Logical and mathematical reasoning about imperative programs: preliminary report

It is well known that reasoning &out compul;ltion can hc carricd cu within Pc;mo Arithmetic [ KlcSZj. hlthougl~ this was dcmunstrarcd originally for ‘l’uring Machine computa:ions. the m&d ildilpts easily to rcasonin g about computiltions of impcrativc programs (see c.g. [%ucSO] and [hI‘SI]). ‘l‘hc cumhcrsomc numeric coding. with which such reasoning frameworks arc plilgucd. is ncccssaly only when (UK Coflfincs oncsclf to the mcagcr language of’ first-order arithmetic: when tic language is cnrichcd. to allow direct rcfcrcncc to programming constructs, one obtains a rcasonahlc framework for reasoning about impcrativc programs. A formalism of this type might be dubbed “Arithmetic of Programs”. In a scnsc. the “Non-Standard I)ynamic I.ogic” of Ncmcti & als. [Ncm82, ANSSZ]. is such an arithmetic.

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