The `conv` tactic tries to close “trivial” goals after itself. As of
now, it uses
`try rfl`, which means it can close goals that are only trivial after
reducing with
default transparency. This is suboptimal
* this can require a fair amount of unfolding, and possibly slow down
the proof
a lot. And the user cannot even prevent it.
* it does not match what `rw` does, and a user might expect the two to
behave the
same.
So this PR changes it to `with_reducible rfl`, matching `rw`’s behavior.
I considered `with_reducible eq_refl` to only solve trivial goals that
involve equality,
but not other relations (e.g. `Perm xs xs`), but a discussion on mathlib
pointed out
that it’s expected and desirable to solve more general reflexive goals:
https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Closing.20after.20.60rw.60.2C.20.60conv.60.3A.20.60eq_refl.60.20instead.20of.20.60rfl.60/near/429851605
This makes changes to the `GetElem` class so that it does not lead to
unnecessary overhead in container like `RBMap`.
The changes are to:
1. Make `getElem?` and `getElem!` part of the `GetElem` class so they
can be overridden in instances.
2. Introduce a `LawfulGetElem` class that contains correctness theorems
for `getElem?` and `getElem!` using the original definitions.
3. Reorganize definitions (e.g, by moving `GetElem` out of
`Init.Prelude`) so that the `GetElem` changes are feasible.
4. Provide `LawfulGetElem` instances to complement all existing
`GetElem` instances in Lean core.
To reduce the size of the PR, this doesn't do the work of providing new
`GetElem` instances for `RBMap`, `HashMap` etc. That will be done in a
separate PR (#3688) that depends on this.
---------
Co-authored-by: Mac Malone <tydeu@hatpress.net>
fixes#3657
These functions are mostly not used by lean itself, but it does affect
two occurrences of `ByteArray.toUInt64LE! <$> IO.getRandomBytes 8` which
I left as is instead of switching them to use `toUInt64BE!` to preserve
behavior; but they are random bytes anyway seeded by the OS so it's
unlikely any use of them depending on particular values was sound to
begin with.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Previously:
If the `rfl` macro was going to fail, it would:
1. expand to `eq_refl`, which is implemented by
`Lean.Elab.Tactic.evalRefl`, and call `Lean.MVarId.refl` which would:
* either try kernel defeq (if in `.default` or `.all` transparency mode)
* otherwise try `IsDefEq`
* then fail.
2. Next expand to the `apply_rfl` tactic, which is implemented by
`Lean.Elab.Tactic.Rfl.evalApplyRfl`, and call `Lean.MVarId.applyRefl`
which would look for lemmas labelled `@[refl]`, and unfortunately in
Mathlib find `Eq.refl`, so try applying that (resulting in another
`IsDefEq`)
3. Because of an accidental duplication, if `Lean.Elab.Tactic.Rfl` was
imported, it would *again* expand to `apply_rfl`.
Now:
1. Same behaviour in `eq_refl`.
2. The `@[refl]` attribute will reject `Eq.refl`, and `MVarId.applyRefl`
will fail when applied to equality goals.
3. The duplication has been removed.
[Before](https://github.com/leanprover/lean4/files/14772220/oi.pdf) and
[after](https://github.com/leanprover/lean4/files/14772226/oi2.pdf).
This gets `ByteArray`, `String.Extra`, `ToString.Macro` and `RCases` out
of the imports of `omega`. I'd hoped to get `Array.Subarray` too, but
it's tangled up in the list literal syntax. Further progress could come
from make `split` use available `Decidable` instances, so we could pull
out `Classical` (and possibly some of `PropLemmas`).
fixes#3770
Also start `rfl` with a `fail` message that is hopefully more helpful
than what we get now (see updated test output). This would be a cheaper
way to address #3302 without changing the implementation of rfl (as
tried in #3714).
This shortens `Array.findIdx?` code, by using termination_by (and
well-founded recursion) instead of a structural recursion trick, with
the intent to make it more proof friendly.
One motivation is that it makes it easier to write a proof that
`Array.findIdx?` and `List.findIdx?` are equivalent. Furthermore, this
will be useful to prove that more complex functions are equivalent.
Closes#3646
System.FilePath.parent did not return the correct parent path in the
case of absolute file paths
Example of previous behavior
```
(FilePath.mk "/foo").parent -> some (FilePath.mk "")
(System.FilePath.mk "/").parent -> some (FilePath.mk "")
```
The new behavior is based on rust's std::path::Path::parent function (as
previously described in comment in System.FilePath)
Example of updated behavior
```
(System.FilePath.mk "/foo").parent -> some (FilePath.mk "/")
(System.FilePath.mk "/").parent -> none
```
Behavior for relative file paths is unchanged
Closes#3618
This updates the rw? tactic from Mathlib to use lazy discriminator trees
and upstreams it.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Sets the default value to `pp.fieldNotation.generalized` to `true`.
Updates tests, and fixes some minor flaws in the implementation of the
generalized field notation pretty printer.
