This change allows the monadic traversal operations on arrays to use monads that
are defined to raise universe levels. This happens, for example, when defining
monads using certain continuation-passing idioms.
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`
This commit also removes Array.hmap.
Motivation: I wanted to use Array.hmap as an example in the paper, but
I found it would be too distracting to explain why we had `Array.hmap`
and `Array.map`.
cc @kha
@kha Trying again :)
I started using the prefix `f` for the `Fin` version (e.g., `fswap` and
`fswapAt`). So, it seemed natural to use the prefix `f` for the `Fin`
versions of `get` and `set`.
BTW, is it too crazy to use `a[i]` (without spaces) as notation for
`a.get i`? The constraint is to make sure `f a [i]` is not ambiguous.
That is, `f a[i]` is `f (a.get i)` and `f a [i]` is `f a (i::nil)`.
This is doable with the new parser.
Then, we could have `a[i]` as notation for `a.fget i` if `i` is a `Fin`,
and `a.get i` if `i` is `Nat`.
Similarly, `a[i := v]` would be notation for `a.fset i v` if `i` is
`Fin`, and `a.set i` if `i` is `Nat`.
It would also be awesome to have
```
let a[i] := v in
e
```
as notation for
```
let a := a[i := v] in
```
The `mforeachAux` function was keeping two references to the array
because it was implemented using `miterate a ⟨a, rfl⟩ ...`
Thus, we would have to allocate a new array even if `a` was not shared.
Another issue is that when invoking `x ← f i v`, the array would still
have a reference to `v`, and consequently `RC(v) > 1`, and `f` would not
be able to perform destructive updates to `v` or reuse its memory cell.
Thus, I removed `mforeach` (we only used it to implement `hmap`: the
homogeneous map), and implemented a new `hmap` which makes sure
destructive updates can be performed modulo the issue with float `let`
inwards I described in the previous commit.
@kha I found the problem described in the previous commit when I was
using `Array.hmap`. If we use `Array`s to implement `Syntax` as we discussed,
then a `hmap` that does not prevent destructive updates from happening is
a must-have. Otherwise, any benefit we get from using `Array`s instead
of `List`s is gone.
@kha I renamed the homogeneous `map` to `hmap`, and added the
heterogeneous one as `map`. As soon as we add user-defined rewriting
rules, we will be able to replace `map` with `hmap` whenever the types
are the same.
