2013 | OriginalPaper | Buchkapitel
Refinements for Free!
verfasst von : Cyril Cohen, Maxime Dénès, Anders Mörtberg
Erschienen in: Certified Programs and Proofs
Verlag: Springer International Publishing
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Formal verification of algorithms often requires a choice between definitions that are easy to reason about and definitions that are computationally efficient. One way to reconcile both consists in adopting a high-level view when proving correctness and then refining stepwise down to an efficient low-level implementation. Some refinement steps are interesting, in the sense that they improve the algorithms involved, while others only express a switch from data representations geared towards proofs to more efficient ones geared towards computations. We relieve the user of these tedious refinements by introducing a framework where correctness is established in a proof-oriented context and automatically transported to computation-oriented data structures. Our design is general enough to encompass a variety of mathematical objects, such as rational numbers, polynomials and matrices over refinable structures. Moreover, the rich formalism of the
Coq
proof assistant enables us to develop this within
Coq
, without having to maintain an external tool.