This PR introduces polymorphic slices in their most basic form. They
come with a notation similar to the new range notation. `Subarray` is
now also a slice and can produce an iterator now. It is intended to
migrate more operations of `Subarray` to the `Slice` wrapper type to
make them available for slices of other types, too.
The PR also moves the `filterMap` combinators into `Init` because they
are used internally to implement iterators on array slices.
This PR adds the types `Std.ExtDTreeMap`, `Std.ExtTreeMap` and
`Std.ExtTreeSet` of extensional tree maps and sets. These are very
similar in construction to the existing extensional hash maps with one
exception: extensional tree maps and sets provide all functions from
regular tree maps and sets. This is possible because in contrast to hash
maps, tree maps are always ordered.
This PR adds a logic of stateful predicates SPred to Std.Do in order to
support reasoning about monadic programs. It comes with a dedicated
proof mode the tactics of which are accessible by importing
Std.Tactic.Do.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR introduces ranges that are polymorphic, in contrast to the
existing `Std.Range` which only supports natural numbers.
Breakdown of core changes:
* `Lean.Parser.Basic`: Modified the number parser (`Lean.Parser.Basic`)
so that it will only consider a *single* dot to be part of a decimal
number. `1..` will no longer be parsed as `1.` followed by `.`, but as
`1` followed by `..`.
* The test `ellipsisProjIssue` ensures that `#check Nat.add ...succ`
produces a syntax error. After introducing the new range notation (see
below), it returns a different (less nice) error message. I updated the
test to reflect the new error message. (The error message will become
nicer as soon as a delaborator for the ranges is implemented. This is
out of scope for this PR.)
Breakdown of standard library changes:
Modified modules: `Init.Data.Range.Polymorphic` (added),
`Init.Data.Iterators`, `Std.Data.Iterators`
* Introduced the type `Std.PRange` that is parameterized over the type
in which the range operates and the shapes of the lower and upper bound.
* Introduced a new notation for ranges. Examples for this notation are:
`1...*`, `1...=3`, `1...<3`, `1<...=2`, `*...=3`.
* Defined lots of typeclasses for different capabilities of ranges,
depending on their shape and underlying type.
* Introduced `Iter(M).size`.
* Introduced the `Iter(M).stepSize n` combinator, which iterates over an
iterator with the given step size `n`. It will drop `n - 1` values
between every value it emits.
* Replaced `LawfulPureIterator` with a new and better typeclass
`LawfulDeterministicIterator`.
* Simplified some lemma statements in the iterator library such as
`IterM.toList_eq_match`, which unnecessarily matched over a `Subtype`,
hindering rewrites due to type dependencies.
Reasons for the concrete choice of notation:
* `lean4-cli` uses `...`-based notation for the `Cmd` notation and it
clashes with `...a` range notation.
* test `2461` fails when using two-dot-based notation because of the
existing `{ a.. }` notation.
This PR adds a generic `MonadLiftT Id m` instance. We do not implement a
`MonadLift Id m` instance because it would slow down instance resolution
and because it would create more non-canonical instances. This change
makes it possible to iterate over a pure iterator, such as `[1, 2,
3].iter`, in arbitrary monads.
This PR adds a new monadic interface for `Async` operations.
This is the design for the `Async` monad that I liked the most. The idea
was refined with the help of @tydeu. Before that, I had some
prerequisites in mind:
1. Good performance
2. Explicit `yield` points, so we could avoid using `bindTask` for every
lifted IO operation
3. A way to avoid creating an infinite chain of `Task`s during recursion
The 2 and 3 points are not covered in this PR, I wish I had a good
solution but right now only a few sketches of this.
### Explicit `yield` points
I thought this would be easy at first, but it actually turned out kinda
tricky. I ended up creating the `suspend` syntax, which is just a small
modification of the lift method (`<- ...`) syntax. It desugars to
`Suspend.suspend task fun _ => ...`. So something like:
```lean
do
IO.println "a"
IO.println "b"
let result := suspend (client.recv? 1024)
IO.println "c"
IO.println "d"
```
Would become:
```lean
Bind.bind (IO.println "a") fun _ =>
Bind.bind (IO.println "b") fun _ =>
Suspend.suspend (client.recv? 1024) fun message =>
Bind.bind (IO.println "c") fun _ =>
IO.println "d"
```
This makes things a bit more efficient. When using `bind`, we would try
to avoid creating a `Task` chain, and the `suspend` would be the only
place we use `Task.bind`. But there's a problem if we use `bind` with
something that needs `suspend`, it’ll block the whole task. Blocking is
the only way to prevent task accumulation when using plain `bind` inside
a structure like that:
```
inductive AsyncResult (ε σ α : Type u) where
| ok : α → σ → AsyncResult ε σ α
| error : ε → σ → AsyncResult ε σ α
| ofTask : Task (EStateM.Result ε σ α) → σ →AsyncResult ε σ α
```
Because we simply need to remove the `ofTask` and transform it into an
`ok`.
