Abstract
Hoare logic [1] 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 [2]. In a model M of Hoare logic, each program ? induces an M-computable function f?M 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 induced by programs is equal to the class of all the M-recursive functions. Moreover, each M-recursive function is $$\sum {_1^{{N^M}}} $$-definable in M, where the universal quantifier is a number quantifier ranging over the standard part of a nonstandard model M.
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