Veriied Proofs concerning Functional Programs

In this paper the development of automatically veriied proofs for functional programs is examined. This examination is made on the basis of a small functional program written in the functional language clean. For this program a proof is constructed in the proof system coq. This proof is automatically veriied by coq. The functional program presented contains two function-constructors for the class of equality-functions. These function-constructors de-ne equality-functions on composed types from equality-functions on basic types. An equality-function for typèList of A' can be composed out of an equality-function for typèA', and one for typèPair of A and B' can be composed out of ones for typèA' and typèB'. In the proof it is shown that these function-constructors preserve equivalence-relations. This means that if the given equality-functions on the basic types are equivalence-relations, then also the constructed equality-function on the composed type must be an equivalence-relation. First the proof will be given informally. Then this informal proof is transformed in two steps to a formal proof in the proof system coq. The correctness of the formal proof is automatically checked by coq.