### Infinite chain of Tasks
If you create an infinite recursive function using `Task` (which is
super common in servers like HTTP ones), it can lead to a lot of memory
usage. Because those tasks get chained forever and won't be freed until
the function returns.
To get around that, I used CPS and instead of just calling `Task.bind`,
I’d spawn a new task and return an "empty" one like:
```lean
fun k => Task.bind (...) fun value => do k value; pure emptyTask
```
This works great with a CPS-style monad, but it generates a huge IR by
itself.
Just doing CPS alone was too much, though, because every lifted
operation created a new continuation and a `Task.bind`. So, I used it
with `suspend` and got a better performance, but the usage is not good
with `suspend`.
### The current monad
Right now, the monad I’m using is super simple. It doesn't solve the
earlier problems, but the API is clean, and the generated IR is small
enough. An example of how we should use it is:
```lean
-- A loop that repeatedly sends a message and waits for a reply.
partial def writeLoop (client : Socket.Client) (message : String) : Async (AsyncTask Unit) := async do
IO.println s!"sending: {message}"
await (← client.send (String.toUTF8 message))
if let some mes ← await (← client.recv? 1024) then
IO.println s!"received: {String.fromUTF8! mes}"
-- use parallel to avoid building up an infinite task chain
parallel (writeLoop client message)
else
IO.println "client disconnected from receiving"
-- Server’s main accept loop, keeps accepting and echoing for new clients.
partial def acceptLoop (server : Socket.Server) (promise : IO.Promise Unit) : Async (AsyncTask Unit) := async do
let client ← await (← server.accept)
await (← client.send (String.toUTF8 "tutturu "))
-- allow multiple clients to connect at the same time
parallel (writeLoop client "hi!!")
-- and keep accepting more clients, parallel again to avoid building up an infinite task chain
parallel (acceptLoop server promise)
-- A simple client that connects and sends a message.
def echoClient (addr : SocketAddress) (message : String) : Async (AsyncTask Unit) := async do
let socket ← Client.mk
await (← socket.connect addr)
parallel (writeLoop socket message)
-- TCP setup: bind, listen, serve, and run a sample client.
partial def mainTCP : Async Unit := do
let addr := SocketAddressV4.mk (.ofParts 127 0 0 1) 8080
let server ← Server.mk
server.bind addr
server.listen 128
-- promise exists since the server is (probably) never going to stop
let promise ← IO.Promise.new
let acceptAction ← acceptLoop server promise
await (← echoClient addr "hi!")
await acceptAction
await promise
-- Entry point
def main : IO Unit := mainTCP.wait
```
---------
Co-authored-by: Henrik Böving <hargonix@gmail.com>
Co-authored-by: Mac Malone <tydeu@hatpress.net>
This PR refactors the juggling of universes in the linear
`noConfusionType` construction: Instead of using `PUnit.{…} → ` in the
to get the branches of `withCtorType` to the same universe level, we use
`PULift`.
This fixes https://github.com/leanprover/lean4/issues/8962, although
probably doesn’t solve all issues of that kind while level equality
checking is incomplete.
This PR updates the `solveMonoStep` function used in the `monotonicity`
tactic to check for definitional equality between the current goal and
the monotonicity proof obtained from a recursive call. This ensures
soundness by preventing incorrect applications when
`Lean.Order.PartialOrder` instances differ—an issue that can arise with
`mutual` blocks defined using the `partial_fixpoint` keyword, where
different `Lean.Order.CCPO` structures may be involved.
Closes https://github.com/leanprover/lean4/issues/8894.
This PR both adds initial `@[grind]` annotations for `BitVec`, and uses
`grind` to remove many proofs from `BitVec/Lemmas`.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR embeds a NatModule into its IntModule completion, which is
injective when we have AddLeftCancel, and monotone when the modules are
ordered. Also adds some (failing) grind test cases that can be verified
once `grind` uses this embedding.
This PR changes the CI setup to generate `lean-pr-testing-NNNN` branches
for Mathlib on the `leanprover-community/mathlib4-nightly-testing` fork,
rather than on the main repo.
