Composing monads using coproducts Export

@article{citeulike:697359, abstract = {Monads are a useful abstraction of computation, as they model diverse computational effects such as stateful computations, exceptions and I/O in a uniform manner. Their potential to provide both a modular semantics and a modular programming style was soon recognised. However, in general, monads proved difficult to compose and so research focused on special mechanisms for their composition such as distributive monads and monad transformers.We present a new approach to this problem which is general in that nearly all monads compose, mathematically elegant in using the standard categorical tools underpinning monads and computationally expressive in supporting a canonical recursion operator. In a nutshell, we propose that two monads should be composed by taking their coproduct . Although abstractly this is a simple idea, the actual construction of the coproduct of two monads is non-trivial. We outline this construction, show how to implement the coproduct within Haskell and demonstrate its usage with a few examples. We also discuss its relationship with other ways of combining monads, in particular distributive laws for monads and monad transformers.}, address = {New York, NY, USA}, author = {L\"{u}th, Christoph and Ghani, Neil}, booktitle = {ICFP '02: Proceedings of the seventh ACM SIGPLAN international conference on Functional programming}, citeulike-article-id = {697359}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=581492}, citeulike-linkout-1 = {http://dx.doi.org/10.1145/581478.581492}, doi = {10.1145/581478.581492}, issn = {0362-1340}, journal = {SIGPLAN Not.}, keywords = {category-theory, coproducts, monads}, month = {September}, number = {9}, pages = {133--144}, posted-at = {2006-06-15 20:28:48}, priority = {2}, publisher = {ACM}, title = {Composing monads using coproducts}, url = {http://dx.doi.org/10.1145/581478.581492}, volume = {37}, year = {2002} }

TY - JOUR ID - citeulike:697359 L3 - citeulike-article-id:697359 N2 - Monads are a useful abstraction of computation, as they model diverse computational effects such as stateful computations, exceptions and I/O in a uniform manner. Their potential to provide both a modular semantics and a modular programming style was soon recognised. However, in general, monads proved difficult to compose and so research focused on special mechanisms for their composition such as distributive monads and monad transformers.We present a new approach to this problem which is general in that nearly all monads compose, mathematically elegant in using the standard categorical tools underpinning monads and computationally expressive in supporting a canonical recursion operator. In a nutshell, we propose that two monads should be composed by taking their coproduct . Although abstractly this is a simple idea, the actual construction of the coproduct of two monads is non-trivial. We outline this construction, show how to implement the coproduct within Haskell and demonstrate its usage with a few examples. We also discuss its relationship with other ways of combining monads, in particular distributive laws for monads and monad transformers. IS - 9 JF - SIGPLAN Not. SN - 0362-1340 AD - New York, NY, USA EP - 144 TI - Composing monads using coproducts PB - ACM VL - 37 T2 - ICFP '02: Proceedings of the seventh ACM SIGPLAN international conference on Functional programming SP - 133 KW - category-theory KW - coproducts KW - monads AU - Lüth, Christoph AU - Ghani, Neil PY - 2002/09// UR - http://dx.doi.org/10.1145/581478.581492 ER -