Deriving Proof Rules from Continuation Semantics

. We claim that a continuation style semantics of a programming language can provide a starting point for constructing its proof system. The basic idea is to see weakest preconditions as a particular instance of continuation style semantics, hence to interpret correctness assertions (e.g. Hoare triples fpg C frg) as inequalities over continuations. This approach also shows a correspondence between labels in a program and annotations. Introduction Already in the 1970's, Jensen [Jen78] noted a strong resemblance between continuation style semantics and weakest preconditions. To see the point, consider the semantic clause usually given for a command sequence in continuation style (see [Sch86, NiN92]). [[C 1 ; C 2 ]] cs k = [[C 1 ]] cs ([[C 2 ]] cs k), for any k continuation and the corresponding clause defining the weakest (liberal) precondition [Dij76]: wlp(C 1 ;C 2 ) r = wlp(C 1 )(wlp(C 2 ) r), for any r postcondition. The two clauses are formally the same and analogous remarks can b..