P-logic: property verification for Haskell programs

Proof-supported logical verification of program properties has been a topic of research interest for more than 30 years. The feasibility of proof construction as a verification technique has been demonstrated through many examples of its application, yet it remains a technique rarely used in practice for a variety of reasons, both technical and sociological. The lack of verification logics for modern programming languages remains a strong deterrent to the use of proof-supported verification. This paper introduces P-logic, a verification logic for Haskell. P-logic is a modal mu-calculus that supports direct expression of recursively-defined properties of complex data structures. The term language of P-logic is Haskell. Logical assertions expressed in P-logic can be interleaved among definitions in a Haskell program text and can incorporate term variables bound in the program context. Properties of finite and infinite data structures can be expressed. The paper describes syntax, proof rules, and semantics of P-logic and provides a few examples of its use.