Hi Harald,
Can you give a link to the paper? Interesting stuff. Thanks.
This is stretching my abilities a bit, but is this what you are after?
data Digit = forall b.(Digits (b Sz)) => Digit (Sz -> b Sz)
instance Digits [Digit] where
d2num [] acc = acc
d2num (Digit x:xs) acc = d2num xs (10*acc + d2num (x Sz) 0)
I assumed you only want D0..D9 as digits, maybe this is too narrow.
I've put this up on hpaste:
http://hpaste.org/8437#a1
Bests,
Anton
On Fri, Jun 20, 2008 at 3:01 PM, Harald ROTTER
Dear Haskellers,
after reading Oleg Kiselyov's paper on number-parameterized types I started to play around with the class Digits that encodes decimal numbers in types. The "typed number" 10 would e.g. be defined as
D1 $ D0 $ Sz
I wondered if it would be possible replace the expression above by a heterogeneous list like
[D1,D0]
so I tried to define
data Digit = forall a b.(Digits a, Digits (b a)) => Digit (a -> b a)
Loading this into ghci yields:
:t Digit D0
<interactive>:1:0: Ambiguous type variable `a' in the constraint: `Digits a' arising from a use of `Digit' at <interactive>:1:0-7 Probable fix: add a type signature that fixes these type variable(s)
Removing the type constraints in the definition of "Digit":
data Digit = forall a b.Digit (a -> b a)
makes it work like this:
:t Digit D0 Digit D0 :: Digit
:t [Digit D0, Digit D1] [Digit D0, Digit D1] :: [Digit]
"Digit", however, is far too general (it also includes e.g. \x -> [x]), but I would like it to be restricted to the Digit class.
Any help is appreciated.
Thanks
Harald.
CODE:
module Test where
data D0 a = D0 a data D1 a = D1 a data D2 a = D2 a data D3 a = D3 a data D4 a = D4 a data D5 a = D5 a data D6 a = D6 a data D7 a = D7 a data D8 a = D8 a data D9 a = D9 a
class Digits ds where d2num :: Num a => ds -> a -> a
data Sz = Sz -- zero size instance Digits Sz where d2num _ acc = acc
instance Digits ds => Digits (D0 ds) where d2num dds acc = d2num (t22 dds) (10*acc) instance Digits ds => Digits (D1 ds) where d2num dds acc = d2num (t22 dds) (10*acc+1) instance Digits ds => Digits (D2 ds) where d2num dds acc = d2num (t22 dds) (10*acc+2) instance Digits ds => Digits (D3 ds) where d2num dds acc = d2num (t22 dds) (10*acc+3) instance Digits ds => Digits (D4 ds) where d2num dds acc = d2num (t22 dds) (10*acc+4) instance Digits ds => Digits (D5 ds) where d2num dds acc = d2num (t22 dds) (10*acc+5) instance Digits ds => Digits (D6 ds) where d2num dds acc = d2num (t22 dds) (10*acc+6) instance Digits ds => Digits (D7 ds) where d2num dds acc = d2num (t22 dds) (10*acc+7) instance Digits ds => Digits (D8 ds) where d2num dds acc = d2num (t22 dds) (10*acc+8) instance Digits ds => Digits (D9 ds) where d2num dds acc = d2num (t22 dds) (10*acc+9)
t22 :: f x -> x t22 = undefined
--data Digit = forall a b.(Digits a, Digits (b a)) => Digit (a -> b a) data Digit = forall a b.Digit (a -> b a)
-------------------------------------------------------------------------------------------------
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