Commit graph

39235 commits

Author SHA1 Message Date
Sebastian Graf
0bcac0d46c
feat: add Option.of_wp_eq and Except.of_wp_eq (#12161)
This PR adds `Option.of_wp_eq` and `Except.of_wp_eq`, similar to the
existing `Except.of_wp`. `Except.of_wp` is deprecated because applying
it requires prior generalization, at which point it is more convenient
to use `Except.of_wp_eq`.
2026-01-26 12:50:23 +00:00
Lean stage0 autoupdater
1bf16f710e chore: update stage0 2026-01-26 12:17:07 +00:00
Henrik Böving
c3d753640a
feat: use static initializers where possible (#12082)
This PR makes the compiler produce C code that statically initializes
close terms when possible. This change reduces startup time as the terms
are directly stored in the binary instead of getting computed at
startup.

The set of terms currently supported by this mechanism are:
- string literals
- ctors called with other statically initializeable arguments
- `Name.mkStrX` and other `Name` ctors as they require special support
due to their computed field and occur frequently due to name literals.

In core there are currently 152,524 closed terms and of these 103,929
(68%) get initialized statically with this PR. The remaining 48585 ones
are not extracted because they use (potentially transitively) various
non trivial pieces of code like `stringToMessageData` etc. We might
decide to add special support for these in the future but for the moment
this feels like it's overfitting too much for core.
2026-01-26 11:22:12 +00:00
Joachim Breitner
e94ed002b5
perf: in FunInd, boldly do not check terms (#12160)
This PR removes calls to `check` that we expect to pass under normal
circumstances. This may be re-added later guarded by a `debug` option.
2026-01-26 11:22:00 +00:00
Sebastian Graf
7564329f06
fix: make Std.Do's post macro universe polymorphic (#12159)
This PR makes Std.Do's `post` macro universe polymorphic by expanding to
`PUnit.unit` instead of `()`.
2026-01-26 11:20:16 +00:00
Eric Wieser
0336a8385b
chore: inline trace nodes (#11954)
This extracts a `postCallback` helper so that only the actual callback
is inlined.

Part of the motivation here is to exclude these tracing frames from
flame graph profiles.

---------

Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
2026-01-26 08:51:25 +00:00
David Thrane Christiansen
c6e530a4f1
doc: add link to reference manual in stack overflow message (#12157)
This PR updates #12137 with a link to the Lean reference manual.

---------

Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
2026-01-26 07:56:48 +00:00
Kim Morrison
97d427b32b
doc: document release notes process and add guard check (#12158)
This PR documents the release notes writing process in detail and adds a
guard check to `release_checklist.py` to ensure release notes are
created for `-rc1` releases before proceeding with downstream repository
updates.

- **doc/dev/release_checklist.md**: Expanded "Writing the release notes"
section with detailed steps for generating, reviewing, and formatting
release notes in Verso format
- **script/release_checklist.py**: Added
`check_release_notes_file_exists()` to verify the release notes file
exists in reference-manual repository
- **.claude/commands/release.md**: Added "Release Notes" section
explaining the process for creating release notes during `-rc1` releases

🤖 Prepared with Claude Code

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
2026-01-26 07:16:01 +00:00
Kim Morrison
bc1a22cc22
chore: add plausible as verso dependency in release_repos.yml (#12155)
verso depends on plausible, but this wasn't recorded in
release_repos.yml. This caused the release checklist to not properly
track the dependency ordering.
2026-01-26 06:55:45 +00:00
Leonardo de Moura
0e28043ec6
feat: add simpTelescope simproc for simplifying binders before intro (#12154)
This PR adds `simpTelescope`, a simproc that simplifies telescope
binders (`have`-expression values and arrow hypotheses) but not the
final body. This is useful for simplifying targets before introducing
hypotheses.
2026-01-25 23:16:30 +00:00
Leonardo de Moura
45862d5486
feat: improves simpArrowTelescope simproc (#12153)
This PR improves the `simpArrowTelescope` simproc that simplifies
non-dependent arrow telescopes: `p₁ → p₂ → ... → q`.

