This PR adds support for `structure` in `mutual` blocks, allowing
inductive types defined by `inductive` and `structure` to be mutually
recursive. The limitations are (1) that the parents in the `extends`
clause must be defined before the `mutual` block and (2) mutually
recursive classes are not allowed (a limitation shared by `class
inductive`). There are also improvements to universe level inference for
inductive types and structures. Breaking change: structure parents now
elaborate with the structure in scope (fix: use qualified names or
rename the structure to avoid shadowing), and structure parents no
longer elaborate with autoimplicits enabled.
Internally, this is a large refactor of both the `inductive` and
`structure` commands. Common material is now in
`Lean.Elab.MutualInductive`, and each command plugs into this mutual
inductive elaboration framework with the logic specific to the
respective command. For example, `structure` has code to add projections
after the inductive types are added to the environment.
Closes#4182
@Kha we do that in Lean 3. It helps when the error is due to incorrect universe levels.
BTW, I had to update `tests/lean/server/content_diag.json` since the
error message is different, but a few other stuff changed too.
Could you please take a look whether the test is still correct?
@Kha This commit adds auto bound implicits to constructors.
I was excited until I tried to define the `Bigstep` type again without
`autoBoundImplicitLocal`, and found small typos.
Example, I had
```
| ifTrue : eval σ₁ b = true → Bigstep (c₁, σ₁) σ₂ t → Bigstep (cond b c₁ c₂, σ₁) σ₂ (t₁ + 1)
```
where `t₁` should be `t`, but the declaration was accepted. I am
wondering whether Isabelle performs some kind of sanity checking,
and/or enforces rules such as: auto-bound implicits may only be
introduced by hypotheses.
Note that this is not an issue for definitions, because the body of
the definition will probably not type check when we have this kind of
typo in the header.
Anyway, I am putting the experiment in this branch for now.
That being said, the `Bigstep` declaration is way nicer with
`autoBoundImplicitLocal`s.
Another option is to add a new option `ctorAutoBoundImplicitLocal`
that is false by default, and activates auto implicit locals for
constructors when set to true.
