@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.
The idea is to reuse the cell. The trick is like the one we used for
improving state_t. It seems to work pretty well. Now, the Lean
version is 29% slower than the C++ one.
cc @kha
@kha The VM versions just throw exceptions. They are just stubs to
make sure we can compile Lean.
I implemented the uint functions in the new runtime, but there are a
few missing cases marked with TODO.
I needed these builtins to be able to compile the C++ generated code for
corelib.
Building a proper `equations` pexpr in Lean is not feasible right now because we
need global+local name resolution, [pattern] attribute retrieval, ... to
reimplement `patexpr_to_pattern`. The `pre_equations` will instead be converted
by the old elaborator using this function (TBD).
With this change, `to_pexpr` can now translate every basic definition body in
`core.lean`.
Now, the nodes in a `rbmap` contain the key and value, and we avoid
one level of indirection. `rbmap`s are more common than `rbtree`.
We implement `rbtree A` as `rbmap A unit`.
Both `alternative` and `monad` implement `applicative`. However,
their default implementations for `seq_right` and `seq_left` are
different. The `alternative` implementation uses the inefficient default
version for `seq_right` available at `applicative`:
```
(seq_right := λ α β a b, const α id <$> a <*> b)
```
instead of the more efficient
```
(seq_right := λ α β x y, x >>= λ _, y)
```
defined at `monad` using the `bind` operator.
This commit makes sure the `applicative` instances for `reader_t`,
`state_t`, `option` and `parsec_t` use the efficient version.
I found the problem when inspecting the generated code for:
```
def symbol (s : string) : parsec' unit :=
(str s *> whitespace) <?> ("'" ++ s ++ "'")
```
