It bothered me that inferring instances of the shape `Decidable (∀ (x : Fin _), _)`
will go linearly through all instances of that shape, even those that are
about `∀ (x : Nat), …`. And that `Decidable (∃ (x : Fin _), _)` gets better
indexing than `Decidable (∀ (x : Fin _), _)`.
Judging from code comments, the discr tree used to index arrow types
with two arguments (domain and body), and that led to bugs due to the
dependency, so the arguments were removed. But it seems that indexing
the domain is completely simple and innocent.
So let’s see what happens…
Mostly only insignificant perf improvements, unfortunately (~Mathlib.Data.Matroid.IndepAxioms — instructions -11.4B, overall build instructions -0.097 %):
http://speed.lean-fro.org/mathlib4/compare/dd333cc1-fa26-42f2-96c6-b0e66047d0b6/to/6875ff8f-a17c-431d-8b8b-2f00799be794
This is just a small baby step compared to the more invasive improvements
done in the [`RefinedDiscrTree` by J. W. Gerbscheid](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Tactic/FunProp/RefinedDiscrTree.html) in mathlib.
it seems to be unused, arguably even for kernel recursors their type
should be usable with `mkRecursorInfo`, and removing this will help
understand the impact of #5679.
Gives more control over pretty printing metavariables.
- When `pp.mvars.levels` is false, then universe level metavariables
pretty print as `_` rather than `?u.22`
- When `pp.mvars.anonymous` is false, then anonymous metavariables
pretty print as `?_` rather than `?m.22`. Named metavariables still
pretty print with their names. When this is false, it also sets
`pp.mvars.levels` to false, since every level metavariable is anonymous.
- When `pp.mvars` is false, then all metavariables pretty print as `?_`
or `_`.
Modifies TryThis to use `pp.mvars.anonymous` rather than doing a
post-delaboration modification. This incidentally improves TryThis since
it now prints universe level metavariables as `_` rather than `?u.22`.
The `decide!` tactic is like `decide`, but when it tries reducing the
`Decidable` instance it uses kernel reduction rather than the
elaborator's reduction.
The kernel ignores transparency, so it can unfold all definitions (for
better or for worse). Furthermore, by using kernel reduction we can
cache the result as an auxiliary lemma — this is more efficient than
`decide`, which needs to reduce the instance twice: once in the
elaborator to check whether the tactic succeeds, and once again in the
kernel during final typechecking.
While RFC #5629 proposes a `decide!` that skips checking altogether
during elaboration, with this PR's `decide!` we can use `decide!` as
more-or-less a drop-in replacement for `decide`, since the tactic will
fail if kernel reduction fails.
This PR also includes two small fixes:
- `blameDecideReductionFailure` now uses `withIncRecDepth`.
- `Lean.Meta.zetaReduce` now instantiates metavariables while zeta
reducing.
Some profiling:
```lean
set_option maxRecDepth 2000
set_option trace.profiler true
set_option trace.profiler.threshold 0
theorem thm1 : 0 < 1 := by decide!
theorem thm1' : 0 < 1 := by decide
theorem thm2 : ∀ x < 400, x * x ≤ 160000 := by decide!
theorem thm2' : ∀ x < 400, x * x ≤ 160000 := by decide
/-
[Elab.command] [0.003655] theorem thm1 : 0 < 1 := by decide!
[Elab.command] [0.003164] theorem thm1' : 0 < 1 := by decide
[Elab.command] [0.133223] theorem thm2 : ∀ x < 400, x * x ≤ 160000 := by decide!
[Elab.command] [0.252310] theorem thm2' : ∀ x < 400, x * x ≤ 160000 := by decide
-/
```
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This refactors and improves the `#eval` command, introducing some new
features.
* Now evaluated results can be represented using `ToExpr` and pretty
printing. This means **hoverable output**. If `ToExpr` fails, it then
tries `Repr` and then `ToString`. The `eval.pp` option controls whether
or not to try `ToExpr`.
