Program Calculation in Coq

Abstract. Program calculation, being a programming technique that derives programs from specification by means of formula manipulation, is a challenging activity. It requires human insights and creativity, and needs systems to help human to focus on clever parts of the derivation by automating tedious ones and verifying correctness of transformations. Different from many existing systems, we show in this paper that Coq, a popular theorem prover, provides a cheap way to implement a powerful system to support program calculation, which has not been recognized so far. We design and implement a set of tactics for the Coq proof assistant to help the user to derive programs by program calculation and to write proofs in calculational form. The use of these tactics is demonstrated through program calculations in Coq based on the theory of lists.