Version 1 (modified by diatchki, 6 years ago) (diff) |
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The only "magic" thing about `GHC.TypeNats` are the instances of `TypeNat`. The rest is implemented like this:

newtype Nat (n :: Nat) = Nat Integer natToInteger :: Nat n -> Integer natToInteger (Nat n) = n integerToNat :: Integer -> (forall n. Nat n -> a) -> a integerToNat n k = k (Nat n)

So, now we just need instances like these:

instance TypeNat 0 where nat = Nat 0 instance TypeNat 1 where nat = Nat 1 instance TypeNat 2 where nat = Nat 2 ...

Because we cannot generate this infinite family of instances, we have
some code in GHC which can solve `TypeNat` predicates on the fly.

The "proof" (aka "dictionary") for `TypeNat 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.`TypeNat`is just such a class. `Nat`is already a`newtype`for`Integer`.

Therefore, the dictionaries for class `TypeNat` are just integers.