A propos de monad
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Date:  19991004 (09:23) 
From:  Frank A. Christoph <christo@n...> 
Subject:  RE: A propos de monad/About monads 
> [ English (executive summary ;) ] > > Monads are a way to encapsulate sideeffects in functionnal > languages. Does anyboody have a more detailed explaination about how > monads really work ? What is the difference between the usual let and > the monad binding ? Someone already gave a URL for Noel Winstanley's presentation of monads in Haskell. I wanted to point out that there are several other resources listed at http://haskell.org/bookshelf/ under "Using Monads". Philippe Esperet wrote: > ``monad'' est le mot anglais correspondant ·<< monade >>, entit· > complexe intervenant dans le syst?e philosophique de Leibniz (Monade > en allemand). I don't understand French, but I parsed this as saying that monads in the sense used here have something to do with Leibniz's philosophical theory of monads, which is false. A monad, as used in Haskell and the progamming language theory literature, is a mathematical structure from category theory. One way to think of it is as a (polymorphic) computation over algebras of a functor. Leibniz's monads were a semimystical attempt at explaining the structure of matter. You might think that at least the origins of the words are related, but I doubt it. Another way to think of the notion of monad is as a categorification of the algebraic notion of monoid (the functions become functors, the points become morphisms, etc.), so I assume "monad" came from "monoid". BTW, another word for "monad" is "triple" (because it is described by one functor and two natural transformations), and I believe the latter is in fact more common in pure mathematical circles. David Brown wrote: > Monads are primarily to encourage a lasy language (such as haskell) to > evaluate sideeffecting operations in a specific order. But monads are also used in Opal, which is an eager language, to keep the base language pure from sideeffects. Also, I often use monads in Haskell which have no sideeffects at all. For example, I might use a nonimperative state transformer to "lay out the plumbing" for an algorithm, i.e., to avoid passing variables around explicitly; the error monad, which is a monad over what in Ocaml corresponds to the option type (functor), is also extremely useful, and has no sideeffects either. FAC