Modifies the structure instance elaborator to
1. Fill in missing fields from sources in strict left-to-right order. In
`{a, b with}`, sometimes the elaborator
would ignore `a` even if both `a` and `b` provided the same field,
depending on what subobject fields they had.
2. Use the sources, or subobjects of the sources, to fill in entire
subobjects of the target structure as much as possible.
Currently, a field cannot be filled directly by a source itself
resulting in the term being eta expanded.
This change avoids this unnecessary and surprisingly costly extra eta
expansion.
Adds two new tests to illustrate the performance benefit (one courtesy
@semorrison). These are currently failing on master and succeed on this
branch.
There is one additional test to exercise the changes to the elaboration
of structure instances.
Changes to make mathlib build are in leanprover-community/mathlib4#9843
Closes#2451
This PR adds two new delaboration settings: `pp.deepTerms : Bool`
(default: `true`) and `pp.deepTerms.threshold : Nat` (default: `20`).
Setting `pp.deepTerms` to `false` will make the delaborator terminate
early after `pp.deepTerms.threshold` layers of recursion and replace the
omitted subterm with the symbol `⋯` if the subterm is deeper than
`pp.deepTerms.threshold / 4` (i.e. it is not shallow). To display the
omitted subterm in the InfoView, `⋯` can be clicked to open a popup with
the delaborated subterm.
<details>
<summary>InfoView with pp.deepTerms set to false (click to show
image)</summary>
</details>
### Implementation
- The delaborator is adjusted to use the new configuration settings and
terminate early if the threshold is exceeded and the corresponding term
to omit is shallow.
- To be able to distinguish `⋯` from regular terms, a new constructor
`Lean.Elab.Info.ofOmissionInfo` is added to `Lean.Elab.Info` that takes
a value of a new type `Lean.Elab.OmissionInfo`.
- `ofOmissionInfo` is needed in `Lean.Widget.makePopup` for the
`Lean.Widget.InteractiveDiagnostics.infoToInteractive` RPC procedure
that is used to display popups when clicking on terms in the InfoView.
It ensures that the expansion of an omitted subterm is delaborated using
`explicit := false`, which is typically set to `true` in popups for
regular terms.
- Several `Info` widget utility functions are adjusted to support
`ofOmissionInfo`.
- The list delaborator is adjusted with special support for `⋯` so that
long lists `[x₁, ..., xₖ, ..., xₙ]` are shortened to `[x₁, ..., xₖ, ⋯]`.
Adds support for `let_fun` to the `intro` and `intros` tactics. Also
adds support to `intro` for anonymous binder names, since the default
variable name for a `letFun` with an eta reduced body is anonymous.
This makes changes to the definitions of Associativity, Commutativity,
Idempotence and Identity classes to be more aligned with Mathlib's
versions.
The changes are:
* Move classes are moved from `Lean` to root namespace.
* Drop `Is` prefix from names.
* Rename `IsNeutral` to `LawfulIdentity` and add Left and Right
subclasses.
* Change neutral/identity element to outParam.
* Introduce `HasIdentity` for operations not intended for proofs to
implement
The identity changes are to make this compatible with
[Mathlib](718042db9d/Mathlib/Init/Algebra/Classes.lean)
and to enable nicer fold operations in Std that can use type classes to
infer the identity/initial element on binary operations.
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
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).
As suggested by @kmill, removing an unnecessary `let` (possibly only
there in the first place for copy/paste reasons) seems to fix the
included test.
This makes `~q()` matching in quote4 noticeably more useful in things
like `norm_num` (as it fixes
https://github.com/leanprover-community/quote4/issues/29)
It also makes a quote4 bug slightly more visible
(https://github.com/leanprover-community/quote4/issues/30), but the bug
there already existed anyway, and isn't caused by this patch.
Fixes#3065
there was a check
if !Structural.recArgHasLooseBVarsAt recFnName fixedPrefixSize e then
that would avoid going through `.refineThrough`/`.addArg` for
matcher/casesOn applications. It seems it tries to detect when refining
the motive/param is pointless, but it was too eager, and cause confusion
with, for example, this reasonably reasonable function:
def foo : (n : Nat) → (i : Fin n) → Bool
| 0, _ => false
| 1, _ => false
| _+2, _ => foo 1 ⟨0, Nat.zero_lt_one⟩
decreasing_by simp_wf; simp_arith
In particular, the `GuessLex` code later expects that the (implict)
`PProd.casesOn` in the implementation of `foo._unary` will refine the
paramter, because else the (rather picky) `unpackArg` fails. But it also
prevents this from being provable.
So let's try without this shortcut.
Fixing this also revealed that `withRecApps` wasn’t looking in all
corners
of a matcherApp/casesOnApp.
