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.
This commit also removes parameter `simpleReduce` from discrimination
trees, and take WHNF configuration options.
Reason: it is more dynamic now. For example, the simplifier
will be able to use different configurations for discrimination tree insertion
and retrieval. We need this feature to address issues #2669 and #2281
This commit also removes the dead Meta.Config field `zetaNonDep`.
