Re: [Haskell-cafe] arr considered harmful

21 Dec 2012


      Oh, I see Ross's trick. By quantifying over the domain & range types, they
can later be specialized to analysis-time types (like circuit labels) or to
run-time types (like Boolean or Integer).

On Thu, Dec 20, 2012 at 4:55 PM, Conal Elliott  wrote:
...
If you require the circuit to be parametric in the value types, you can
...
limit the types of function you can pass to arr to simple plumbing.
See the netlist example at the end of my "Fun of Programming" slides (
http://www.soi.city.ac.uk/~ross/papers/fop.html).
I'm running into this same issue: I have something (another circuits
formulation) that's almost an arrow but doesn't support arr. I'd like to
use arrow notation, but then I run afoul of my missing arr. I'd like to
understand Ross's suggestion and how to apply it. (I've read the "FoP"
slides.)
Ross: do you mean to say that you were able to implement arr and thus run
your circuit examples via the standard arrow desugarer?
Ryan: did you get a working solution to the problem you described for your
Circuit arrow?
Thanks.  -- Conal
On Mon, Oct 31, 2011 at 6:52 PM, Paterson, Ross wrote:
...
...
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
Ryan Ingram writes:
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.
If you require the circuit to be parametric in the value types, you can
limit the types of function you can pass to arr to simple plumbing.
See the netlist example at the end of my "Fun of Programming" slides (
http://www.soi.city.ac.uk/~ross/papers/fop.html).
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