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Verification Condition Generator (VCG) tools have been effective in simplifying the task of proving programs correct. However, in the past these VCG tools have in general not themselves been mechanically proven, so any proof using and depending on these VCGs might have contained errors. In our work, we define and rigorously prove correct a VCG tool within… (More)

The quotient operation is a standard feature of set theory, where a set is partitioned into subsets by an equivalence relation. We reinterpret this idea for higher order logic, where types are divided by an equivalence relation to create new types, called quotient types. We present a design to mechanically construct quotient types as new types in the logic,… (More)

A new logic is posited for the widely used HOL theorem prover, as an extension of the existing higher order logic of the HOL4 system. The logic is extended to three levels, adding kinds to the existing levels of types and terms. New types include type operator variables and universal types as in System F. Impredicativity is avoided through the… (More)

The veriication of programs that contain mutually recursive procedures is a diicult task, and one which has not been satisfactorily addressed in the literature. Published proof rules have been later discovered to be unsound. Veriication Condition Generator (VCG) tools have been eeective in partially automating the veriication of programs, but in the past… (More)

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