This PR add instances showing that the Grothendieck (i.e. additive)
envelope of a semiring is an ordered ring if the original semiring is
ordered (and satisfies ExistsAddOfLE), and in this case the embedding is
monotone.
This PR improves the case splitting strategy used in `grind`, and
ensures `grind` also considers simple `match`-conditions for
case-splitting. Example:
```lean
example (x y : Nat)
: 0 < match x, y with
| 0, 0 => 1
| _, _ => x + y := by -- x or y must be greater than 0
grind
```
This PR changes `toLCNF` to stop caching translations of expressions
upon seeing an expression marked `never_extract`. This is more
coarse-grained than it needs to be, but it is difficult to do any
better, as the new compiler's `Expr` cache is based on structural
identity (rather than the pointer identity of the old compiler).
The newly added `tests/compiler/never_extract.lean` is also converted
into a `run` tests, because during development I found the order of the
output to `stderr` to be a bit finicky. The reason for making it a
`compiler` test in the first place is that closed term decls work
slightly differently between native code and the interpreter, and it
would be good to test both, but we already have separate tests for
`never_extract` and closed term extraction.
Fixes#8944.
This PR adds a procedure that efficiently transforms `let` expressions
into `have` expressions (`Meta.letToHave`). This is exposed as the
`let_to_have` tactic.
It uses the `withTrackingZetaDelta` technique: the expression is
typechecked, and any `let` variables that don't enter the zeta delta set
are nondependent. The procedure uses a number of heuristics to limit the
amount of typechecking performed. For example, it is ok to skip
subexpressions that do not contain fvars, mvars, or `let`s.
This PR implements support for normalization for commutative semirings
that do not implement `AddRightCancel`. Examples:
```lean
variable (R : Type u) [CommSemiring R]
example (a b c : R) : a * (b + c) = a * c + b * a := by grind
example (a b : R) : (a + b)^2 = a^2 + 2 * a * b + b^2 := by grind
example (a b : R) : (a + 2 * b)^2 = a^2 + 4 * a * b + 4 * b^2 := by grind
example (a b : R) : (a + 2 * b)^2 = 4 * b^2 + b * 4 * a + a^2 := by grind
```
This PR fixes the handling of the `never_extract` attribute in the
compiler's CSE pass. There is an interesting debate to be had about
exactly how hard the compiler should try to avoid duplicating anything
that transitively uses `never_extract`, but this is the simplest form
and roughly matches the check in the old compiler (although due to
different handling of local function decls in the two compilers, the
consequences might be slightly different).
This gets half of the way to #8944.
This PR adds support to the server for the new module setup process by
changing how `lake setup-file` is used.
In the new server setup, `lake setup-file` is invoked with the file name
of the edited module passed as a CLI argument and with the parsed header
passed to standard input in JSON form. Standard input is used to avoid
potentially exceeding the CLI length limits on Windows. Lake will build
the module's imports along with any other dependencies and then return
the module's workspace configuration via JSON (now in the form of
`ModuleSetup`). The server then post-processes this configuration a bit
and returns it back to the Lean language processor.
The server's header is currently only fully respected by Lake for
external modules (files that are not part of any workspace library). For
workspace modules, the saved module header is currently used to build
imports (as has been done since #7909). A follow-up Lake PR will align
both cases to follow the server's header.
Lean search paths (e.g., `LEAN_PATH`, `LEAN_SRC_PATH`) are no longer
negotiated between the server and Lake. These environment variables are
already configured during sever setup by `lake serve` and do not change
on a per-file basis. Lake can also pre-resolve the `.olean` files of
imports via the `importArts` field of `ModuleSetup`, limiting the
potential utility of communicating `LEAN_PATH`.
This PR adds explanations for a few errors concerning noncomputability,
redundant match alternatives, and invalid inductive declarations.
These adopt a lower-case error naming style, which is also applied to
existing error explanation tests.
This PR introduces antitonicity lemmas that support the elaboration of
mixed inductive-coinductive predicates defined using the
`least_fixpoint` / `greatest_fixpoint` constructs.
For instance, the following definition elaborates correctly because all
occurrences of the inductively defined predicate `tock `within the
coinductive definition of `tick` appear in negative positions. The dual
situation applies to the definition of `tock`:
```
mutual
def tick : Prop :=
tock → tick
greatest_fixpoint
def tock : Prop :=
tick → tock
least_fixpoint
end
```
This PR allows `simp` to recognize and warn about simp lemmas that are
likely looping in the current simp set. It does so automatically
whenever simplification fails with the dreaded “max recursion depth”
error fails, but it can be made to do it always with `set_option
linter.loopingSimpArgs true`. This check is not on by default because it
is somewhat costly, and can warn about simp calls that still happen to
work.