The simproc now also applies telescope-specific simplifications:
- `False → q` to `True` (when `q : Prop`)
- `True → q` to `q` (when `q : Prop`)
- `p → True` to `True`
2026-01-25 22:29:38 +00:00
Leonardo de Moura
ba8c2ed4ee
feat: add simpArrowTelescope for compact proofs of arrow simplification (#12152)
This PR adds `simpArrowTelescope`, a simproc that simplifies telescopes
of non-dependent arrows (p₁ → p₂ → ... → q) while avoiding quadratic
proof growth.

When using `Expr.forallE` to represent nested implications, each nesting
level bumps de Bruijn indices in subterms, destroying sharing even with
hash-consing. For example, a free variable `x` gets different de Bruijn
representations at each depth, causing proof terms to grow.

`simpArrowTelescope` works by:

- Converting arrows to `Arrow p q` (a definitional wrapper)
- Simplifying each component
- Converting back to `→` form

Since `Arrow` arguments are not under binders, subterms remain identical
across nesting levels and can be shared.

The `simp_4` benchmark demonstrates the improvement:

With `forallE`: ~160ms, proof_size ≈ 173k
With `Arrow`: ~43ms, proof_size ≈ 16k
Tradeoff: `simpArrowTelescope` misses simplifications that depend on the
arrow structure (e.g., `p → p` to `True`), since post-methods aren't
applied to intermediate arrows. Thus, it is not used by default. to use
it, one has to set `simpArrowTelescope` as a `pre`-method.
2026-01-25 20:43:59 +00:00
Kim Morrison
9e241a4087
fix: revert "split ngen on async elab" (#12148)
This PR reverts #12000, which introduced a regression where `simp`
incorrectly rejects valid rewrites for perm lemmas.

The issue is that `NameGenerator.mkChild` creates names that don't
maintain the ordering assumption used by `acLt` for perm lemma
decisions. For example, after the change:
- Child generator creates names like `_uniq.102.2`
- Parent continues with `_uniq.7`
- But `Name.lt (.num (.num `_uniq 102) 2) (.num `_uniq 7)` is true

This causes fvars created later (in async tasks) to compare as smaller
than fvars created earlier, breaking the assumption that later fvars
compare greater according to `Name.lt`.

Fixes #12136.

🤖 Prepared with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
2026-01-25 03:18:24 +00:00
Leonardo de Moura
e90f6f77db
test: local rewrite with Sym.simp (#12147)
This PR adds a new API for helping users write focused rewrites.
2026-01-25 01:32:50 +00:00
Leonardo de Moura
9deb9ab59d
refactor: move commonly shared expressions to SymM (#12145)
This PR moves the pre-shared commonly used expressions from `GrindM` to
`SymM`.
2026-01-25 00:17:53 +00:00
Leonardo de Moura
6de7100f69
feat: add Goal API for SymM + grind (#12143)
This PR adds an API for building symbolic simulation engines and
verification
condition generators that leverage `grind`. The API wraps `Sym`
operations to
work with `grind`'s `Goal` type, enabling lightweight symbolic execution
while
carrying `grind` state for discharge steps.

New operations on `Goal`:
- `mkGoal`: create a `Goal` from an `MVarId`
- `introN`, `intros`: introduce binders
- `apply`: apply backward rules
- `simp`, `simpIgnoringNoProgress`: simplify using `Sym.Simp`
- `internalize`, `internalizeAll`: add hypotheses to the E-graph
- `grind`: attempt to close the goal using `grind`
- `assumption`: close by matching a hypothesis

A new test demonstrates the API on a stateful program with conditionals,
using `grind` to discharge arithmetic side conditions.
2026-01-24 20:30:08 +00:00
Mac Malone
6f409e0eea
fix: lake: --no-build exit code w/ release fetch (#12142)
This PR fixes a bug introduced in #12086 where a `lake build :release
--no-build` would exit with code 1 rather than the `--no-build ` code 3.
Now both the bug from #12086 and this bug are fixed.
2026-01-24 17:03:07 +00:00
Sebastian Ullrich
3de1cc54c5
test: compiler test with big meta closure (#12141) 2026-01-24 15:18:33 +00:00
Kim Morrison
a3755fe0a5
fix: add syntax to recommended_spelling for inv (#12139)
This PR adds `«term_⁻¹»` to the `recommended_spelling` for `inv`,
matching
the pattern used by all other operators which include both the function
and the syntax in their spelling lists.

