David Barbour dmbarbour at gmail.com
Tue Nov 1 15:39:37 CET 2011

```On Mon, Oct 31, 2011 at 5:33 PM, Ryan Ingram <ryani.spam at gmail.com> wrote:

>
> 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.
>

As mentioned by others, Adam Megacz's generalized arrow (and its syntax)
could accomplish this. But if all you want is VHDL and the like, consider
Conal Elliott's work on Vertigo, Pan, Compiling Embedded Languages [1], and
the similar work on the Haskell GPipe package.

[1] http://conal.net/papers/jfp-saig/

Regards,

Dave

> 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
>
> _______________________________________________