for SSFT24 summer school: https://github.com/david-christiansen/ssft24
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Add docstrings, usage examples, and doc tests for `String.prev`,
`.front`, `.back`, `.atEnd`.
Improve docstring examples for `String.next` based on discussion
examples for `String.prev`.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This ensures that rotateLeft/Right behave correctly even when the
rotation amount is larger than the bitwidth.
This shall be followed up with `getLsb` theorems for rotations for
LeanSAT.
We choose to write `aux` definitions since it is cleaner to reason about
the `aux` theorems with the assumption that `rotation-amount <
bit-width`, followed by auxiliary lemmas that link the behavior of
rotation to the canonical case when `rotation-amount < bit-width`.
Proof strategy we will execute based on these definitions: [Link to
proof of
`getLsb_rotateLeft`](a0b18ec0f4/src/Init/Data/BitVec/Lemmas.lean (L1129-L1204))
---------
Co-authored-by: Tobias Grosser <github@grosser.es>
To eliminate parsing differences between Windows and other platforms,
the frontend now normalizes all CRLF line endings to LF, like [in
Rust](https://github.com/rust-lang/rust/issues/62865).
Effects:
- This makes Lake hashes be faithful to what Lean sees (Lake already
normalizes line endings before computing hashes).
- Docstrings now have normalized line endings. In particular, this fixes
`#guard_msgs` failing multiline tests for Windows users using CRLF.
- Now strings don't have different lengths depending on the platform.
Before this PR, the following theorem is true for LF and false for CRLF
files.
```lean
example : "
".length = 1 := rfl
```
Note: the normalization will take `\r\r\n` and turn it into `\r\n`. In
the elaborator, we reject loose `\r`'s that appear in whitespace. Rust
instead takes the approach of making the normalization routine fail.
They do this so that there's no downstream confusion about any `\r\n`
that appears.
Implementation note: the LSP maintains its own copy of a source file
that it updates when edit operations are applied. We are assuming that
edit operations never split or join CRLFs. If this assumption is not
correct, then the LSP copy of a source file can become slightly out of
sync. If this is an issue, there is some discussion
[here](https://github.com/leanprover/lean4/pull/3903#discussion_r1592930085).
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
Show that shifting a natural number left and then shifting right by the
same amount is a no-op.
I originally proved this in a different PR, ended up not needing the
fact after all, but it still seemed like a generally useful simp lemma
to have.
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
This PR adds theorems that relate unsigned bitvector comparisons
`BitVec.ult` and `BitVec.ule` to `BitVec.carry`. These lemmas are a
prerequisite to bit-blasting these comparisons in LeanSAT.
in #4158 I was experimenting with a change to the simplifier that
affectes the order in which lemmas were tried, and of course it breaks
proofs all over the place whenever we have a non-confluent simp set.
Among the first breakages encountered, a large fraction was due to
`simp` rewriting with `List.length_pos : 0 < length l ↔ l ≠ []`.
This does not strike me a as a good simp lemma: If `l` is a manifest
constructor, the simplifier will reduce `length` and solve it anyways,
and if it isn't then an inequality usually isn’t very simp friendly. It
is also highly non-confluent with any kind of `length`-lemma we might
have.
This therefore removes it from the standard simp set.
Adds `IO.getTaskState` which returns the state of a `Task` in the Lean
runtime's task manager. The `TaskState` inductive has 3 constructors:
`waiting`, `running`, and `finished`. The `waiting` constructor
encompasses the waiting and queued states within the C task object
documentation, because the task object does not provide a low cost way
to distinguish these different forms of waiting. Furthermore, it seems
unlikely for consumers to wish to distinguish between these internal
states. The `running` constructor encompasses both the running and
promised states in C docs. While not ideal, the C implementation does
not provide a way to distinguish between a running `Task` and a waiting
`Promise.result` (they both have null closures).
we keep running into examples where working with well-founded recursion
is slow because defeq checks (which are all over the place, including
failing ones that are back-tracked) unfold well-founded definitions.
The definition of a function defined by well-founded recursion should be
an implementation detail that should only be peeked inside by the
equation generator and the functional induction generator.
We now mark the mutual recursive function as irreducible (if the user
did not
set a flag explicitly), and use `withAtLeastTransparency .all` when
producing
the equations.
