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 areâ€¦ (More)

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 beenâ€¦ (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 theâ€¦ (More)

This paper describes a proof of the Church-Rosser theorem within the Higher Order Logic (HOL) theorem prover. This follows the proof by Tait/Martin-LÃ¶f, preserving the elegance of the classicâ€¦ (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 callâ€¦ (More)

The quotient operation is a standard feature of set theory, where a set is divided into subsets by an equivalence relation; the resulting subsets of equivalent elements are called equivalenceâ€¦ (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 laterâ€¦ (More)