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Summary: Verifying Haskell Programs Using Constructive Type Theory #
Andreas Abel Marcin Benke Ana Bove John Hughes Ulf Norell
Chalmers University of Technology
{abel,marcin,bove,rjmh,ulfn}@cs.chalmers.se
Abstract
Proof assistants based on dependent type theory are closely related
to functional programming languages, and so it is tempting to use
them to prove the correctness of functional programs. In this paper,
we show how Agda, such a proof assistant, can be used to prove
theorems about Haskell programs. Haskell programs are translated
into an Agda model of their semantics, by translating via GHC's
Core language into a monadic form specially adapted to represent
Haskell's polymorphism in Agda's predicative type system. The
translation can support reasoning about either total values only, or
total and partial values, by instantiating the monad appropriately.
We claim that, although these Agda models are generated by a rel
atively complex translation process, proofs about them are simple
and natural, and we offer a number of examples to support this
claim.
Categories and Subject Descriptors D.1.1 [Programming Tech
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