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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)

We discuss ideas for using the Higher-Order Logic (HOL) theorem-proving system as an infrastructure for programs that reference or carry proofs of their correctness. Such programs , which we call Proof-Referencing Code (PRC), could be useful or even essential for applications where security of mobile code is important, but where authentication is… (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)

Realistic production systems require an integrated combination of forward and backward reasoning to reflect appropriately the processes of natural human expert reasoning. A control mechanism that consists solely of forward reasoning is not an effective way to promptly focus the system's attention as calculation proceeds. Very often expert system programmers… (More)