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 α induces an M-computable function f α 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 α 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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Cungen Cao is a professor in the Institute of Computing Technology, Chinese Academy of Sciences, China. His main research interest is knowledge representation.
Yuefei Sui is a professor in the Institute of Computing Technology, Chinese Academy of Sciences, China. His main interests include knowledge representation, applied logic and the theory of computability.
Zaiyue Zhang is a professor in Jiangsu University of Sciences and Technology, China. His main interests include applied logic and computer theory.
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Cao, C., Sui, Y. & Zhang, Z. The M-computations induced by accessibility relations in nonstandard models M of Hoare logic. Front. Comput. Sci. 10, 717–725 (2016). https://doi.org/10.1007/s11704-015-4024-2
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DOI: https://doi.org/10.1007/s11704-015-4024-2