Recursive predefinitions contains “rec app” markers as mdata in the
predefinitions,
but sometimes these get in the way of termination checking, when you
have
```
[mdata (fun x => f)] arg
```
Therefore, the `preprocess` pass floats them out of applications
(originally
only for structural recursion, since #2818 also for well-founded
recursion).
But the code was incomplete: Because `Meta.transform` calls `post` on `f
x y` only
once (and not also on `f x`) one has to float out of nested applications
as well.
A consequence of this can be that in a recursive proof, `rw [foo]` does
not work
although `rw [foo _ _]` does.
Also adding the testcase where @david-christiansen and I stumbled over
this
(Maybe the two preprocess modules can be combined, now that #2973 is
landed, will try that
in a follow-up).
This change
* moves `termination_by` and `decreasing_by` next to the function they
apply to
* simplify the syntax of `termination_by`
* apply the `decreasing_by` goal to all goals at once, for better
interactive use.
See the section in `RELEASES.md` for more details and migration advise.
This is a hard breaking change, requiring developers to touch every
`termination_by` in their code base. We decided to still do it as a
hard-breaking change, because supporting both old and new syntax at the
same time would be non-trivial, and not save that much. Moreover, this
requires changes to some metaprograms that developers might have
written, and supporting both syntaxes at the same time would make
_their_ migration harder.
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.
