/HOL, which ensures a rigorous treatment of the subject and thus reliable
results. The paper gives some new insights in the nature of Hoare logic, in particular motivates a stronger rule of consequence
and a new flexible Call rule.
Keywords axiomatic semantics - Hoare logic - mutual recursion - soundness - relative completeness - local variables - call-by-value parameters - Isabelle/HOL
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