arr considered harmful
2011-11-01 00:33:14 GMT
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
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.
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