Reported at
https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/.60recommended_spelling.60.20for.20.60.C2.ABterm_.E2.81.BB.C2.B9.C2.BB.60

🤖 Prepared with Claude Code

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
2026-01-24 11:04:36 +00:00
Leonardo de Moura
4c1e4a77b4
test: MetaM vs SymM on do notation (#12134)
This PR adds a new benchmark `shallow_add_sub_cancel.lean` that
demonstrates symbolic simulation using a shallow embedding into monadic
`do` notation, as opposed to the deep embedding approach in
`add_sub_cancel.lean`.

The shallow embedding approach:
- Uses Lean's `StateM` monad directly instead of a custom command
language

- Defines `Exec s k post` as a simple predicate: `post (k s).1 (k s).2`

- Proves helper theorems for reasoning about monadic operations (`pure`,
`bind`, `get`, `set`, `modify`, `ite`)

- Programs are written in actual `do`-notation rather than a custom AST

The benchmark solves goals using both the `MetaM` and `SymM` frameworks,
showing that the shallow embedding integrates well with the symbolic
simulation infrastructure. `SymM` is again way faster than `MetaM`

### Symbolic simulation benchmark — tactic time only

Problem size `n` corresponds to a program with `4·n` monadic actions.

| n   | MetaM tactic (ms) | SymM tactic (ms) | Speedup |
|-----|-------------------|------------------|---------|
| 10  | 82.10  | 11.37 | ~7.2×  |
| 20  | 176.21 | 17.71 | ~9.9×  |
| 30  | 306.47 | 25.39 | ~12.1× |
| 40  | 509.52 | 34.53 | ~14.7× |
| 50  | 689.19 | 43.51 | ~15.8× |
| 60  | 905.86 | 52.47 | ~17.3× |
| 70  | 1172.31 | 62.50 | ~18.8× |
| 80  | 1448.48 | 70.65 | ~20.5× |
| 90  | 1787.15 | 80.89 | ~22.1× |
| 100 | 2128.12 | 90.77 | ~23.5× |

<img width="580" height="455" alt="image"
src="https://github.com/user-attachments/assets/3511aaab-4d53-4520-8302-65d2d100df4a"
/>
2026-01-24 03:38:02 +00:00
Kim Morrison
896da85304
fix: CI CMakeLists.txt version check extracts wrong value (#12131)
This PR fixes a bug in the CI version validation where `grep -oE
'[0-9]+'` matches
multiple numbers from the comment on the same line:

```
set(LEAN_VERSION_IS_RELEASE 1)  # This number is 1 in the release revision, and 0 otherwise.
```

The grep extracts `1`, `1`, and `0`, causing the comparison to fail.

🤖 Prepared with Claude Code
2026-01-24 00:34:31 +00:00
Kim Morrison
11cd55b4f1
chore: check reference-manual release notes title in release checklist (#12130)
This PR adds a check to the release checklist script that verifies the
reference-manual release notes title matches the release type:

- For RC releases (e.g., v4.27.0-rc1): verifies the title contains the
exact
  RC suffix (e.g., "Lean 4.27.0-rc1")
- For final releases (e.g., v4.27.0): verifies the title does NOT
contain
  any "-rc" suffix (e.g., "Lean 4.27.0")

The check looks at the PR branch (bump_to_vX.Y.Z) for the release notes
file
at `Manual/Releases/v4_X_Y.lean` and parses the `#doc (Manual) "Lean
..."` line.

🤖 Prepared with Claude Code

---------

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
2026-01-24 00:33:53 +00:00
Kim Morrison
88823b27a6
doc: document nightly infrastructure in release command (#12129)
This PR adds documentation about the nightly build infrastructure to the
`/release` command to help future release managers understand the
relationship between branches and tags:

- `nightly` and `nightly-with-mathlib` are **branches** in
`leanprover/lean4`
- Dated tags like `nightly-YYYY-MM-DD` are **tags** in
`leanprover/lean4-nightly`
- When a nightly succeeds with mathlib, all three should point to the
same commit

🤖 Prepared with Claude Code

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
2026-01-24 00:06:44 +00:00
Henrik Böving
c9facc8102
fix: move allocation of execvp args before fork (#12123)
This PR fixes an issue that may sporadically trigger ASAN to got into a
deadlock when running a subprocess through the `IO.Process.spawn`
framework.

