On Tue, Aug 25, 2009 at 12:07 AM, Ryan Ingram
unsafeCoerce is ugly and I wouldn't count on that working properly.
Here's a real solution: ...
Thanks very much! I'm beginning to understand the code. The only thing I don't understand is why you need:
newtype Witness x = Witness { unWitness :: x } witnessNat :: forall n. Nat n => n witnessNat = theWitness where theWitness = unWitness $ induction (undefined `asTypeOf` theWitness) (Witness Z) (Witness . S . unWitness)
I understand that 'witnessNat' is a overloaded value-level generator for Nats. So for example: 'witnessNat :: S (S (S Z))' returns the value: 'S (S (S Z))'. Then you use it in the implementation of 'toList' and 'fromList':
toList = ... induction (witnessNat :: n) ... fromList = ... induction (witnessNat :: n) ...
I guess so that 'induction' will then receive the right 'Nat' _value_. However the following also works:
toList = ... induction (undefined :: n) ... fromList = ... induction (undefined :: n) ...
Indeed, 'witnessNat' itself is implemented this way:
witnessNat = theWitness where theWitness = ... induction (undefined `asTypeOf` theWitness) ...
So the 'n' in 'induction n' is just a "type carrying parameter" i.e. it doesn't need to have a run-time representation. Al dough it looks like that a case analysis on 'n' is made at run-time in:
instance Nat n => Nat (S n) where caseNat (S n) _ s = s n
But I guess that is desugared away because 'S' is implemented as a newtype:
newtype S n = S n
Indeed, when I make an actual datatype of it then 'witnessNat :: S (S (S Z))' will crash with "*** Exception: Prelude.undefined". Again, thanks very much for this! Do you mind if I use this code in the levmar package (soon to be released on hackage)? regards, Bas