This PR completes aligning `List`/`Array`/`Vector` lemmas about
`flatten`. `Vector.flatten` was previously missing, and has been added
(for rectangular sizes only). A small number of missing `Option` lemmas
were also need to get the proofs to go through.
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.
by showing the matrix of calls and measures, and what we know about that
call (=, <, ≤, ?), e.g.
guessLexFailures.lean:27:0-33:31: error: Could not find a decreasing
measure.
The arguments relate at each recursive call as follows:
(<, ≤, =: relation proved, ? all proofs failed, _: no proof attempted)
x1 x2 x3
1) 29:6-25 = = =
2) 30:6-23 = ? <
3) 31:6-23 < _ _
Please use `termination_by` to specify a decreasing measure
It’s a bit more verbose for mutual functions.
It will use the user-specified argument names for functions written
```
foo (n : Nat) := …
```
but not with pattern matching like
```
foo : Nat → …
| n => …
```
This can be refined later and separately (and maybe right away in
`expandMatchAltsWhereDecls`).
If here is only one plausible measure, there is no point having the
`GuessLex` code see if it
is terminating, running all the tactics, only for the `MkFix` code then
run the tactics again.
So if there is only one plausible measure (non-mutual recursion with
only one varying
parameter), just use that measure.
Side benefit: If the function isn’t terminating, more detailed error
messages are shown
(failing proof goals), located at the recursive calls.
This improves Lean’s capabilities to guess the termination measure for
well-founded
recursion, by also trying lexicographic orders. For example:
def ackermann (n m : Nat) := match n, m with
| 0, m => m + 1
| .succ n, 0 => ackermann n 1
| .succ n, .succ m => ackermann n (ackermann (n + 1) m)
now just works.
The module docstring of `Lean.Elab.PreDefinition.WF.GuessLex` tells the
technical story.
Fixes#2837
