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Constructing applicative functors

Paterson, R. A. (2012). Constructing applicative functors. Paper presented at the 11th International Conference, Mathematics of Program Construction, 25 - 27 Jun 2012, Madrid, Spain.


Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of constructing useful functors of this type, just as transformers are used to construct computational monads. For example, coends, familiar to functional programmers as existential types, yield a range of useful applicative functors, including left Kan extensions. Other constructions are final fixed points, a limited sum construction, and a generalization of the semi-direct product of monoids. Implementations in Haskell are included where possible.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: The final publication is available at Springer via
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Computer Science
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