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QuickSpec is a theory exploration system which tests a Haskell program to find equational properties of it, automatically. The equations can be used to help understand the program, or as lemmas to help prove the program correct. QuickSpec is largely automatic: the user just supplies the functions to be tested and QuickCheck data generators. Previous theory exploration systems, including earlier versions of QuickSpec itself, scaled poorly. This paper describes a new architecture for theory exploration with which we can find vastly more complex laws than before, and much faster. We demonstrate theory exploration in QuickSpec on problems both from functional programming and mathematics.

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In this paper we revisit the connection between parametricity and noninterference. Our primary contribution is a proof of noninterference for a polyvariant variation of the Dependency Core Calculus of Abadi et al. in the Calculus of Constructions. The proof is modular: it leverages parametricity for the Calculus of Constructionsand the encoding of data abstraction using existential types.This perspective gives rise to simple and understandable proofs of noninterference from parametricity. All our contributions have been mechanised in the Agda proof assistant.

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