This closes#5111. In the end, this implemented much simpler logic than
described there (and tried in the abandoned #8688; see that PR
description for more background information), but it didn’t work as well
as I thought. The current logic is:
“Simplify the RHS of the simp theorem, complain if that fails”.
It is a reasonable policy for a Lean project to say that all simp
invocation should be so that this linter does not complain. Often it is
just a matter of explicitly disabling some simp theorems from the
default simp set, to make it clear and robust that in this call, we do
not want them to trigger. But given that often such simp call happen to
work, it’s too pedantic to impose it on everyone.
This PR adds the `+generalize` option to the `let` and `have` syntaxes.
For example, `have +generalize n := a + b; body` replaces all instances
of `a + b` in the expected type with `n` when elaborating `body`. This
can be likened to a term version of the `generalize` tactic. One can
combine this with `eq` in `have +generalize (eq := h) n := a + b; body`
as an analogue of `generalize h : n = a + b`.
This PR finishes post-stage0-cleanup after #8914 and #8929. Also:
- adds configuration options for `haveI` and `letI` terms.
- adds `letConfig` parser alias
This PR implements first-class support for nondependent let expressions
in the elaborator; recall that a let expression `let x : t := v; b` is
called *nondependent* if `fun x : t => b` typechecks, and the notation
for a nondependent let expression is `have x := v; b`. Previously we
encoded `have` using the `letFun` function, but now we make use of the
`nondep` flag in the `Expr.letE` constructor for the encoding. This has
been given full support throughout the metaprogramming interface and the
elaborator. Key changes to the metaprogramming interface:
- Local context `ldecl`s with `nondep := true` are generally treated as
`cdecl`s. This is because in the body of a `have` expression the
variable is opaque. Functions like `LocalDecl.isLet` by default return
`false` for nondependent `ldecl`s. In the rare case where it is needed,
they take an additional optional `allowNondep : Bool` flag (defaults to
`false`) if the variable is being processed in a context where the value
is relevant.
- Functions such as `mkLetFVars` by default generalize nondependent let
variables and create lambda expressions for them. The
`generalizeNondepLet` flag (default true) can be set to false if `have`
expressions should be produced instead. **Breaking change:** Uses of
`letLambdaTelescope`/`mkLetFVars` need to use `generalizeNondepLet :=
false`. See the next item.
- There are now some mapping functions to make telescoping operations
more convenient. See `mapLetTelescope` and `mapLambdaLetTelescope`.
There is also `mapLetDecl` as a counterpart to `withLetDecl` for
creating `let`/`have` expressions.
- Important note about the `generalizeNondepLet` flag: it should only be
used for variables in a local context that the metaprogram "owns". Since
nondependent let variables are treated as constants in most cases, the
`value` field might refer to variables that do not exist, if for example
those variables were cleared or reverted. Using `mapLetDecl` is always
fine.
- The simplifier will cache its let dependence calculations in the
nondep field of let expressions.
- The `intro` tactic still produces *dependent* local variables. Given
that the simplifier will transform lets into haves, it would be
surprising if that would prevent `intro` from creating a local variable
whose value cannot be used.
Note that nondependence of lets is not checked by the kernel. To
external checker authors: If the elaborator gets the nondep flag wrong,
we consider this to be an elaborator error. Feel free to typecheck `letE
n t v b true` as if it were `app (lam n t b default) v` and please
report issues.
This PR follows up from #8751, which made sure the nondep flag was
preserved in the C++ interface.
This PR is a followup to #8914, fixing an oversight where
`letIdDeclBinders` is was not updated with the new format. This relies
on some bootstrapping code to stay in place, but we do bootstrap cleanup
that is currently possible.
This PR adds a linter (`linter.unusedSimpArgs`) that complains when a
simp argument (`simp [foo]`) is unused. It should do the right thing if
the `simp` invocation is run multiple times, e.g. inside `all_goals`. It
does not trigger when the `simp` call is inside a macro. The linter
message contains a clickable hint to remove the simp argument.
I chose to display a separate warning for each unused argument. This
means that the user has to click multiple times to remove all of them
(and wait for re-elaboration in between). But this just means multiple
endorphine kicks, and the main benefit over a single warning that would
have to span the whole argument list is that already the squigglies tell
the users about unused arguments.
This closes#4483.
