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 should be useful for proving as well. To exploit object‐oriented structuring mechanisms for verification, we extend the object‐model of Pierce and Turner, based on the higher‐order typed λ‐calculus $F_{\leq}^{\,\omega}$ with a logical component. By enriching the (functional) signature of objects with a specification, methods and their correctness proofs are packed together in 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. © 1998 John Wiley & Sons, Inc.

An object-oriented calculus with term constraints

“…The work most similar to ours is, on one hand, Hofmann et al's verification method (Hofmann et al, 1996;Hofmann et al, 1998). It treats objects as abstract data types and is able to prove if the functional implementation matches the specification part.…”