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2013-11-23T20:36:03.267
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<code>SelectMany</code> in C# corresponds to bind in Haskell <code>(>>=)</code> or <code>flatMap</code> in Scala. The signature of <code>>>=</code> in Haskell is: <pre><code>(>>=) :: Monad m => m a -> (a -> m b) -> m b </code></pre> so bind is an operation used to construct one monadic value from another. In the case of C# <code>m</code> in the above signature is <code>IEnumerable</code>, <code>IObservable</code>, <code>IQueryable</code> etc. For <code>IEnumerable</code>, <code>SelectMany</code> is therefore <pre><code>IEnumerable<A> -> (A -> IEnumerable) -> IEnumerable </code></pre> or in C# <pre><code>public static IEnumerable SelectMany<A, B>(this IEnumerable<A> first, Func<A, IEnumerable> selector) </code></pre> The meaning of bind depends on the monad type, for IEnumerable, each element in the input sequence is used to create a new sequence, and the resulting sequence of sequences is flattened to produce the output sequence. There is another formulation of bind which may make this more clear. While monads are often described in terms of their implementation of bind, monads must also support two other operations, <code>map</code> and <code>join</code>. <code>map</code> corresponds to Select in C# and looks like: <pre><code>map :: Monad m => (a -> b) -> (ma -> m b) </code></pre> so it is a 'structure preserving' way of lifting a regular function over a monadic value. <code>join</code> has the type <pre><code>join :: Monad m => m m a -> m a </code></pre> so join is used to flatten nested monadic values. In C# this would look like <pre><code>public static IEnumerable<A> Join<A>(this IEnumerable<IEnumerable<A>> nested) </code></pre> <code>bind</code> can be implemented in terms of map and join as <pre><code>m >>= f = join (map f m) </code></pre> so to answer the original question, <code>SelectMany</code> corresponds to <code>bind</code> or <code>flatMap</code> in other languages. Bind is not just flattening, but can be seen as a transformation followed by a flattening of nested monadic values (e.g. sequences in the case of <code>IEnumerable<T></code>). <code>join</code> for <code>IEnumerable<T></code> does not exist in the current linq extensions.
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1. POLINQ SelectMany is bind?
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1. USLee
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1. COWow. I don't understand what is going on here, but your examples merging IEnumerable with Haskell concepts are giving me the idea I CAN understand it. Excellent treatment. Thanks.
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