the support for mutual structural recursion (new since #4575) is
extended so that Lean tries to infer it even without annotations.
* The error message when termination checking fails looks quite
different now. Maybe a bit better, maybe with more room for
improvements.
* If there are too many combinations (with an arbitrary cut-off) for a
given argument type, it will just give up and ask the user to use
`termination_by structural`.
* It is now legal to specify `termination_by structural` on not
necessarily all functions of a clique; this simply restricts the
combinations of arguments that Lean considers.
---------
Co-authored-by: Tobias Grosser <tobias@grosser.es>
this is in preparation for #4542, and extracts from `findRecArg` the
functionality for trying one particular argument.
It also refactors the code a bit. In particular
* It reports errors in the order of the parameters, not the order of
in which they are tried (it tries non-indices first).
* For every argument it will say why it wasn't tried, even if the
reason is quite obviously (fixed prefix, or `Prop`-typed etc.)
Therefore there is some error message churn.
This didn't work before
```
def f (n : Nat) : Nat :=
match n with
| 0 => 0
| n + 1 => (f) n
```
because the `RecApp` metadata marker gets in the way. More practically
relevant, such code is to be produced when using `rw` or `simp` in
recursive theorems (see included test case).
We can fix this by preprocessing the definitions and floating the
`.mdata` marker out of applications.
For structural recursion, there already exists a `preprocess` function;
this now also floats out `.mdata` markers.
For well-founded recursion, this introduces an analogous `preprocess`
function.
Fixes#2810.
One test case output changes: With the `.mdata` out of the way, we get a
different error message. Seems fine.
Alternative approaches are:
* Leaving the `.mdata` marker where it is, and looking around it.
Tried in #2813, but not nice (many many places where `withApp` etc.
need to be adjusted).
* Moving the `.mdata` _inside_ the application, so that `withApp` still
works. Tried in #2814. Also not nice, the invariant that the `.mdata`
is around the `.const` is tedious to maintain.
