The dual of substitution is redecoration Export

@article{citeulike:355413, abstract = {It is well known that type constructors of incomplete trees (trees with variables) carry the structure of a monad with substitution as the extension operation. Less known are the facts that the same is true of type constructors of incomplete cotrees (=non-wellfounded trees) and that the corresponding monads exhibit a special structure. We wish to draw attention to the dual facts which are as meaningful for functional programming: type constructors of decorated cotrees carry the structure of a comonad with redecoration as the coextension operation, and so do---even more interestingly--type constructors of decorated trees.}, address = {Exeter, UK, UK}, author = {Uustalu, Tarmo and Vene, Varmo}, citeulike-article-id = {355413}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=644413}, isbn = {1841500704}, keywords = {category-theory, functional-programming, monads, types}, pages = {99--110}, posted-at = {2005-10-20 07:57:37}, priority = {2}, publisher = {Intellect Books}, title = {The dual of substitution is redecoration}, url = {http://portal.acm.org/citation.cfm?id=644413}, year = {2002} }

TY - JOUR ID - citeulike:355413 L3 - citeulike-article-id:355413 N2 - It is well known that type constructors of incomplete trees (trees with variables) carry the structure of a monad with substitution as the extension operation. Less known are the facts that the same is true of type constructors of incomplete cotrees (=non-wellfounded trees) and that the corresponding monads exhibit a special structure. We wish to draw attention to the dual facts which are as meaningful for functional programming: type constructors of decorated cotrees carry the structure of a comonad with redecoration as the coextension operation, and so do---even more interestingly--type constructors of decorated trees. SN - 1841500704 AD - Exeter, UK, UK EP - 110 TI - The dual of substitution is redecoration PB - Intellect Books SP - 99 KW - category-theory KW - functional-programming KW - monads KW - types AU - Uustalu, Tarmo AU - Vene, Varmo PY - 2002/// UR - http://portal.acm.org/citation.cfm?id=644413 ER -