* There is now **auto-derivation** of `Repr` instances, enabled with the
`pp.derive.repr` option (default to **true**). For example:
```lean
inductive Baz
| a | b
#eval Baz.a
-- Baz.a
```
It simply does `deriving instance Repr for Baz` when there's no way to
represent `Baz`. If core Lean gets `ToExpr` derive handlers, they could
be used here as well.
* The option `eval.type` controls whether or not to include the type in
the output. For now the default is false.
* Now things like `#eval do return 2` work. It tries using
`CommandElabM`, `TermElabM`, or `IO` when the monad is unknown.
* Now there is no longer `Lean.Eval` or `Lean.MetaEval`. These each used
to be responsible for both adapting monads and printing results. The
concerns have been split into two. (1) The `MonadEval` class is
responsible for adapting monads for evaluation (it is similar to
`MonadLift`, but instances are allowed to use default data when
initializing state) and (2) finding a way to represent results is
handled separately.
* Error messages about failed instance synthesis are now more precise.
Once it detects that a `MonadEval` class applies, then the error message
will be specific about missing `ToExpr`/`Repr`/`ToString` instances.
* Fixes a bug where `Repr`/`ToString` instances can't be found by
unfolding types "under the monad". For example, this works now:
```lean
def Foo := List Nat
def Foo.mk (l : List Nat) : Foo := l
#eval show Lean.CoreM Foo from do return Foo.mk [1,2,3]
```
* Elaboration errors now abort evaluation. This eliminates some
not-so-relevant error messages.
* Now evaluating a value of type `m Unit` never prints a blank message.
* Fixes bugs where evaluating `MetaM` and `CoreM` wouldn't collect log
messages.
The `run_cmd`, `run_elab`, and `run_meta` commands are now frontends for
`#eval`.
... while at it also call `trivial` to close goals that can be trivially
closed.
---------
Co-authored-by: Siddharth <siddu.druid@gmail.com>
Co-authored-by: Henrik Böving <hargonix@gmail.com>
when the transparency mode is `.all`, then one expects `getFunInfo` and
`inferType` to also work with that transparency mode.
Fixes#5562Fixes#2975Fixes#2194
ac_nf is a counterpart to ac_rfl, which normalizes bitvector expressions
with respect to associativity and commutativity.
While there, also add test coverage for ac_rfl and ac_nf for BitVec,
complementing the existing test coverage.
after this change, `simp` will be able to discharge side-goals that,
after simplification, are of the form `∀ …, a = b` with `a =?= b`.
Usually these side-goals are solved by simplification using `eq_self`,
but that does not work when there are metavariables involved.
This enables us to have rewrite rules like
```
theorem List.foldl_subtype (p : α → Prop) (l : List (Subtype p)) (f : β → Subtype p → β)
(g : β → α → β) (b : β)
(hf : ∀ b x h, f b ⟨x, h⟩ = g b x) :
l.foldl f b = (l.map (·.val)).foldl g b := by
```
where the parameter `g` does not appear on the lhs, but can be solved
for using the `hf` equation. See `tests/lean/run/simpHigherOrder.lean`
for more examples.
The motivating use-case is that `simp` should be able to clean up the
usual
```
l.attach.map (fun <x, _> => x)
```
idiom often seen in well-founded recursive functions with nested
recursion.
Care needs to be taken with adding such rules to the default simp set if
the lhs is very general, and thus causes them to be tried everywhere.
Performance impact of just this PR (no additional simp rules) on mathlib
is unsuspicious:
http://speed.lean-fro.org/mathlib4/compare/b5bc44c7-e53c-4b6c-9184-bbfea54c4f80/to/ae1d769b-2ff2-4894-940c-042d5a698353
I tried a few alternatives, e.g. letting `simp` apply `eq_self` without
bumping the mvar depth, or just solve equalities directly, but that
broke too much things, and adding code to the default discharger seemed
simpler.
`elabEvalUnsafe` already does something similar: it also instantiates
universe metavariables, but it is not clear to me whether that is
sensible here.
