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What would be a good place to go to understand arrows? Ideally, I am just looking for some place with a concise definition with motivation from some good examples, something similar to Wadler's exposition on monads.
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(->) is often called the "function arrow" or "function type constructor", and while it does have some special syntax, there's not that much special about it. It's essentially an infix type operator. Give it two types, and it gives you the type of functions between those types.
The Arrow (either (->) or MyArr ) is an abstraction of a computation. For a function b -> c , b is the input and c is the output. For a MyArr b c , b is the input and c is the output.
The left arrow gets used in do notation as something similar to variable binding, in list comprehensions for the same (I'm assuming they are the same, as list comprehensions look like condensed do blocks), and in pattern guards, which have the form (p <- e). All of those constructs bind a new variable.
In Haskell a monad is represented as a type constructor (call it m ), a function that builds values of that type ( a -> m a ), and a function that combines values of that type with computations that produce values of that type to produce a new computation for values of that type ( m a -> (a -> m b) -> m b ).
http://en.wikibooks.org/wiki/Haskell/Understanding_arrows
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