Some of the functions for working with Arrows are quite handy to use on pairs. But I can't understand how the types of these functions unify with a pair. In general, I find the types of the Arrow related functions to be quite confusing.
For example, we have first :: a b c -> a (b, d) (c, d), which means little to me. But it can be used to, say, increment the first number in a pair:
Prelude Control.Arrow> :t first (+1)
first (+1) :: (Num b) => (b, d) -> (b, d)
And
Prelude Control.Arrow> :t (&&&)
(&&&) :: (Arrow a) => a b c -> a b c' -> a b (c, c')
Prelude Control.Arrow> :t (pred &&& succ)
(pred &&& succ) :: (Enum b) => b -> (b, b)
Could someone please explain how this works?
There is an instance for Arrow (->). So
(&&&) :: (Arrow a) => a b c -> a b c' -> a b (c,c')
has the instantiation
(&&&) :: (->) b c -> (->) b c' -> (->) b (c,c')
or, written in more conventional notation,
(&&&) :: (b -> c) -> (b -> c') -> (b -> (c,c'))
The rest should follow from that.
I use the arrow functions (especially (***) and (&&&)) all the time on the (->) instance. My usage of those combinators for any other instance of Arrow is very rare. So whenever you see a b c, think "(generalized) function from b to c", which works for regular functions too.