To be conservative, I leave it out of this PR.
See https://github.com/leanprover/lean4/pull/3090#discussion_r1432007590
for a comparison between `#eval` and `Meta.evalExpr`. This PR is not
trying to fully align them, but just to fix one particular misalignment
that I am impacted by.
Closes#3091
building upon #3714, this (almost) implements the second half of #3302.
The main effect is that we now get a better error message when `rfl`
fails. For
```lean
example : n+1+m = n + (1+m) := by rfl
```
instead of the wall of text
```
The rfl tactic failed. Possible reasons:
- The goal is not a reflexive relation (neither `=` nor a relation with a @[refl] lemma).
- The arguments of the relation are not equal.
Try using the reflexivity lemma for your relation explicitly, e.g. `exact Eq.refl _` or
`exact HEq.rfl` etc.
n m : Nat
⊢ n + 1 + m = n + (1 + m)
```
we now get
```
error: tactic 'rfl' failed, the left-hand side
n + 1 + m
is not definitionally equal to the right-hand side
n + (1 + m)
n m : Nat
⊢ n + 1 + m = n + (1 + m)
```
Unfortunately, because of very subtle differences in semantics (which
transparency setting is used when reducing the goal and whether the
“implicit lambda” feature applies) I could not make this simply the only
`rfl` implementation. So `rfl` remains a macro and is still expanded to
`eq_refl` (difference transparency setting) and `exact Iff.rfl` and
`exact HEq.rfl` (implicit lambda) to not break existing code. This can
be revised later, so this still closes: #3302.
A user might still be puzzled *why* to terms are not defeq. Explaining
that better (“reduced to… and reduces to… etc.”) would also be great,
but that’s not specific to `rfl`, so better left for some other time.
Modifies how the declaration command elaborator reports when there are
unassigned metavariables. The visible effects are that (1) now errors
like "don't know how to synthesize implicit argument" and "failed to
infer 'let' declaration type" take precedence over universe level
issues, (2) universe level metavariables are reported as metavariables
(rather than as `u_1`, `u_2`, etc.), and (3) if the universe level
metavariables appear in `let` binding types or `fun` binder types, the
error is localized there.
Motivation: Reporting unsolved expression metavariables is more
important than universe level issues (typically universe issues are from
unsolved expression metavariables). Furthermore, `let` and `fun` binders
can't introduce universe polymorphism, so we can "blame" such bindings
for universe metavariables, if possible.
Example 1: Now the errors are on `x` and `none` (reporting expression
metavariables) rather than on `example` (which reported universe level
metavariables).
```lean
example : IO Unit := do
let x := none
pure ()
```
Example 2: Now there is a "failed to infer universe levels in 'let'
declaration type" error on `PUnit`.
```lean
def foo : IO Unit := do
let x : PUnit := PUnit.unit
pure ()
```
In more detail:
* `elabMutualDef` used to turn all level mvars into fresh level
parameters before doing an analysis for "hidden levels". This analysis
turns out to be exactly the same as instead creating fresh parameters
for level mvars in only pre-definitions' types and then looking for
level metavariables in their bodies. With this PR, error messages refer
to the same level metavariables in the Infoview, rather than obscure
generated `u_1`, `u_2`, ... level parameters.
* This PR made it possible to push the "hidden levels" check into
`addPreDefinitions`, after the checks for unassigned expression mvars.
It used to be that if the "hidden levels" check produced an "invalid
occurrence of universe level" error it would suppress errors for
unassigned expression mvars, and now it is the other way around.
* There is now a list of `LevelMVarErrorInfo` objects in the `TermElabM`
state. These record expressions that should receive a localized error if
they still contain level metavariables. Currently `let` expressions and
binder types in general register such info. Error messages make use of a
new `exposeLevelMVars` function that adds pretty printer annotations
that try to expose all universe level metavariables.
* When there are universe level metavariables, for error recovery the
definition is still added to the environment after assigning each
metavariable to level 0.
