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
The trace class Meta.synthInstance.answer isn't registered, so it can't
be used.
I set `inherited := true`, because I think it is a useful trace to have.
In particular it tells you when an instance has been found that has a
too large size. This is very useful information.
Summary:
- Take `synthPendingDepth` into account when caching TC results
- Add `maxSynthPendingDepth` option with default := 2.
- Add support for tracking `synthPending` failures when using
`set_option diagnostics true`
closes#2522closes#3313closes#3927
Identical to #4114 but with `maxSynthPendingDepth := 1`
closes#4114
cc @semorrison
This reverts commit 706a4cfd73 introduced
in #3970
As explained in #4124, `findM?` can become a footgun if used in monads
which induce side-effects such as caching. This PR removes that
function, and fixes the code introduced by #3398 for which the function
was first added.
cc @semorrison.
Closes#3386
Currently, when generating the signature of an injectivity lemma for a
certain constructor `c : forall xs, Foo a_1 ... a_n`,
`mkInjectiveTheoremTypeCore?` will differentiate between variables which
are bound to stay the same between the two equal values (i.e inductive
indices), and non-fixed ones. To do that, the function currently checks
whether a variable `x ∈ xs` appears in the final co-domain `Foo a_1 ...
a_n` of the constructor. This condition isn't enough however. As shown
in the linked issue, the codomain may also depend on variables which
appears in the type of free vars contained in `Foo a_1 ... a_n`, but not
in the term itself. This PR fixes the issue by also checking the types
of any free variable occuring in the final codomain, so as to ensure
injectivity lemmas are well-typed.
Because of the last-added-tried-first rule for macros, all the special
purpose `decreasing_trivial` rules are tried for most recursive
definitions out there, and because they use `apply` and `assumption`
with default transparency may cause some definitoins to be unfolded over
and over again.
A quick test with one of the functions in the leansat project shows that
elaboration time goes down from 600ms to 375ms when using
```
decreasing_by all_goals decreasing_with with_reducible decreasing_trivial
```
instead of
```
decreasing_by all_goals decreasing_with decreasing_trivial
```
This change uses `with_reducible` in most of these macros.
This means that these tactics will no longer work when the
relations/definitions they look for is hidden behind a definition.
This affected in particular `Array.sizeOf_get`, which now has a
companion `sizeOf_getElem`.
In addition, there were three tactics using `apply` to apply Nat-related
lemmas
that we now expect `omega` to solve. We still need them when building
`Init` modules
that don’t have access to `omega`, but they now live in
`decreasing_trivial_pre_omega`,
meant to be only used internally.
It currently only reports how many times each declaration has been
unfolded, and how often the `isDefEq` heuristic for `f a =?= f b` has
been used. Only counters above the threshold are reported.
