# Difference between revisions of "Monad (sans metaphors)"

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− | [[Category:Glossary]] |
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− | [[Category:Monad|*]] |
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− | === Introduction === |
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− | Many discussions of Haskell [[Monad|Monads]] seek to explain them through the use of a variety of metaphors. This page attempts to simply provide a more technical yet straightforward description of Monads in Haskell. |
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− | === So what ''is'' a monad? === |
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− | A Monad is a type constructor with two operations, implementing a standard interface and following a few simple rules. |
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− | The Monad type class tells you the interface (what operations you've got, and their types), the Monad laws tell you what all types implementing that interface should have in common. |
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− | The Monadic interface gives you two operations: one to throw things into a Monad thing (<hask>return</hask>), and one to chain two Monad things together <hask>(>>=)</hask>. The chaining explicitly caters for information flowing from the first to the second parameter of <hask>(>>=)</hask>. |
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− | The Monad laws tell you two useful facts about Monad things thrown together in that way: whatever it is the Monad does, anything just thrown into it will take no part in that action, and whichever way you use that chaining operation, the |
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− | structure of chaining is irrelevant - only the ordering of chained Monad things matters. |
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− | There are usually other ways to create 'primitive' Monadic things, which can be combined into complex Monadic structures using the operations from the Monad interface. |
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− | There is usually a way to interpret Monadic structures built in this way - a 'run' operation of some kind. Examples include: |
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− | * I/O: The 'primitive Monadic things' are basic I/O operations. The 'run' operation is outside the language, applied to 'Main.main', and interprets (abstract) IO Monad structures sequentially, starting with the leftmost innermost I/O operation in the structure and applying the second argument of <hask>(>>=)</hask> to the result of executing the first. |
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− | * []: The 'primitive Monadic things' are lists. The 'run' operation is the identity, i.e the lists are directly exposed as data structures. <hask>return</hask> creates a singleton list. <hask>(>>=)</hask> applies its second argument to each element of its first argument and concatenates the results (<hask>concatMap</hask>). |
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− | * State: The 'primitive Monadic things' are operations on a state type, returning a result and a state. 'run' is <hask>runState</hask> and applies a (possibly) complex Monadic thing to an input state, returning a result and a (modified) state. <hask>return</hask> returns its parameter, passing its input state unchanged. <hask>(>>=)</hask> applies its first parameter to the input state, applies its second parameter to the result value and result state of the first. |
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− | == Source == |
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− | * Claus Reinke on Haskell-Cafe: [http://www.haskell.org/pipermail/haskell-cafe/2007-August/029851.html Monad Description For Imperative Programmer] |