this is the simplest of the constructions to be ported from C++ to Lean,
so I’ll PR this one first.
This begins to put each construction into its own file, as it was the
case with C++.
For validation I developed this in a separate repository at
https://github.com/nomeata/lean-constructions/tree/fad715e
and checked that all `.recOn` declarations found in Lean and Mathlib are
identical (per `==`) to the ones produced by the C code.
This PR introduces complete simprocs for all the Int versions of
div/mod, and makes some small refactoring of Int lemmas and
library_search.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
The linters in Batteries can be used to spot mistakes in Lean. See the
message on
[Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Go-to-def.20on.20typeclass.20fields.20and.20type-dependent.20notation/near/442613564).
These are the different linters with errors:
- unusedArguments:
There are many unused instance arguments, especially a redundant `[Monad
m]` is very common
- checkUnivs:
There was a problem with universes in a definition in
`Init.Control.StateCps`. I fixed it by adding a `variable` statement for
the implicit arguments in the file.
- defLemma:
many proofs are written as `def` instead of `theorem`, most notably
`rfl`. Because `rfl` is used as a match pattern, it must be a def. Is
this desirable?
The keyword `abbrev` is sometimes used for an alias of a theorem, which
also results in a def. I would want to replace it with the `alias`
keyword to fix this, but it isn't available.
- dupNamespace:
I fixed some of these, but left `Tactic.Tactic` and `Parser.Parser` as
they are as these seem intended.
- unusedHaveSuffices:
I cleaned up a few proofs with unused `have` or `suffices`
- explicitVarsOfIff:
I didn't fix any of these, because that would be a breaking change.
- simpNF:
I didn't fix any of these, because I think that requires knowing the
intended simplification order.
this is a first step towards porting the code `constructions.cpp` to
Lean: It leaves the construction of the `Declaration` untouched, but
moves adding the declarations to the environment, and setting various
attributes, to the Lean world.
This allows the remaining logic (the construction of the `Declaration`)
to be implemented in Lean separately and easily compared to the C++
implementation, before we replace that too.
To that end, `Declaraion` gains an `BEq` instance.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
Co-authored-by: Arthur Adjedj <arthur.adjedj@ens-paris-saclay.fr>
I removed a redundant `if tFn.isMVar || sFn.isMVar then ... else return
LBool.undef` in the `else` clause of
```
if !tFn.isMVar && !sFn.isMVar then
return LBool.undef
else
```
I made a modification to the `mkLambdaFVars` function, adding a
`etaReduce : Bool` parameter that determines whether a new lambda of the
form `fun x => f x` should be replaced by `f`. I then set this option to
true at `isDefEq` when processing metavariable assignments.
This means that many unnecessary eta unreduced expression are now
reduced. This is beneficial for users, so that they do not have to deal
with such unreduced expressions. It is also beneficial for performance,
leading to a 0.6% improvement in build instructions. Most notably,
`Mathlib.Algebra.DirectLimit`, previously a top 50 slowest file, has
sped up by 40%.
Quite a number of proof in mathlib broke. Many of these involve removing
a now unnecessary `simp only`. In other cases, a simp or rewrite doesn't
work anymore, such as a `simp_rw [mul_comm]` that was used to rewrite
`fun x => 2*x`, but now this term has turned into `HMul.hMul 2`.
Closes#4386
This assigns priorities to the equational lemmas so that more specific
ones
are tried first before a possible catch-all with possible
side-conditions.
We assign very low priorities to match the simplifiers behavior when
unfolding
a definition, which happens in `simpLoop`’ `visitPreContinue` after
applying
rewrite rules.
Definitions with more than 100 equational theorems will use priority 1
for all
but the last (a heuristic, not perfect).
fixes#4173, to some extent.
presumably this avoids unnecessary work when `omega` is used in tactic
combinators where the error message is never seen. Measurement did not
show
any significant changes, though.
With an artificial sleep in
```diff
diff --git a/src/Lean/Elab/Tactic/Omega/Frontend.lean b/src/Lean/Elab/Tactic/Omega/Frontend.lean
index fd297eef60..31ea3f6bd0 100644
--- a/src/Lean/Elab/Tactic/Omega/Frontend.lean
+++ b/src/Lean/Elab/Tactic/Omega/Frontend.lean
@@ -538,6 +538,7 @@ def formatErrorMessage (p : Problem) : OmegaM MessageData := do
else
let as ← atoms
return .ofLazyM (es := as) do
+ IO.sleep 10000
let mask ← mentioned as p.constraints
let names ← varNames mask
return m!"a possible counterexample may satisfy the constraints\n" ++
```
I can observe that `omega` is slow and `try omega` fast, so it seems to
work at least.
This came up when watching new Lean users in a class situation. A number
of them were confused when they omitted a namespace on a constructor
name, and Lean treated the variable as a pattern that matches anything.