Fixes#3175
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.
Allow `simproc`s to be declared without setting the `[simproc]`
attribute. A `simproc` declaration is function + pattern.
Motivation: allow them to be provided as arguments to `simp` **and** `simp only`.
TODO: track their use in `simp`.
TODO: builtin simprocs
See new test for example that takes exponential time without new simp
theorems.
TODO: replace auxiliary theorems with simprocs as soon as we implement them.
#2966 was the `@[extern]` bug that prompted development of the
`test_extern` command, but then we merged the fix to #2966 without
updating the tests to use `test_extern`.
Fixes reference implementation of `ByteArray.copySlice`, as reported
https://github.com/leanprover/lean4/issues/2966.
Adds tests.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
until around 7fe6881 the way to define well-founded recursions was to
specify a `WellFoundedRelation` on the argument explicitly. This was
rather low-level, for example one had to predict the packing of multiple
arguments into `PProd`s, the packing of mutual functions into `PSum`s,
and the cliques that were calculated.
Then the current `termination_by` syntax was introduced, where you
specify the termination argument at a higher level (one clause per
functions, unpacked arguments), and the `WellFoundedRelation` is found
using type class resolution.
The old syntax was kept around as `termination_by'`. This is not used
anywhere in the lean, std, mathlib or the theorem-proving-in-lean
repositories,
and three occurrences I found in the wild can do without
In particular, it should be possible to express anything that the old
syntax
supported also with the new one, possibly requiring a helper type with a
suitable instance, or the following generic wrapper that now lives in
std
```
def wrap {α : Sort u} {r : α → α → Prop} (h : WellFounded r) (x : α) : {x : α // Acc r x}
```
Since the old syntax is unused, has an unhelpful name and relies on
internals, this removes the support. Now is a good time before the
refactoring that's planned in #2921.
The test suite was updated without particular surprises.
The parametric `terminationHint` parser is gone, which means we can
match on syntax more easily now, in `expandDecreasingBy?`.
With
set_option showInferredTerminationBy true
this prints a message like
Inferred termination argument:
termination_by
ackermann n m => (sizeOf n, sizeOf m)
it tries hard to use names that
* match the names that the user used, if present
* have no daggers (so that it can be copied)
* do not shadow each other
* do not shadow anything from the environment (just to be nice)
it does so by appending sufficient `'` to the name.
Some of the emitted `sizeOf` calls are unnecessary, but they are needed
sometimes with dependent parameters. A follow-up PR will not emit them
for non-dependent arguments, so that in most cases the output is pretty.
Somewhen down the road we also want a code action, maybe triggered by
`termination_by?`. This should come after #2921, as that simplifies that
feature (no need to merge termination arguments from different cliques
for example.)
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
The `packMutual` code ought to reliably replace all recursive calls to
the functions in `preDefs`, even when they are under- or over-applied.
Therefore eta-expand if need rsp. keep extra arguments around.
Needs a tweak to `Meta.transform` to avoid mistaking the `f` in
`f x1 x2` as a zero-arity application.
Includes a test case.
This fixes#2628 and #2883.
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.
the code stumbled over recursive functions whose type doesn’t have
enough manifest foralls, like:
```
def FunType := Nat → Nat
mutual
def foo : FunType
| .zero => 0
| .succ n => bar n
def bar : FunType
| .zero => 0
| .succ n => foo n
end
termination_by foo n => n; bar n => n
```
This can be fixed by using `whnf` in appropriate places, to expose the
`.forall` constructor.
Fixes#2925, comes with test case.
previously, it would ignore a recursive call that has extra arguments,
which can happen when the recursive functions return something of
function type. Therefore just leave them extra arguments in place.
Fixes#2883.
`simp` was previously swallowing runtime exceptions and masking an
issue with this example.
`runT` is defined by well-founded recursion, but reducing the ground
term `runT x` takes a long time when `decide := true`.
Remark PR #2722 changes the `decide` default value to `false`.
When `decide := true`, we should probably have better diagnostics /
error messages for this kind of situation.
The notation `a ∈ as` for Arrays was previously only defined with
`DecidableEq` on the elements, for (apparently) no good reason. This
drops this requirements (by using `a ∈ as.data`), and simplifies a bunch
of proofs by simply lifting the corresponding proof from lists.
Also, `sizeOf_lt_of_mem` was defined, but not set up to be picked up by
`decreasing_trivial` in the same way that the corresponding List lemma
was set up, so this adds the tactic setup.
The definition for `a ∈ as` is intentionally not defeq to `a ∈ as.data`
so that the termination tactics for Arrays don’t spuriously apply when
recursing through lists.
