This changes how Nat typeclass checks in offset terms from syntactic
equality to definitional equality with "instances" transparency.
This may have a negative performance penalty in `isOffset?`, but it
should be small in common cases since the relevant instances are small
terms.
This closes#3836
This removes simp attributes from `Nat.succ.injEq` and
`Nat.succ_sub_succ_eq_sub` to replace them with simprocs. This is
because any reductions involving `Nat.succ` has a high risk of leading
proof performance problems when dealing with even moderately large
numbers.
Here are a couple examples that will both report a maximum recursion
depth error currently. These examples are fixed by this PR.
```
example : (123456: Nat) = 12345667 := by
simp
example (x : Nat) (p : x = 0) : 1000 - (x + 1000) = 0 := by
simp
```
Possibly the more principled fix is to not have `simp` invoke
dischargers under `withReducible`.
In the meantime, this ensures that `falseOrByContra` still succeeds with
`intro1` on a `Not` goal, which previously was breaking `omega` as a
simp discharger.
Closes#3805.
When `discharge?` failed, the `usedSimps` was being restored, but the
cache wasn't. This bug was exposed by issue #3710.
This PR makes the following changes:
- We restore the `cache` at `discharge?`. We use `SMap` to ensure the
operation is efficient.
- We don't need the field `dischargeDepth` anymore at `Simp.Result`.
- `UsedSimps` should use `PHashMap` since it is not used linearly.
closes#3710
---------
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Now, only `(<- ...)`s occurring in the condition of a pure if-then-else
are lifted.
That is, `if (<- foo) then ... else ...` is ok, but `if ... then (<-
foo) else ...` is not. See #3713closes#3713
This PR also adjusts this repo. Note that some of the `(<- ...)` were
harmless since they were just accessing some
read-only state.
It have to keep it as a private definition for now. We currently only
support duplicate theorems in different modules. Splitters are generated
on demand, and are also used to write code.
* Setting `pp.mvars` to false causes metavariables to pretty print as
`?_`.
* Setting `pp.mvars.withType` to true causes metavariables to pretty
print with type ascriptions.
Motivation: when making tests, it is inconvenient using `#guard_msgs`
when there are metavariables, since the unique numbering is subject to
change.
This feature does not use `⋯` omissions since a metavariable is already
in a sense an omitted term. If repeated metavariables do not appear in
an expression, there is a chance that a term pretty printed with
`pp.mvars` set to false can still elaborate to the correct term, unlike
for other omissions.
(In the future we could consider an option that pretty prints uniquely
numbered metavariables as `?m✝`, `?m✝¹`, `?m✝²`, etc. to be able to tell
them apart, at least in the same pretty printed expression. It would
take care to make sure that these names are stable across different
hovers.)
Closes#3781
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 PR includes the following fixes:
- Reserved name resolution inside namespaces
- Equation theorems for `match`er declarations are not private anymore
- Equation theorems for `match`er declarations are realizable
- `foo.match_<idx>.splitter` is now a reserved name
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.
no need to enter `derive_functional_induction` anymore.
(Will remove the support for `derive_functional_induction` after the
next stage0 update, since we are already using it in Init.)
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 extends `derive_functional_induction` to work with structural
recursion as well.
It produces the less general, more concrete induction rule where the
induction hypothesis is
specialized for every argument of the recursive call, not just the the
one that the function
is recursing on.
Care is taken so that the induction principle and it's motive take the
arguments in the same
order as the original function.
While I was it, also makes sure that the order of the cases in the
induction principle matches
the order of recursive calls in the function better.
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
Given a definition `foo`, they were previously called `foo._unfold`
until 4.7.0. We tried to rename them to `foo.def`, but it created too
many issues in the Mathlib repo. We decided to rename it again to
`foo.eq_def`. The new name is also consistent with the `eq_<idx>`
theorems generated for different "cases". That is, `foo.eq_def` is the
equality theorem for the whole definition, and `foo.eq_<idx>` is the
equality theorem for case `<idx>`.
cc @semorrison
Given
```lean
structure A where
x : Nat
structure B extends A where
y : Nat
```
rather than pretty printing `{ x := 1, y := 2 : B }` as `{ toA := { x :=
1 }, y := 2 }`, it now pretty prints as `{ x := 1, y := 2 }`.
