Re: [Haskell-cafe] Explaining monads

Hello,

On 8/14/07, Jeff Polakow wrote:

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One general intuition about monads is that they represent computations rather than simple (already computed) values:

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x :: Int -- x is an Int x :: Monad m => m Int -- x is a computation of an Int

What's a "computation"? It seems to me that in a lazy language, x::Int represents a computation of an int, not an "already computed" value.

This intuition for monads as "computations" is independent of operational semantics.

x::[Int] is a computation that returns multiple values. x::(Int,Int) is a computation that returns a pair of values. x::() is a computation that returns nothing. x::Map a b is a computation that gives a way to associate values of type a with values of type b. Some of these are monads, some are not. What's the difference between them? Why are you calling certain values "computations"?

Of course, the type [Int] denotes a value which is a list of Ints; additionally [Int] can be viewed as a value representing the nondeterministic computation of a single Int. Generally, the type Monad m => m Int can be viewed as a value representing the computation of an Int. However, I do not mean to imply that everything which can be viewed as a computation of something is a monad. In any case, this is only meant to be a general (i.e. high-level) intuition. BTW, this intuition was, more or less, the one used by Moggi when describing how monads can be used to describe denotational models for languages. -Jeff --- This e-mail may contain confidential and/or privileged information. If you are not the intended recipient (or have received this e-mail in error) please notify the sender immediately and destroy this e-mail. Any unauthorized copying, disclosure or distribution of the material in this e-mail is strictly forbidden.