For example, this program is accepted but may not do what the user
thinks:
```
inductive Tree (α : Type) where
| leaf
| branch (left : Tree α) (val : α) (right : Tree α)
def depth : Tree α → Nat
| leaf => 0
```
Adding a `branch` case to `depth` results in a confusing message.
With this linter, Lean marks `leaf` with:
```
Local variable 'leaf' resembles constructor 'Tree.leaf' - write '.leaf' (with a dot) or 'Tree.leaf' to use the constructor.
note: this linter can be disabled with `set_option linter.constructorNameAsVariable false`
```
Additionally, the error message that occurs when invalid names are
applied in patterns now suggests similar names. This means that:
```
def length (list : List α) : Nat :=
match list with
| nil => 0
| cons x xs => length xs + 1
```
now results in the following warning on `nil`:
```
warning: Local variable 'nil' resembles constructor 'List.nil' - write '.nil' (with a dot) or 'List.nil' to use the constructor.
note: this linter can be disabled with `set_option linter.constructorNameAsVariable false`
```
and error on `cons`:
```
invalid pattern, constructor or constant marked with '[match_pattern]' expected
Suggestion: 'List.cons' is similar
```
The list of suggested constructors is generated before the type of the
pattern is known, so it's less accurate, but it truncates the list to
ten elements to avoid being overwhelming. This mostly comes up with
`mk`.
so that the pretty-printed origin is clickable, and avoid the
unnecessary `@`.
Particularly nice is this fix:
```diff
/--
-info: [Meta.Tactic.simp.discharge] @bar discharge ✅
+info: [Meta.Tactic.simp.discharge] bar discharge ✅
autoParam T _auto✝
- [Meta.Tactic.simp.rewrite] { }:1000, T ==> True
-[Meta.Tactic.simp.rewrite] @bar:1000, U ==> True
+ [Meta.Tactic.simp.rewrite] T.mk:1000, T ==> True
+[Meta.Tactic.simp.rewrite] bar:1000, U ==> True
-/
```
types like
```
inductive Many (α : Type u) where
| none : Many α
| more : α → (Unit → Many α) → Many α
```
have a `.brecOn` only supports motives producing `Type u`, but not `Sort
u`, but our induction principles produce `Prop`. So the previous
implementation of functional induction would fail for functions that
structurally recurse over such types.
We recognize this case now and, rather hazardously, replace `.brecOn`
with `.binductionOn` (and thus `.below ` with `.ibelow` and `PProd` with
`And`). This assumes that these definitions are highly analogous.
This also improves the error message when realizing a reserved name
fails with an exception, by prepending
```
Failed to realize constant {id}:
```
to the error message.
Fixes#4320
Remark: when splitting an `if-then-else` term, the subgoals now have
tags `isTrue` and `isFalse` instead of `inl` and `inr`.
closes#4313
---------
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
The `save` happened in a slightly different context from the restore,
which a refinement of the `saveOrRestoreFull` signature now makes
impossible.
Fixes#4328
this fixes a usability paper cut that just annoyed me. When editing a
larger simp proof, I usually want to see the goal state after the simp,
and this is what I see while the `simp` command is complete. But then,
when I start typing, and necessarily type incomplete lemma names, that
error makes `simp` do nothing again and I see the original goal state.
In fact, if a prefix of the simp theorem name I am typing is a valid
identifier, it jumps even more around.
With this PR, using `logException`, I still get the red squiggly lines
for the unknown identifer, but `simp` just ignores that argument and
still shows me the final goal. Much nicer.
I also demoted the message for `[-foo]` when `foo` isn’t `simp` to a
warning and gave it the correct `ref`.
See it in action here: (in the middle, when you suddenly see the
terminal,
I am switching lean versions.)
https://github.com/leanprover/lean4/assets/148037/8cb3c563-1354-4c2d-bcee-26dfa1005ae0
Extends Lean's incremental reporting and reuse between commands into
various steps inside declarations:
* headers and bodies of each (mutual) definition/theorem
* `theorem ... := by` for each contained tactic step, including
recursively inside supported combinators currently consisting of
* `·` (cdot), `case`, `next`
* `induction`, `cases`
* macros such as `next` unfolding to the above
*Incremental reuse* means not recomputing any such steps if they are not
affected by a document change. *Incremental reporting* includes the
parts seen in the recording above: the progress bar and messages. Other
language server features such as hover etc. are *not yet* supported
incrementally, i.e. they are shown only when the declaration has been
fully processed as before.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Given `h` with type `x + k = y + k'` (or `h : k = k')`, `cases h`
produced a proof of size linear in `min k k'`. `isDefEq` has support for
offset, but `unifyEq?` did not have it, and a stack overflow occurred
while processing the resulting proof. This PR fixes this issue.
closes#4219
### Explanation
In the case that `assignSyntheticOpaque := true` and the given
metavariable is `syntheticOpaque` and the depth of the metavariable is
not the current depth, `isReadOnlyOrSyntheticOpaque` returns false, even
though the metavariable is read-only because of being declared at a
smaller depth. This causes the metavariable to (wrongly) be able to be
instantiated by `isDefEq`.
