@kha I have added support for opaque constants to the old C++ frontend,
and made sure the new frontend can still parse `library/init/core.lean`.
The kernel should enforce that opaque constants are really opaque, and
the following example should fail
```
constant x : nat := 0
theorem foo : x = 0 := rfl
```
If it doesn't, it is a bug.
Here are some remaining issues:
1- `environment.mk_empty` is currently an axiom because we cannot create
an inhabitant of an opaque type. A possible solution is to use
`option environment` instead of `environment`.
2- There is no support for opaque constants in the new
frontend. However, I modified it to handle axioms, and fixed the literal
values with decl_cmd_kind. I tried to mark some of my changes with
comments, but it is probably much easier for you to just check the
commit change list.
3- I did not add any support for automatically constructing `e`
at `constant x : t := e`. I think we can do this later
after we replace the old frontend with the new one. BTW, it took only a
few minutes to provide the inhabitants manually.
We don't need to use `opaque` for `thunk` and `task`. Their recursor and
projections can be implemented in constant time. We just need to create
a closure which uses the runtime thunk_get/task_get primitive.
@kha I was working in the new declaration type and using tasks there.
Since we don't have tasks yet in Lean, I decided to start refactoring
the `thunk` type. I defined it as:
```
-- TODO(Leo): mark as opaque, it is implemented by the new runtime
structure thunk (α : Type u) : Type u :=
(fn : unit → α)
def thunk.pure {α : Type u} (a : α) : thunk α :=
⟨λ _, a⟩
def thunk.get {α : Type u} (t : thunk α) : α :=
t.fn ()
```
The idea is to use the runtime primitives to implement them.
Then, I realized the support for `thunk`s in the elaborator are quite
hacky. Given `f x`, if `f`'s domain has type `thunk A`, we elaborate
`f x` as `f (fun _, x)` even if `x` has type `thunk A`.
This is quite bad, for example, suppose we have
```
def f (x : thunk A) := ...
```
Then, the following definition is type incorrect.
```
def g (x : thunk A) := f x
```
and we are forced to write
```
def g (x : thunk A) := f (x ())
```
The term `f (x ())` will be elaborated as `f (fun _, x ())` and an
unnecessary closure is created at runtime.
This mechanism inherited from Lean 3 is also incompatible with the
new thunk definition. Given `x : thunk A`, I want to write `x.get`
to retrieve the value instead of `x ()` as in Lean 3.
However, `x.get` expands into the nonsensical `(fun _, x).get`.
So, I decided to view the mapping `A` to `thunk A` as a "coercion".
I used double quotes, because it is a macro instead of a function.
If it were a coercion, then we would be using `thunk.pure` to coerce
values but this is not we want most of the time.
For example, given `f : thunk A -> B` and a term `t : A`, when we write
`f t`, we want it to be converted into `f (fun _, t)` instead of
`f (thunk.pure t)` which would eagerly compute `t`. The transformation
`t` into `fun _, t` is syntactic.
We cannot implement it using type classes. I implemented it as
a hard-coded extra case like the one from `Prop` to `bool`.
We can also add a coercion from `thunk A` to `A` to avoid the `.get`.
That being said, I had a few breakages in the code base since we only
use coercions when the given and expected type do not contain
metavariables.
We now define nat.le using (nat.ble : nat -> nat -> bool) function.
We will add builtin support for reducing `nat.ble` efficiently when the arguments are the to be added nat literals.
