The M-computations induced by accessibility relations in nonstandard models M of Hoare logic

Abstract

Hoare logic is a logic used as a way of specifying semantics of programming languages, which has been extended to be a separation logic to reason about mutable heap structure. In a model M of Hoare logic, each program α induces an M-computable function f^M_α on the universe of M; and the M-recursive functions are defined on M. It will be proved that the class of all the M-computable functions f^M_α induced by programs is equal to the class of all the M-recursive functions. Moreover, each M-recursive function is Σ^NM_{<?Pub Caret1?>1} -definable in M, where the universal quantifier is a number quantifier ranging over the standard part of a nonstandard model M.

Keywords

Hoare logic / recursive function / computable function / nonstandard model of Peano arithmetic

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