Inheritance of Proofs

Abstract

The Curry-Howard isomorphism, a fundamental property shared by many type theories, establishes a direct correspondence between programs and proofs. This suggests that the same structuring principles that ease programming be used to simplify proving as well. To exploit object-oriented structuring mechanisms for veriication, we extend the object-model of Pierce and Turner, based on the higher-order typed-calculus F ! , with a logical component. By enriching the (functional) signature of objects with a speciication, the methods and their correctness proofs are packed together in the objects. The uniform treatment of methods and proofs gives rise in a natural way to object-oriented proving principles | including inheritance of proofs, late binding of proofs, and encapsulation of proofs | as analogues to object-oriented programming principles. We have used Lego, a type-theoretic proof checker, to explore the feasibility of this approach. In particular, we have veriied a small hierarchy of classes. 1. Introduction Many programming languages have been developed to ease modular and structured design of programs. The popularity of powerful structuring techniques, including object-oriented ones, is a convincing argument that those mechanisms support the programming task. Depending on the programming style, they cater to divide-and-conquer strategies for breaking down large programs into abstract data types, modules, objects, or similar. Since the resulting components ideally mirror the decomposition of the problem into conceptually