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# Proposed changes to arrow notation

This page describes a couple of proposed changes to the notation enabled with -XArrows. (current documentation)

## Changing the types of arrow operators

Currently, the type of each argument of an operator (and its result) is required have the form

a (...(e,t1), ... tn) t

where `e` is a type variable shared by all these types, but the arrow types `a` can vary. The User's Guide has these examples:

ArrowPlus a => (<+>) :: a e c -> a e c -> a e c untilA :: ArrowChoice a => a e () -> a e Bool -> a e () handleA :: ... => a e c -> a (e,Ex) c -> a e c bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d runReader :: ... => a e c -> a' (e,State) c runState :: ... => a e c -> a' (e,State) (c,State) bind :: Arrow a => a e b -> a (e,b) c -> a e c bind_ :: Arrow a => a e b -> a e c -> a e c cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b

The problem is that to work out how many `ti`s there are, the type checker needs to be able to determine whether a type is a pair type or this Skolem variable `e`, and this can't be done with GHC's new constraint-based type system.

The plan is to re-arrange the shapes of the argument and result types to

a (e, (t1, ... (tn, ())...)) t

For the above examples, the new types will be

ArrowPlus a => (<+>) :: a (e,()) c -> a (e,()) c -> a (e,()) c untilA :: ArrowChoice a => a (e,()) () -> a (e,()) Bool -> a (e,()) () handleA :: ... => a (e,()) c -> a (e,(Ex,())) c -> a (e,()) c bracketA :: ... => a (e,()) b -> a (e,(b,())) c -> a (e,(c,())) d -> a (e,()) d runReader :: ... => a (e,()) c -> a' (e,(State,())) c runState :: ... => a (e,()) c -> a' (e,(State,())) (c,State) bind :: Arrow a => a (e,()) b -> a (e,(b,())) c -> a (e,()) c bind_ :: Arrow a => a (e,()) b -> a (e,()) c -> a (e,()) c cond :: ArrowChoice a => a (e,()) b -> a (e,()) b -> a (e,(Bool,())) b

Now in the cases of `(<+>)`, `untilA` and `bind`, the new types are specializations of the old, so those operators will still work, but the others will need to be re-defined with the new types.

## Generalizing the types of commands

The translation of many of the different varieties of command does not require the full `Arrow` class, but rather just

premap :: Arrow a => (b -> b') -> a b' c -> a b c premap f g = arr f >>> g

So the proposal is to introduce a superclass of `Arrow` with just this:

class PreArrow a where premap :: Arrow a => (b -> b') -> a b' c -> a b c

and require that class instead of `Arrow` for the types of those constructs. (libraries proposal)

This shouldn't break any code that uses arrows, but will require rewriting of instances of `Arrow`.