The general issue here is that we run `fork()` and then perform an
allocation in the child before going to `execvp` (for allocating the
arguments to `execvp`). As it turns out, doing this can cause a race
condition in ASAN that ultimately causes a deadlock in the child. This
was fixed upstream but then rolled back (see
https://github.com/google/sanitizers/issues/774). Thus, we must avoid
allocating any memory in between `fork` and `execvp`.
2026-01-23 23:12:23 +00:00
Lean stage0 autoupdater
63d1b530ba chore: update stage0 2026-01-23 18:35:59 +00:00
Sebastian Ullrich
3f09741fb9
chore: revert "fix: do not compile with -fwrapv" (#12125)
We are seeing (non-deterministically?) some ubsan reports from implicit
casting to `int`:
https://github.com/leanprover/lean4/actions/runs/21290374536/job/61282105493?pr=12082

Reverts leanprover/lean4#12098
2026-01-23 17:39:52 +00:00
Sebastian Ullrich
9f9531fa13
fix: getParentDeclName? inside where inside public def (#12119)
This PR fixes the call hierarchy for `where` declarations under the
module system

---------

Co-authored-by: mhuisi <mhuisi@protonmail.com>
2026-01-23 17:32:05 +00:00
David Thrane Christiansen
dae0d6fa05
fix: context for info trees and warning hints in Verso docstrings (#12121)
This PR wraps info trees produced by the `lean` Verso docstring
codeblock in a context info node.

Closes #12065.
2026-01-23 16:22:09 +00:00
David Thrane Christiansen
4a3401f69a
fix: enable Verso docstrings in where-blocks (#12122)
This PR adds support for Verso docstrings in `where` clauses.

Closes #12066.
2026-01-23 14:02:11 +00:00
Paul Reichert
4526cdda5f
fix: fix verso's +warning hint (#12116)
This PR fixes the verso hint that appears when using `sorry` in an
example block. It previously said: `` The `+error` flag indicates that
warnings are expected: +warning `` This PR replaces `error` with
`warning`. Fixes #12064
2026-01-23 13:31:02 +00:00
Eric Wieser
c4639150c1
fix: do not compile with -fwrapv (#12098)
This PR removes the requirement that libraries compiled against the lean
headers must use `-fwrapv`.

clang
[documents](https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html#:~:text=Note%20that%20checks%20are%20still%20added%20even%20when%20%2Dfwrapv%20is%20enabled)
that `-fwrapv` does not automatically turn off the integer overflow
sanitizer; and so overflow should still be avoided in normal execution.
2026-01-23 12:14:17 +00:00
Kim Morrison
37870c168b
chore: more updates to grind_indexmap test case (#12120) 2026-01-23 10:38:05 +00:00
Kim Morrison
57003e5c79
chore: updates to grind_indexmap test case (#12115)
This PR contains further updates to the `IndexMap` test case in
preparation for a demo at Lean Together.
2026-01-23 06:19:51 +00:00
Kim Morrison
b2f485e352
chore: grind test file demonstrating interactive use (#12114) 2026-01-23 04:55:09 +00:00
Mac Malone
5e29d7660a
feat: lake: +mod target keys for modules in deps (#12112)
This PR revives the ability to specify modules in dependencies via the
basic `+mod` target key.