This bug was found at the proof of
[RingHom.PropertyIsLocal.sourceAffineLocally_of_source_openCover](https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/Morphisms/RingHomProperties.html#RingHom.PropertyIsLocal.sourceAffineLocally_of_source_openCover),
which involves a type class synthesis for `CommRing ?m.2404`, and the
synthesis manages to instantiate this metavariable into different
values, even though `synthInstance?` increases the metavariable depth.
This synthesis fails after 1 second.
I found the bug while modifying the instance synthesis code: the
modified code spent several minutes on this failed synthesis.
### Test
The problem can be verified with the test:
```
run_meta do
let m ← mkFreshExprMVar (Expr.sort levelOne) MetavarKind.syntheticOpaque
withAssignableSyntheticOpaque do
withNewMCtxDepth do
let eq ← isDefEq m (.const ``Nat [])
Lean.logInfo m! "{eq}"
```
this unification used to succeed, giving `true`, and this fix makes it
return `false`.
### Impact on Mathlib
This fix causes a change in the behaviour of `congr`, `convert` and
friends, which breaks a couple of proofs in mathlib. Most of these are
fixed by supplying more arguments.
I fixed these proofs, and
[benched](http://speed.lean-fro.org/mathlib4/compare/b821bfd9-3769-4930-b77f-0adc6f9d218f/to/e7b27246-a3e6-496a-b552-ff4b45c7236e?hash2=4f3c460cc1668820c9af8418a87a23db44c7acab)
mathlib. The result is that most files are unaffected, but some files
are significantly improved. This is most prominent in
Mathlib.RingTheory.Jacobson, where the number of instructions has
decreased by 28%. The overall improvement is a 0.3% reduction in
instructions.
[Zulip
message](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Ways.20to.20speed.20up.20Mathlib/near/439218960)
luckily the necessary functionality already exists in the form of
`addPPExplicitToExposeDiff`. But it is not cheap, and we should not run
this code
when the error message isn’t shown, so we should do this lazily.
We already had `MessageData.ofPPFormat` to assemble the error message
lazily, but it
was restricted to returning `FormatWithInfo`, a data type that doesn’t
admit a nice
API to compose more complex messages (like `Format` or `MessageData`
has; an attempt to
fix that is in #3926).
Therefore we split the functionality of `.ofPPFormat` into
`.ofFormatWithInfo` and `.ofLazy`,
and use `.ofLazy` to compute the more complex error message of `apply`.
Fixes#3232.
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: Wojciech Nawrocki <wjnawrocki@protonmail.com>
The `simp` tactic uses a discrimination tree to select candidate
theorems that will be used to rewrite an expression. This indexing data
structure minimizes the number of theorems that need to be tried and
improves performance. However, indexing modulo reducibility is
challenging, and a theorem that could be applied, when taking reduction
into account, may be missed. For example, suppose we have a `simp`
theorem `foo : forall x y, f x (x, y).2 = y`, and we are trying to
simplify the expression `f a b <= b`. `foo` will not be tried by `simp`
because the second argument of `f a b` is not a projection of a pair.
However, `f a b` is definitionally equal to `f a (a, b).2` since we can
reduce `(a, b).2`.
In Lean 3, we had a much simpler indexing data structure where only the
head symbol was taken into account. For the theorem `foo`, the head
symbol is `f`. Thus, the theorem would be considered by `simp`.
This commit adds the option `Simp.Config.index`. When `simp (config := {
index := false })`, only the head symbol is considered when retrieving
theorems, as in Lean 3. Moreover, if `set_option diagnostics true`,
`simp` will check whether every applied theorem would also have been
applied if `index := true`, and report them. This feature can help users
diagnose tricky issues in code that has been ported from libraries
developed using Lean 3 and then ported to Lean 4. In the following
example, it will report that `foo` is a problematic theorem.
```lean
opaque f : Nat → Nat → Nat
@[simp] theorem foo : f x (x, y).2 = y := by sorry
example : f a b ≤ b := by
set_option diagnostics true in
simp (config := { index := false })
```
In the example above, the following diagnostic message is produced.
```lean
[simp] theorems with bad keys
foo, key: [f, *, Prod.1, Prod.mk, Nat, Nat, *, *]
```
With the information above, users can annotate theorems such as `foo`
using `no_index` for problematic subterms.
Example:
```lean
opaque f : Nat → Nat → Nat
@[simp] theorem foo : f x (no_index (x, y).2) = y := by sorry
example : f a b ≤ b := by
simp -- `foo` is still applied
```
cc @semorrison
cc @PatrickMassot
