J.-C. Filliâtre. A theory of monads parameterized by effects. Research Report 1367, LRI, Université Paris Sud, November 1999.

Monads were introduced in computer science to express the semantics of programs with computational effects, while type and effect inference was introduced to mark out those effects. In this article, we propose a combination of the notions of effects and monads, where the monadic operators are parameterized by effects. We establish some relationships between those generalized monads and the classical ones. Then we use a generalized monad to translate imperative programs into purely functional ones. We establish the correctness of that translation. This work has been put into practice in the Coq proof assistant to establish the correctness of imperative programs.

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