Implementation-wise, this removes deprecation of `BuildKey.module` and
once again uses it for `+mod` target keys. It also adds a test for
depending on a module of a dependency via `needs`.
2026-01-23 02:35:02 +00:00
Kim Morrison
567cf74f1b
feat: updates to grind_indexmap test case (#12111)
This PR updates the `grind_indexmap.lean` tests, in preparation for
using them in a Lean Together talk.
2026-01-22 23:54:19 +00:00
Mac Malone
fa2ddf1c56
chore: lake: disable import all check in module disambiguation (#12104)
This PR disables an overlooked check (in #12045) of `import all` during
module disambiguation.
2026-01-22 18:12:14 +00:00
Mac Malone
f9af240bc4
fix: lake: query :deps output (#12105)
This PR fixes the `lake query` output for targets which produce an
`Array` or `List` of a value with a custom `QueryText` or `QueryJson`
instance (e.g., `deps` and `transDeps`).
2026-01-22 17:52:43 +00:00
Joachim Breitner
3bfeb0bc1f
refactor: use isRecursiveDefinition when validating macro_inline (#12106)
This PR uses `isRecursiveDefinition` when validating `macro_inline`,
instead of rummaging in the internals of the definition.
2026-01-22 16:31:34 +00:00
Garmelon
8447586fea
chore: make bench suite more similar to mathlib's (#12091)
The most important change is that all bench scripts now must always
output to `measurements.jsonl` instead of being allowed to output
results on stdout/err.
2026-01-22 14:20:10 +00:00
Lean stage0 autoupdater
470e3b7fd0 chore: update stage0 2026-01-22 12:59:28 +00:00
Paul Reichert
0a0323734b
feat: suggest Int*.toNatClamp for Int*.toNat (#11979)
This PR adds `suggest_for` annotations such that `Int*.toNatClamp` is
suggested for `Int*.toNat`.
2026-01-22 08:51:51 +00:00
Markus Himmel
69b058dc82
feat: Fin and Char ranges (#12058)
This PR implements iteration over ranges for `Fin` and `Char`.

To this end, we introduce machinery for pulling back lawfulness of
`UpwardEnumerable` along an injective map and study the function
`Char.ordinal : Char -> Fin Char.numCodePoints`.
2026-01-22 07:44:55 +00:00
David Thrane Christiansen
2c48ae7dfb
chore: make Verso module docstring API more like that for Markdown (#12093)
This PR makes the Verso module docstring API more like the Markdown
module docstring API, enabling downstream consumers to use them the same
way.
2026-01-22 04:45:49 +00:00
Leonardo de Moura
c81a8897a9
feat: improve Sym.simp APIs and new benchmark data (#12101)
This PR improves the the `Sym.simp` APIs. It is now easier to reuse the
simplifier cache between different simplification steps. We use the APIs
to improve the benchmark at #12100.

### Symbolic simulation with simplifier cache reuse (SymM)

Problem size `n` corresponds to a program with `2·n + 2` instructions.

| n   | Tactic time (ms) | Kernel time (ms) |
|-----|------------------|------------------|
| 10  | 4.53  | 4.29  |
| 20  | 5.56  | 6.91  |
| 30  | 6.46  | 8.67  |
| 40  | 8.07  | 11.20 |
| 50  | 9.37  | 13.63 |
| 60  | 11.89 | 15.43 |
| 70  | 12.43 | 18.28 |
| 80  | 14.07 | 20.72 |
| 90  | 15.62 | 23.41 |
| 100 | 17.39 | 24.80 |
| 200 | 30.35 | 48.39 |
| 300 | 45.41 | 72.84 |
| 400 | 59.17 | 97.67 |
| 500 | 79.63 | 138.99 |
| 600 | 100.05 | 173.67 |
| 700 | 119.77 | 208.80 |

<img width="571" height="455" alt="image"
src="https://github.com/user-attachments/assets/70da7ea2-b5d2-405e-985c-bfa358455afc"
/>
2026-01-22 03:37:16 +00:00
Mac Malone
3bc63aefb7
fix: lake: small cache issues (#12037)
This PR fixes two Lake cache issues: a bug where a failed upload would
not produce an error and a mistake in the `--wfail` checks of the cache
commands.
2026-01-22 03:27:30 +00:00
Leonardo de Moura
fa40491c78
test: benchmark MetaM vs SymM (#12100)
This PR adds a comparison between `MetaM` and `SymM` for a benchmark was
proposed during the Lean@Google Hackathon.

### Benchmark description

In this benchmark, we define the semantics of a very simple imperative
language using an inductive predicate

```
Exec prog events mem lctx post
```

The predicate holds if, when executing the program `prog` with an
initial list of events `events`, memory `mem`, and local context `lctx`,
the postcondition `post` holds.