* There's a new `Lean.Util.CollectLevelMVars` module for collecting
level metavariables from expressions.
Closes#2058
This implements the first half of #3302: It improves the extensible
`apply_rfl` tactic (the one that looks at `refl` attributes, part of
the `rfl` macro) to
* Check itself and ahead of time that the lhs and rhs are defEq, and
give
a nice consistent error message when they don't (instead of just passing
on
the less helpful error message from `apply Foo.refl`), and using the
machinery that `apply` uses to elaborate expressions to highlight diffs
in implicit arguments.
* Also handle `Eq` and `HEq` (built in) and `Iff` (using the attribute)
Care is taken that, as before, the current transparency setting affects
comparing the lhs and rhs, but not the reduction of the relation
So before we had
```lean
opaque P : Nat → Nat → Prop
@[refl] axiom P.refl (n : Nat) : P n n
/--
error: tactic 'apply' failed, failed to unify
P ?n ?n
with
P 42 23
⊢ P 42 23
-/
#guard_msgs in
example : P 42 23 := by apply_rfl
opaque withImplicitNat {n : Nat} : Nat
/--
error: tactic 'apply' failed, failed to unify
P ?n ?n
with
P withImplicitNat withImplicitNat
⊢ P withImplicitNat withImplicitNat
-/
#guard_msgs in
example : P (@withImplicitNat 42) (@withImplicitNat 23) := by apply_rfl
```
and with this PR the messages we get are
```
error: tactic 'apply_rfl' failed, The lhs
42
is not definitionally equal to rhs
23
⊢ P 42 23
```
resp.
```
error: tactic 'apply_rfl' failed, The lhs
@withImplicitNat 42
is not definitionally equal to rhs
@withImplicitNat 23
⊢ P withImplicitNat withImplicitNat
```
A test file checks the various failure modes and error messages.
I believe this `apply_rfl` can serve as the only implementation of
`rfl`, which would then complete #3302, and actually expose these
improved
error messages to the user. But as that seems to require a
non-trivial bootstrapping dance, it’ll be separate.
closes#5333
This PR tries to address issue #5333.
My conjecture is that the binder annotations for `C.toB` and
`Algebra.toSMul` are not ideal. `Algebra.toSMul` is one of declarations
where the new command `set_synth_order` was used. Both classes, `C` and
`Algebra`, are parametric over instances, and in both cases, the issue
arises due to projection instances: `C.toB` and `Algebra.toSMul`. Let's
focus on the binder annotations for `C.toB`. They are as follows:
```
C.toB [inst : A 20000] [self : @C inst] : @B ...
```
As a projection, it seems odd that `inst` is an instance-implicit
argument instead of an implicit one, given that its value is fixed by
`self`. We observe the same issue in `Algebra.toSMul`:
```
Algebra.toSMul {R : Type u} {A : Type v} [inst1 : CommSemiring R] [inst2 : Semiring A]
[self : @Algebra R A inst1 inst2] : SMul R A
```
The PR changes the binder annotations as follows:
```
C.toB {inst : A 20000} [self : @C inst] : @B ...
```
and
```
Algebra.toSMul {R : Type u} {A : Type v} {inst1 : CommSemiring R} {inst2 : Semiring A}
[self : @Algebra R A inst1 inst2] : SMul R A
```
In both cases, the `set_synth_order` is used to force `self` to be
processed first.
In the MWE, there is no instance for `C ...`, and `C.toB` is quickly
discarded. I suspect a similar issue occurs when trying to use
`Algebra.toSMul`, where there is no `@Algebra R A ... ...`, but Lean
spends unnecessary time trying to synthesize `CommSemiring R` and
`Semiring A` instances. I believe the new binder annotations make sense,
as if there is a way to synthesize `Algebra R A ... ...`, it will tell
us how to retrieve the instance-implicit arguments.
TODO:
- Impact on Mathlib.
- Document changes.
