Editing Monad (category theory) (section)

== Uses ==

Monads are used in [[functional programming]] to express types of sequential computation (sometimes with side-effects). See [[monads in functional programming]], and the more mathematically oriented Wikibook module [[b:Haskell/Category theory]].

Monads are used in the [[denotational semantics]] of impure functional and [[Imperative programming|imperative programming languages]].<ref>{{Cite book |last=Wadler |first=Philip |title=Program Design Calculi |chapter=Monads for functional programming |date=1993 |editor-last=Broy |editor-first=Manfred |chapter-url=https://link.springer.com/chapter/10.1007/978-3-662-02880-3_8 |series=NATO ASI Series |volume=118 |language=en |location=Berlin, Heidelberg |publisher=Springer |pages=233–264 |doi=10.1007/978-3-662-02880-3_8 |isbn=978-3-662-02880-3}} "The concept of a monad, which arises from category theory, has been applied by Moggi to structure the denotational semantics of programming languages."</ref><ref>{{Cite journal |last=Mulry |first=Philip S. |date=1998-01-01 |title=Monads in Semantics |journal=Electronic Notes in Theoretical Computer Science |series=US-Brazil Joint Workshops on the Formal Foundations of Software Systems |language=en |volume=14 |pages=275–286 |doi=10.1016/S1571-0661(05)80241-5 |issn=1571-0661|doi-access=free }}</ref>

In categorical logic, an analogy has been drawn between the monad-comonad theory, and [[modal logic]] via [[closure operator]]s, [[interior algebra]]s, and their relation to [[Mathematical model|models]] of [[S4 algebra|S4]] and [[intuitionistic logic]]s.