Now generalized field notation won't be used for any function that has a
`motive` argument. This is intended to prevent recursors from pretty
printing using it as (1) recursors are more like control flow structures
than actual functions and (2) generalized field notation tends to cause
elaboration problems for recursors.
Note: be sure functions that have an `@[app_unexpander]` use
`@[pp_nodot]` if applicable. For example, `List.toArray` needs
`@[pp_nodot]` to ensure the unexpander prints it using `#[...]`
notation.
This attribute, which was implemented in #3640, is applied to the
following structures: `Sigma`, `PSigma`, `PProd`, `And`, `Subtype`, and
`Fin`. These were given this attribute in Lean 3.
This coercion caused difficult-to-diagnose bugs sometimes. Because there
are some situations where converting a string to a name should be done
by parsing the string, and others where it should not, an explicit
choice seems better here.
---------
Co-authored-by: Mac Malone <tydeu@hatpress.net>
This is a rewrite of the `UnusedVariables` lint to inline and simplify
many of the dependent functions to try to improve the performance of
this lint, which quite often shows up in perf reports.
* The mvar assignment scanning is one of the most expensive parts of the
process, so we do two things to improve this:
* Lazily perform the scan only if we need it
* Use an object-pointer hashmap to ensure that we don't have quadratic
behavior when there are many mvar assignments with slight differences.
* The dependency on `Lean.Server` is removed, meaning we don't need to
do the LSP conversion stuff anymore. The main logic of reference finding
is inlined.
* We take `fvarAliases` into account, and union together fvars which are
aliases of a base fvar. (It would be great if we had `UnionFind` here.)
More docs will be added once we confirm an actual perf improvement.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
Sends a diagnostic informing the user to run Restart File when a file
dependency is saved.
Based on #3014 because this feature was easier to implement with the new
architecture.
ToDo:
- [x] Adjust vscode-lean4 to display a notification when this diagnostic
appears in a non-annoying way
(https://github.com/leanprover/vscode-lean4/pull/393)
- [x] Use a file watcher to identify changes to files not tracked by VS
Code
- [x] Rebase onto master when #3014 is merged
These are used in Mathlib's `congr!` and `convert` tactics, which will
be upstreamed soon.
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
- Removes the public definitions `Array.eraseIdxAux` and
`Array.eraseIdxSzAux` which were implementation details.
- Motivation: `Array.eraseIdxAux` and `Array.eraseIdxSzAux` were clearly
not intended to remain public, but simply making them private would make
it inconvenient to unfold them when writing proofs in Std.
- Adds documentation comments to the public `Array.eraseIdx`-related
definitions which remain.
- Removes `Array.eraseIdx'` which was just `Array.feraseIdx` wrapped in
a subtype and adds `Array.size_feraseIdx` to prove the subtype property
as a standalone theorem.
Co-Authored-By: Daniel Windham <daniel@atlascomputing.org>
- Add support for reserved declaration names. We use them for theorems
generated on demand.
- Equation theorems are not private declarations anymore.
- Generate equation theorems on demand when resolving symbols.
- Prevent users from creating declarations using reserved names. Users
can bypass it using meta-programming.
See next test for examples.
Replaces `@[eliminator]` with two attributes `@[induction_eliminator]`
and `@[cases_eliminator]` for defining custom eliminators for the
`induction` and `cases` tactics, respectively.
Adds `Nat.recAux` and `Nat.casesAuxOn`, which are eliminators that are
defeq to `Nat.rec` and `Nat.casesOn`, but these use `0` and `n + 1`
rather than `Nat.zero` and `Nat.succ n`.
For example, using `induction` to prove that the factorial function is
positive now has the following goal states (thanks also to #3616 for the
goal state after unfolding).
```lean
example : 0 < fact x := by
induction x with
| zero => decide
| succ x ih =>
/-
x : Nat
ih : 0 < fact x
⊢ 0 < fact (x + 1)
-/
unfold fact
/-
...
⊢ 0 < (x + 1) * fact x
-/
simpa using ih
```
Thanks to @adamtopaz for initial work on splitting the `@[eliminator]`
attribute.
This migrates lemmas about Nat `compare`, `min`, `max`, `dvd`, `gcd`,
`lcm` and `div`/`mod` from Std to Lean itself.
Std still has some additional recursors, `CoPrime` and a few additional
definitions that might merit further discussion prior to upstreaming.
This adds a number of lemmas for simplification of `Bool` and `Prop`
terms. It pulls lemmas from Mathlib and adds additional lemmas where
confluence or consistency suggested they are needed.
It has been tested against Mathlib using some automated test
infrastructure.
That testing module is not yet included in this PR, but will be included
as part of this.
Note. There are currently some comments saying the origin of the simp
rule. These will be removed prior to merging, but are added to clarify
where the rule came from during review.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Proves
`Nat.mod_mul : x % (a * b) = x % a + a * (x / a % b)` and
`Nat.mod_pow_succ : x % b ^ (k + 1) = x % b ^ k + b ^ k * ((x / b ^ k) %
b)`, helpful for bitblasting.
