Verifying Haskell programs by combining testing and proving

We propose a method for improving confidence in the correctness of Haskell programs by combining testing and proving. Testing is used for debugging programs and specification before a costly proof attempt. During a proof development, testing also quickly eliminates wrong conjectures. Proving helps us to decompose a testing task in a way that is guaranteed to be correct. To demonstrate the method, we have extended the Agda/Alfa proof assistant for dependent type theory with a tool for random testing. As an example, we show how the correctness of a BDD-algorithm written in Haskell is verified by testing properties of component functions. We also discuss faithful translations from Haskell to type theory.