Making Init and Std clean wrt to this linter revealed close to 1000
unused simp args, a pleasant experience for anyone enjoying tidying
things: #8905
This PR modifies `let` and `have` term syntaxes to be consistent with
each other. Adds configuration options; for example, `have` is
equivalent to `let +nondep`, for *nondependent* lets. Other options
include `+usedOnly` (for `let_tmp`), `+zeta` (for `letI`/`haveI`), and
`+postponeValue` (for `let_delayed)`. There is also `let (eq := h) x :=
v; b` for introducing `h : x = v` when elaborating `b`. The `eq` option
works for pattern matching as well, for example `let (eq := h) (x, y) :=
p; b`.
Future PRs will add these options to tactic syntax, once a stage0 update
has been done.
This PR implements support for (commutative) semirings in `grind`. It
uses the Grothendieck completion to construct a (commutative) ring
`Lean.Grind.Ring.OfSemiring.Q α` from a (commutative) semiring `α`. This
construction is mostly useful for semirings that implement
`AddRightCancel α`. Otherwise, the function `toQ` is not injective.
Examples:
```lean
example (x y : Nat) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
grind
example [CommSemiring α] [AddRightCancel α] (x y : α) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
grind
example (a b : Nat) : 3 * a * b = a * b * 3 := by grind
example (k z : Nat) : k * (z * 2 * (z * 2 + 1)) = z * (k * (2 * (z * 2 + 1))) := by grind
example [CommSemiring α] [AddRightCancel α] [IsCharP α 0] (x y : α)
: x^2*y = 1 → x*y^2 = y → x + y = 1 → False := by
grind
```
This PR makes `simp` consult its own cache more often, to avoid
replicating work.
Before, the simp cache was checked upon entry of `simpImpl` only, which
then calls `simpLoop`, which recursively iterates the `pre`-lemmas,
without checking the cache again.
Now, `simpLoop` itself checks the cache. This seems more principled,
given that `simpLoop` is actually putting entries into the cache for
each of its calls, so it’s more uniform if it checks the cache itself.
This avoids repeated rewrites. For example given
```
theorem ab : a = b := testSorry
theorem bc : b = c := testSorry
example (h : P c) : P b ∧ P a := by simp [ab, bc, h]
```
simp would rewrite `b ==> c` twice (once as part of `b ==> c` and then
again as part of `a ==> b ==> c`). And it’d be order dependent: With
```
example (h : P c) : P a ∧ P b := by simp [ab, bc, h]
```
the `a ==> b ==> c` chain would insert `b ==> c` into the cache, and
picked up by `simpImpl` when rewriting `P b`.
With this change, `b ==> c` is performed only once in both examples.
Instruction counts on stdlib and mathlib both show a mild improvement
across the board (0.5%), with individual modules improving by up to 4%
in stdlib and even more in mathlib.
(This does not check the cache before applying `post`, which explains
where there are still some repeated rewrites in the trace logs. But I’m
less sure about inserting a cache check here and so I am treading
carefully here. It’s also going to be at most one `post` application
that’s duplicated, because if `post` returns `.visit`, we go back to
`pre` and thus a cache check.)
This PR refactors the way simp arguments are elaborated: Instead of
changing the `SimpTheorems` structure as we go, this elaborates each
argument to a more declarative description of what it does, and then
apply those. This enables more interesting checks of simp arguments that
need to happen in the context of the eventually constructed simp context
(the checks in #8688), or after simp has run (unused argument linter
#8901).
The new data structure describing an elaborated simp argument isn’t the
most elegant, but follows from the code.
While I am at it, move handling of `[*]` into `elabSimpArgs`. Downstream
adaption branches exist (but may not be fully up to date because of the
permission changes).
While I am at it, I cleaned up `SimpTheorems.lean` file a bit (sorting
declarations, mild renaming) and added documentation.
This PR make sure that the local instance cache calculation applies more
reductions. In #2199 there was an issue where metavariables could
prevent local variables from being considered as local instances. We use
a slightly different approach that ensures that, for example, `let`s at
the ends of telescopes do not cause similar problems. These reductions
were already being calculated, so this does not require any additional
work to be done.
Metaprogramming interface addition: the various forall telescope
functions that do reduction now have a `whnfType` flag (default false).
If it's true, then the callback `k` is given the WHNF of the type. This
is a free operation, since the telescope function already computes it.
This PR refactors `Lean.Grind.NatModule/IntModule/Ring.IsOrdered`.
We ensure the the diamond from `Ring` to `NatModule` via either
`Semiring` or `IntModule` is defeq, which was not previously the case.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
