Monad-Based Logics for Computational Effects

Till Mossakowski

In: M. Johnson, V. Vene (Hrsg.). AMAST 2006. International Conference on Algebraic Methodology and Software Technology (AMAST-06) 11th July 5-8 Kuressaare Estonia Seiten 3-4 Lecture Notes in Computer Science 4019 Springer Berlin 2006.


The presence of computational effects, such as state, store, exceptions, input, output, non-determinism, backtracking etc., complicates the reasoning about programs. In particular, usually for each effect (or each combination of these), an own logic needs to be designed. Monads are a well-known tool from category theory that originally has been invented for studying algebraic structures. Monads have been used very successfully by Moggi to model computational effects (in particular, all of those mentioned above) in an elegent way. This has been applied both to the semantics of programming languages and to the encapsulation of effects in pure functional languages such as Haskell. Several logics for reasoning about monadic programs have been introduced, such as evaluation logic, Hoare logic and dynamic logic. Some of these logics have a semantics and proof calculus given in a completely monad independent (and hence, effect independent) way. We give an overview of these logics, discuss completeness of their calculi, as well as some application of these logics to the reasoning about Haskell and Java programs, and a coding in the theorem prover Isabelle.

Weitere Links

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence