Category talk:Monads: Difference between revisions

::::::::::::(2) Change of list length is roughly equivalent to a type change. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 21:29, 31 January 2016 (UTC)

:::::::::::::I think these issues may now be resolved by the edits, but FWIW, the problem with characterising monads by foregrounding algebraic datatypes was mainly one of emphasis. A monad is a category – a set of related morphisms or functions, if you like – it's not a datatype – and the simplest monad, in which the Return function is equivalent to the ID function [[wp:Monad_(functional_programming)#Identity_monad|(see under Identity Monad)]], involves no 'wrapper' or modal context at all. From the practical coding perspective, a monad is a pattern of function nesting, and the practical steps involved in creating that pattern consist of writing two functions. As you point out, a useful monad is very likely to involve some kind of modal wrapper (though even the identity monad is used in programming), but while that may be an empirically (though not formally) *almost* necessary condition, it is neither practically sufficient, nor conceptually central enough to provide an adequate substitute for foregrounding the monadic functions themselves, and the value of the function nesting which they enable. (In my personal view :-) [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 17:42, 2 February 2016 (UTC)

 

==Structure of Monads on Rosetta Code==