The option `pp.structureInstances.flatten` controls whether to flatten
structure instances like this.
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.
Refactors app delaborator, merging in the projection delaborator, to
support pretty printing with generalized field notation.
Renames option `pp.structureProjections` to `pp.fieldNotation` and adds
sub-option `pp.fieldNotation.generalized` to enable/disable generalized
field notation. Adds `@[pp_nodot]` attribute to permanently disable
using field notation for a given declaration.
For now, the default value of `pp.fieldNotation.generalized` is false
since we need a stage0 update to add `@[pp_nodot]` to some core
definitions (such as `List.toArray`) before updating the tests.
[Zulip
discussion](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/.60pp.2EgeneralizedFieldNotation.60/near/425856054)
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>
Closes#3706
This derive handler's implementation is very similar to `BEq`'s, which
already ignores unused alternative so as to work correctly on indexed
inductive types. This PR simply implements the same solution as the one
present in
[`BEq.lean`](2c15cdda04/src/Lean/Elab/Deriving/BEq.lean (L94)).
After some tests, it doesn't seem like any other derive handler present
in Core suffers from the same issue (though some handlers don't work on
indexed inductives for other reasons).
using the `substVars` tactic on the goal can remove too much
information, as it does not take into account that the `motive` may
depend on the fixed parameters.
This is fixed by etracting `substVar` from `subst` which expects the
`x`, not the `h : x = rhs`, and then using this tactic on the local
declarations _after_ the `motive` exclusively.
- 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.
Fixes#1170.
This PR adds the module name to `RefIdent` in order to distinguish
conflicting names from different files. This also fixes related issues
in find-references or the call hierarchy feature.
It also adds some docstrings and stylistically refactors a bunch of
code.
This introduces the `ArgsPacker` module and abstraction, to replace the
exising `PackDomain`/`PackMutual` code. The motivation was that we now
have more uses besides `Fix.lean` (`GuessLex` and `FunInd`), and the
code was spread in various places.
The goals are
* consistent function naming withing the the `PSigma` handling, the
`PSum` handling, and the combined interface
* avoid taking a type apart just based on the `PSigma`/`PSum` nesting,
to be robust in case the user happens to be using `PSigma`/`PSum`
somewhere. Therefore, always pass an `arity` or `numFuncs` or `varNames`
around.
* keep all the `PSigma`/`PSum` encoding logic contained within one
module (`ArgsPacker`), and keep that module independent of its users (so
no `EqnInfos` visible here).
* pick good variable names when matching on a packed argument
* the unary function now is either called `fun1._unary` or
`fun1._mutual`, never `fun1._unary._mutual`.
This file has less heavy dependencies than `PackMutual` had, so build
parallelism is improved as well.
This makes trailing whitespace visible and protectes them against
trimming by the editor, by appending the symbol ⏎ to such a line (and
also to any line that ends with such a symbol, to avoid ambiguities in
the case the message already had that symbol).
(Only the code action output / docstring parsing is affected; the error
message as sent
to the InfoView is unaffected.)
Fixes#3571
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.
Floris van Doorn [reported on
Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/have.20tactic.20error.20recovery/near/425283053)
that it is confusing that the `have : T := e` tactic completely fails if
the body `e` is not of type `T`. This is in contrast to `have : T := by
exact e`, which does not completely fail when `e` is not of type `T`.
This ends up being caused by `elabTermEnsuringType` throwing an error
when it fails to insert a coercion. Now, it detects this case, and it
checks the `errToSorry` flag to decide whether to throw the error or to
log the error and insert a `sorry`.
This is justified by `elabTermEnsuringType` being a frontend to
`elabTerm`, which inserts `sorry` on error.
An alternative would be to make `ensureType` respect `errToSorry`, but
there exists code that expects being able to catch when `ensureType`
fails. Making such code manipulate `errToSorry` seems error prone, and
this function is not a main entry point to the term elaborator, unlike
`elabTermEnsuringType`.