Proofs can be fixed by using rewriting, or – a bit blunt, but nice for
adjusting
existing proofs – using `unseal` (a.k.a. `attribute [local
semireducible]`).
Mathlib performance does not change a whole lot:
http://speed.lean-fro.org/mathlib4/compare/08b82265-75db-4a28-b12b-08751b9ad04a/to/16f46d5e-28b1-41c4-a107-a6f6594841f8
Build instructions -0.126 %, four modules with significant instructions
decrease.
To reduce impact, these definitions were changed:
* `Nat.mod`, to make `1 % n` reduce definitionally, so that `1` as a
`Fin 2` literal
works nicely. Theorems with larger `Fin` literals tend to need a `unseal
Nat.modCore`
https://github.com/leanprover/lean4/pull/4098
* `List.ofFn` rewritten to be structurally recursive and not go via
`Array.ofFn`:
https://github.com/leanprover-community/batteries/pull/784
Alternative designs explored were
* Making `WellFounded.fix` irreducible.
One benefit is that recursive functions with equal definitions (possibly
after
instantiating fixed parameters) are defeq; this is used in mathlib to
relate
[`OrdinalApprox.gfpApprox`](https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/FixedPointApproximants.html#OrdinalApprox.gfpApprox)
with `.lfpApprox`.
But the downside is that one cannot use `unseal` in a
targeted way, being explicit in which recursive function needs to be
reducible here.
And in cases where Lean does unwanted unfolding, we’d still unfold the
recursive
definition once to expose `WellFounded.fix`, leading to large terms for
often no good
reason.
* Defining `WellFounded.fix` to unroll defintionally once before hitting
a irreducible
`WellFounded.fixF`. This was explored in #4002. It shares most of the
ups and downs
with the previous variant, with the additional neat benefit that
function calls that
do not lead to recursive cases (e.g. a `[]` base case) reduce nicely.
This means that
the majority of existing `rfl` proofs continue to work.
Issue #4051, which demonstrates how badly things can go if wf recursive
functions can be
unrolled, showed that making the recursive function irreducible there
leads to noticeably
faster elaboration than making `WellFounded.fix` irreducible; this is
good evidence that
the present PR is the way to go.
This fixes https://github.com/leanprover/lean4/issues/3988
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
Fixes#3270 by moving the deprecation check from
`Lean.Elab.Term.mkConsts` to `Lean.Elab.Term.mkConst`, so
`Lean.Elab.Term.mkBaseProjections`, `.elabAppLValsAux`, `.elabAppFn`,
and `.elabForIn` also hit the check. Not all of these really need to hit
the check, so I'll run `!bench` to see if it's a problem.
this is in preparation for #4061. Once that lands, `1 % 42 = 1` will no
longer hold definitionally (at least not without an ungly `unseal
Nat.modCore in` around). This affects mathlib in a few places,
essentially every time a `1 : Fin (n+1)` literal is written.
So this extends the existing special case for `0 % n = 0` to `1 % n`.
Add docstrings and usage examples for `String.length`, `.push`,
`.append`, `.get?`, `.set`, `.modyify`, and `.next`. Update docstrings
and add usage examples for `String.toList`, `.get`, and `.get!`.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
otherwise it remains in the equational theorem and may cause the
“unused have linter” to trigger. By moving the proof into
`decreasing_by`, the equational theorems are unencumbered by termination
arguments.
see also
https://github.com/leanprover/std4/pull/690#issuecomment-2095378609
This PR upstreams lemmas about List/Array operations already defined in
Lean from std/batteries.
Happy to take suggestions about increasing or decreasing scope.
---------
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Adds `IO.Process.getCurrentDir` and `IO.Process.setCurrentDir` for
retrieving and setting, respectively, the current working directory of a
process. The names of the functions are inspired by Rust (e.g.,
[`set_current_dir`](https://doc.rust-lang.org/std/env/fn.set_current_dir.html)).
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.
`Name.append` has special handling of macro scopes, and it would cause
`unresolveNameGlobal` to panic. Using `Name.appendCore` to append name
parts is justified by the fact that it's being used to reassemble a
disassembled name.
Closes#2291
Previously the `ac_rfl` tactic was only really usable when depending on
mathlib. With these instances, `ac_rfl` can deal with the various
operations defined in Lean.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
