Syntax in the explanation

I was reading https://github.com/HigherOrderCO/Kind1/blob/master/blog/1-beyond-inductive-datatypes.md, and there's one part I don't quite understand.

```
// Natural numbers
Nat: Type
self(P: Nat -> Type) ->
(zero: P(Nat.zero)) ->
(succ: (pred: Nat) -> P(Nat.succ(pred))) ->
P(self)
```

If it's like the code below, it makes sense to me.

```
// Natural numbers
Nat: Type
(self : Nat) ->
(P: Nat -> Type) ->
(zero: P(Nat.zero)) ->
(succ: (pred: Nat) -> P(Nat.succ(pred))) ->
P(self)
```

So what is `self`?