The only "magic" thing about `GHC.TypeLits`

are the instances of `SingI`

. The rest is implemented like this:

```
newtype Sing n = Sing (SingRep n)
type family SingRep a
type instance SingRep (n :: Nat) = Integer
type instance SingRep (n :: Symbol) = String
fromSing :: Sing n -> SingRep n
fromSing (Sing n) = n
```

So, now we just need instances like these:

```
instance SingI 0 where sing = Sing 0
instance SingI 1 where sing = Sing 1
instance SingI "hello" where sing = Sing "hello"
...
```

Because we cannot generate this infinite family of instances, we have
some code in GHC which can solve `SingI`

predicates on the fly.

The "proof" (aka "dictionary") for `SingI n`

is just the number (or string) `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.`SingI`

is just such a class. -
`Sing`

is already a`newtype`

for`Integer`

or`String`

, depending on the kind of its parameter.

Therefore, the dictionaries for class `SingI`

are just integers or strings, depending on the kind of the parameter.