In Lean 4, we will support the more general
`a + ·` ==> `fun x, a + x`
`· + b` ==> `fun x, x + b`
`· + ·` ==> `fun x y, x + y`
`f · y` ==> `fun x, f a y`
`g · · b` ==> `fun x y, g x y b`
Old `Nat.repeat` => `Nat.for`
Old `Nat.mrepeat` => `Nat.mfor`
New `Nat.repeat` has type
```
def repeat {α : Type u} (f : α → α) (n : Nat) (a : α) : α :=
``
`List.repeat` => `List.replicate` (like in Haskell)
Avoid weird `ℕ` in List library
@kha: I initially planned to use the UTF8 API only in very special
cases, but I found them to be super useful. They allow us to implement
an efficient String library mostly in Lean.
However, the there was a problem: `abbrev String.Pos := USize`.
This definition is fine for a low level API, but this is not the case
anymore. By having `String.Pos := USize`, we will not be able to
prove natural theorems for the `String` API. For example,
`String.map id s = s` did not hold. We would have to include the
artificial antecedent `s.length <= usizeMax` (or something like this).
I suspect it would be very painful.
So, this commit defines `String.Pos` as `Nat`. The performance
overhead seems to be very small.
The `offset` field is problematic because it prevents us from having an
efficient way of moving back and forth between `String.Pos` and `String.Iterator`.
@kha I temporarily added `String.OldIterator` for making sure the
parser doesn't break. This is a temporary fix that will be eliminated
after we replace `parsec`.
@kha I am finding the UTF8 API super useful. So, I am giving nice names
to it. The API is safe for users and the runtime implementation should
match the reference one.
@kha I've added
iterator.extract : iterator -> iterator -> option string
It returns `none` if the iterators are "incompatible".
If this function is inconvenient to use, we can change it and return the
empty string in these cases.
Given iterators `it1` and `it2`, if they are sharing the same string
object in memory, then the cost is O(pos(it2) - pos(it1)).
If not, we have an extra O(N) step where we check whether the strings
being iterated by it1 and it2 are equal (`N` is the size of the strings).
In most applications, I believe the iterators will share the string
object.
I didn't test the code much. BTW, I found an unrelated bug at
vm_string.cpp. So, I'm not very confident this code is rock solid.