---------
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
Co-authored-by: Johan Commelin <johan@commelin.net>
A round of clean-up for the context of the functional induction
principle cases.
* Already previously, with `match e with | p => …`, functional induction
would ensure that `h : e = p` is in scope, but it wouldn’t work in
dependent cases. Now it introduces heterogeneous equality where needed
(fixes#4146)
* These equalities are now added always (previously we omitted them when
the discriminant was a variable that occurred in the goal, on the
grounds that the goal gets refined through the match, but it’s more
consistent to introduce the equality in any case)
* We no longer use `MVarId.cleanup` to clean up the goal; it was
sometimes too aggressive (fixes#5347)
* Instead, we clean up more carefully and with a custom strategy:
* First, we substitute all variables without a user-accessible name, if
we can.
* Then, we substitute all variable, if we can, outside in.
* As we do that, we look for `HEq`s that we can turn into `Eq`s to
substitute some more
* We substitute unused `let`s.
**Breaking change**: In some cases leads to a different functional
induction principle (different names and order of assumptions, for
example).
From the new doc-string:
```quote
In early versions of Lean, the typeclasses provided by `/` and `%`
were defined in terms of `tdiv` and `tmod`, and these were named simply as `div` and `mod`.
However we decided it was better to use `ediv` and `emod`,
as they are consistent with the conventions used in SMTLib, Mathlib,
and often mathematical reasoning is easier with these conventions.
At that time, we did not rename `div` and `mod` to `tdiv` and `tmod` (along with all their lemma).
In September 2024, we decided to do this rename (with deprecations in place),
and later we intend to rename `ediv` and `emod` to `div` and `mod`, as nearly all users will only
ever need to use these functions and their associated lemmas.
```
This is "upstreaming" mathlib's `unfold_let` tactic by incorporating its
functionality into `unfold`. Now `unfold` can, in addition to unfolding
global definitions, unfold local definitions. The PR also updates the
`conv` version of the tactic.
An improvement over `unfold_let` is that it beta reduces unfolded local
functions.
Two features not present in `unfold` are that (1) `unfold_let` with no
arguments does zeta delta reduction of *all* local definitions, and also
(2) `unfold_let` can interleave unfoldings (in contrast, `unfold a b c`
is exactly the same as `unfold a; unfold b; unfold c`).
Closes RFC #4090
Sebastian mentioned that the use of the kernel defeq was to work around
a performance issue that was fixed since. Let's see if we can do
without.
This is also a semantic change: Ground terms (no free vars, no mvars)
are reduced at
“all” transparency even if the the transparency setting is default. This
was the case
even before 03f6b87647 switched to the
kernel defeq
checking for performance. It seems that this is rather surprising
behavior from the user
point of view. The fallout on batteries and mathlib is rather limited,
only a few
`rfl` proofs seem to have (inadvertently or not) have relied on this.
The speedcenter reports no significant regressions on core or mathlib.
This renames `BitVec.getLsb` to `getLsbD` (`D` for "default" value, i.e.
false), and introduces `getLsb?` and `getLsb'` (which we can rename to
`getLsb` after a deprecation cycle).
(Similarly for `getMsb`.)
Also adds a `GetElem` class so we can use `x[i]` and `x[i]?` notation.
Later, we will turn
```
theorem getLsbD_eq_getElem?_getD (x : BitVec w) (i : Nat) (h : i < w) :
x.getLsbD i = x[i]?.getD false
```
on as a `@[simp]` lemma.
This PR doesn't attempt to demonstrate the benefits, but I think both
arguments are going to get easier, and this will bring the BitVec API
closer in line to List/Array, etc.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
in #4154 and #5129 the rules for equational lemmas have changed, and new
options were introduced that can be used to revert to the pre-4.12
behavior. Hopefully nobody really needs these options besides for
backwards compatibility, therefore we put these options in the
`backward` option name space.
So the previous behavior can be achieved by setting
```lean
set_option backward.eqns.nonrecursive false
set_option backward.eqns.deepRecursiveSplit false
```
