|Version 4 (modified by diatchki, 4 years ago) (diff)|
The only "magic" thing about GHC.TypeNats are the instances of NatI. The rest is implemented like this:
newtype TNat (n :: Nat) = TNat Integer tNatInteger :: TNat n -> Integer tNatInteger (TNat n) = n
So, now we just need instances like these:
instance NatI 0 where nat = TNat 0 instance NatI 1 where nat = TNat 1 instance NatI 2 where nat = TNat 2 ...
Because we cannot generate this infinite family of instances, we have some code in GHC which can solve NatI predicates on the fly.
The "proof" (aka "dictionary") for NatI n is just the number n. This is OK because:
- GHC uses a newtype to represent the dictionaries for classes that have just a single method and no super-classes. NatI is just such a class.
- TNat is already a newtype for Integer.
Therefore, the dictionaries for class NatI are just integers.