[Haskell-cafe] arr considered harmful

[Daniel Peebles]

Have you seen Adam Megacz's work on generalized arrows? I think he proposes
to kill arr and has done a decent amount of work on it.

On Mon, Oct 31, 2011 at 8:33 PM, Ryan Ingram <ryani.spam at gmail.com> wrote:

> I know it's a bit of an 'intentionally provocative' title, but with the
> recent discussions on Arrows I thought it timely to bring this up.
>
> Most of the conversion from arrow syntax into arrows uses 'arr' to move
> components around. However, arr is totally opaque to the arrow itself, and
> prevents describing some very useful objects as arrows.
>
> For example, I would love to be able to use the arrow syntax to define
> objects of this type:
>
> data Circuit a b where
>     Const :: Bool -> Circuit () Bool
>     Wire :: Circuit a a
>     Delay :: Circuit a a
>     And :: Circuit (Bool,Bool) Bool
>     Or :: Circuit (Bool,Bool) Bool
>     Not :: Circuit Bool Bool
>     Then :: Circuit a b -> Circuit b c -> Circuit a c
>     Pair :: Circuit a c -> Circuit b d -> Circuit (a,b) (c,d)
>     First :: Circuit a b -> Circuit (a,c) (b,c)
>     Swap :: Circuit (a,b) (b,a)
>     AssocL :: Circuit ((a,b),c) (a,(b,c))
>     AssocR :: Circuit (a,(b,c)) ((a,b),c)
>     Loop :: Circuit (a,b) (a,c) -> Circuit b c
> etc.
>
> Then we can have code that examines this concrete data representation,
> converts it to VHDL, optimizes it, etc.
>
> However, due to the presence of the opaque 'arr', there's no way to make
> this type an arrow without adding an 'escape hatch'
>     Arr :: (a -> b) -> Circuit a b
> which breaks the abstraction: circuit is supposed to represent an actual
> boolean circuit; (Arr not) is not a valid circuit because we've lost the
> information about the existence of a 'Not' gate.
>
> The arrow syntax translation uses arr to do plumbing of variables.  I
> think a promising project would be to figure out exactly what plumbing is
> needed, and add those functions to a sort of 'PrimitiveArrow' class.  All
> of these plumbing functions are trivially implemented in terms of 'arr',
> when it exists, but if it doesn't, it should be possible to use the arrow
> syntax regardless.
>
>   -- ryan
>
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