Monad-Independent Dynamic Logic in Has Casl

Monads have been recognized by Moggi as an elegant device for dealing with stateful computation in functional programming languages. In previous work, we have introduced a Hoare calculus for partial correctness of monadic programs. All this has been done in an entirely monad-independent way. Here, we extend this to a monad-independent dynamic logic (assuming a moderate amount of additional infrastructure for the monad). Dynamic logic is more expressive than the Hoare calculus; in particular, it allows reasoning about termination and total correctness. The background formalism for these concepts is the logic of HasCasl, a higher-order language for functional specification and programming. As an example application, we develop a monad-independent Hoare calculus for total correctness based on our dynamic logic, and illustrate this calculus by a termination proof for Dijkstra’s non-deterministic implementation of Euclid’s algorithm.