We then consider the following program:

```
input b
a := b
a := a + a
a := a - b
...
a := a + a
a := a - b
```

That is, after reading an input value `b`, the program repeatedly
updates the variable `a` by doubling it and then subtracting `b`.

We prove that, for any initial memory `m` and local context `l`, and
starting from the empty list of events, the following postcondition
holds:

```
fun t' m' l' =>
  m' = m ∧                      -- memory did not change
  ∃ v : Word,
    t' = [IOEvent.IN v] ∧       -- exactly one input event
    l'.get "a" = some v         -- `a` contains the input value
```

In other words, executing the program produces exactly one input event,
leaves the memory unchanged, and ensures that the final value of `a` is
equal to the input value.

### Symbolic simulation benchmark (problem size `n`, with `2·n + 2`
instructions)

| Problem size (n) | MetaM time (ms) | MetaM kernel (ms) | SymM time
(ms) | SymM kernel (ms) | Total speedup |

|------------------|------------------|-------------------|----------------|------------------|---------------|
| 10  | 94.83  | 6.60  | 7.04  | 6.18  | ~13.5× |
| 20  | 218.92 | 13.33 | 14.15 | 13.02 | ~15.5× |
| 30  | 375.10 | 22.95 | 26.51 | 19.81 | ~14.2× |
| 40  | 563.82 | 34.99 | 40.42 | 29.55 | ~14.0× |
| 50  | 815.89 | 53.78 | 60.84 | 42.25 | ~13.4× |
| 60  | 1081.09 | 73.46 | 80.99 | 53.52 | ~13.3× | 
| 70  | 1400.80 | 102.70 | 106.02 | 68.61 | ~13.2× | 
| 80  | 1772.19 | 126.65 | 134.23 | 87.64 | ~13.2× |
| 90  | 2203.41 | 161.68 | 168.26 | 115.52 | ~13.1× | 
| 100 | 2474.09 | 191.23 | 209.13 | 143.86 | ~11.8× |

<img width="580" height="455" alt="image"
src="https://github.com/user-attachments/assets/bc7058fa-e71a-4c2c-be28-860f39166965"
/>

 ### Symbolic simulation with extra simplification (SymM)

Problem size `n` corresponds to a program with `2·n + 2` instructions.

| n   | Total time (ms) | Kernel time (ms) | Non-kernel time (ms) |
|-----|------------------|------------------|----------------------|
| 10  | 6.33  | 3.97 | 2.36 |
| 20  | 10.30 | 5.59 | 4.71 |
| 30  | 13.72 | 7.38 | 6.34 |
| 40  | 17.85 | 8.84 | 9.01 |
| 50  | 21.90 | 10.63 | 11.27 |
| 60  | 27.00 | 12.56 | 14.44 |
| 70  | 32.02 | 14.04 | 17.98 |
| 80  | 37.25 | 15.76 | 21.49 |
| 90  | 42.55 | 17.95 | 24.60 |
| 100 | 49.30 | 20.03 | 29.27 |
| 200 | 125.56 | 38.21 | 87.36 |
| 300 | 293.58 | 66.79 | 226.79 |
| 400 | 361.87 | 78.96 | 282.91 |
| 500 | 518.51 | 102.51 | 416.00 |
| 600 | 716.63 | 122.81 | 593.82 |
2026-01-22 01:38:56 +00:00
Leonardo de Moura
af438425d5
perf: avoid mkAppM in Sym.simp (#12099)
This PR ensures `Sym.simpGoal` does not use `mkAppM`. It also increases
the default number of maximum steps in `Sym.simp`.
2026-01-22 00:01:43 +00:00
Mac Malone
648e1b1877
fix: lake: --no-build failure w/ optional release fetch (#12086)
This PR fixes a bug where a `lake build --no-build` would exit with code
`3` if the optional job to fetch a GitHub or Reservoir release for a
package failed (even if nothing else needed rebuilding).
2026-01-21 23:14:54 +00:00
Leonardo de Moura
f84aa23d6d
feat: metavar cleanup in Sym.simp (#12096)
This PR cleanups temporary metavariables generated when applying
rewriting rules in `Sym.simp`.
2026-01-21 21:36:17 +00:00