This PR implements counterexamples for grind linarith. Example:
```lean
example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (a b c d : α)
: b ≥ 0 → c > b → d > b → a ≠ b + c → a > b + c → a < b + d → False := by
grind
```
produces the counterexample
```
a := 7/2
b := 1
c := 2
d := 3
```
```lean
example [IntModule α] [LinearOrder α] [IntModule.IsOrdered α] (a b c d : α)
: a ≤ b → a - c ≥ 0 + d → d ≤ 0 → b = c → a ≠ b → False := by
grind
```
generates the counterexample
```
a := 0
b := 1
c := 1
d := -1
```
This PR changes the `show t` tactic to match its documentation.
Previously it was a synonym for `change t`, but now it finds the first
goal that unifies with the term `t` and moves it to the front of the
goal list.
Thanks to `mmap`, startup time is not necessarily related to this
figure, but it can be used as a rough measure for that and how much data
the module depends on, i.e. the rebuild chance.
Also adds new cumulative benchmarks for this metric as well as the
number of imported constants and env ext entries.
This PR implements disequality splitting and non-chronological
backtracking for the `grind` linarith procedure.
```lean
example [IntModule α] [LinearOrder α] [IntModule.IsOrdered α] (a b c d : α)
: a ≤ b → a - c ≥ 0 + d → d ≤ 0 → d ≥ 0 → b = c → a ≠ b → False := by
grind
```
This PR adds the pre-stage0-update infrastructure for named error
messages. It adds macro syntax for registering and throwing named errors
(without elaborators), mechanisms for displaying error names in the
Infoview and at the command line, and the ability to link to error
explanations in the manual (once they are added).
This PR adds documentation to builtin attributes like `@[refl]` or
`@[implemented_by]`.
Closes#8432
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: David Thrane Christiansen <david@lean-fro.org>
This PR handles constants with erased types in `toMonoType`. It is much
harder to write a test case for this than you would think, because most
references to such types get replaced with `lcErased` earlier.
This PR fixes an internalization bug in the interface between linarith
and ring modules in `grind`. The `CommRing` module may create new terms
during normalization.
This PR implements support for inequalities in the `grind` linear
arithmetic procedure and simplifies its design. Some examples that can
already be solved:
```lean
open Lean.Grind
example [IntModule α] [Preorder α] [IntModule.IsOrdered α] (a b c d : α)
: a + d < c → b = a + (2:Int)*d → b - d > c → False := by
grind
example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (a b : α)
: a = 0 → b = 1 → a + b ≤ 2 := by
grind
example [CommRing α] [Preorder α] [Ring.IsOrdered α] (a b c d e : α) :
2*a + b ≥ 1 → b ≥ 0 → c ≥ 0 → d ≥ 0 → e ≥ 0
→ a ≥ 3*c → c ≥ 6*e → d - e*5 ≥ 0
→ a + b + 3*c + d + 2*e < 0 → False := by
grind
```
This PR implements the main framework of the model search procedure for
the linarith component in grind. It currently handles only inequalities.
It can already solve simple goals such as
```lean
example [IntModule α] [Preorder α] [IntModule.IsOrdered α] (a b c : α)
: a < b → b < c → c < a → False := by
grind
example [IntModule α] [LinearOrder α] [IntModule.IsOrdered α] (a b c : α)
: a < b → b < c + d → a - d < c := by
grind
```
This PR implements the infrastructure for constructing proof terms in
the linarith procedure in `grind`. It also adds the `ToExpr` instances
for the reified objects.
This PR introduces an explicit `defeq` attribute to mark theorems that
can be used by `dsimp`. The benefit of an explicit attribute over the
prior logic of looking at the proof body is that we can reliably omit
theorem bodies across module boundaries. It also helps with intra-file
parallelism.
If a theorem is syntactically defined by `:= rfl`, then the attribute is
assumed and need not given explicitly. This is a purely syntactic check
and can be fooled, e.g. if in the current namespace, `rfl` is not
actually “the” `rfl` of `Eq`. In that case, some other syntax has be
used, such as `:= (rfl)`. This is also the way to go if a theorem can be
proved by `defeq`, but one does not actually want `dsimp` to use this
fact.
The `defeq` attribute will look at the *type* of the declaration, not
the body, to check if it really holds definitionally. Because of
different reduction settings, this can sometimes go wrong. Then one
should also write `:= (rfl)`, if one does not want this to be a defeq
theorem. (If one does then this is currently not possible, but it’s
probably a bad idea anyways).
The `set_option debug.tactic.simp.checkDefEqAttr true`, `dsimp` will
warn if could not apply a lemma due to a missing `defeq` attribute.
With `set_option backward.dsimp.useDefEqAttr.get false` one can revert
to the old behavior of inferring rfl-ness based on the theorem body.
Both options will go away eventually (too bad we can’t mark them as
deprecated right away, see #7969)
Meta programs that generate theorems (e.g. equational theorems) can use
`inferDefEqAttr` to set the attribute based on the theorem body of the
just created declaration.
This builds on #8501 to update Init to `@[expose]` a fair amount of
definitions that, if not exposed, would prevent some existing `:= rfl`
theorems from being `defeq` theorems. In the interest of starting
backwards compatible, I exposed these function. Hopefully many can be
un-exposed later again.
A mathlib adaption branch exists that includes both the meta programming
fixes and changes to the theorems (e.g. changing `:= by rfl` to `:=
rfl`).
With the module system there is now no special handling for `defeq`
theorem bodies, because we don’t look at the body anymore. The previous
hack is removed. The `defeq`-ness of the theorem needs to be checked in
the context of the theorem’s *type*; the error message contains a hint
if the defeq check fails because of the exported context.
This PR provides a special empty iterator type. Although its behavior
can be emulated with a list iterator (for example), having a special
type has the advantage of being easier to optimize for the compiler.
This PR makes the equational theorems of non-exposed defs private. If
the author of a module chose not to expose the body of their function,
then they likely don't want that implementation to leak through
equational theorems. Helps with #8419.
There is some amount of incidential complexity due to how `private`
works in lean, by mangling the name: lots of code paths that need now do
the right thing™ about private and non-private names, including the
whole reserved name machinery.
So this includes a number of refactorings:
* The logic for calculating an equational theorem name (or similar) is
now done by a single function, `mkEqLikeNameFor`, rather than all over
the place.
* Since the name of the equational theorem now depends on the current
context (in particular whether it’s a proper module, or a non-module
file), the forward map from declaration to equational theorem doesn’t
quite work anymore. This map is deleted; the list of equational theorems
are now always found by looking for declaration of the expected names
(`alreadyGenerated). If users define such theorems themselves (and make
it past the “do not allow reserved names to be declared”) they get to
keep both pieces.
* Because this map was deleted, mathlib’s `eqns` command can no longer
easily warn if equational lemmas have already been generated too early
(adaption branch exists). But in general I think lean could provide a
more principled way of supporting custom unfold lemmas, and ideally the
whole equational theorem machinery is just using that.
* The ReservedNamePredicate is used by `resolveExact`, so we need to
make sure that it returns the right name, including privateness. It is
not ok to just reserve both the private and non-private name but then
later in the ReservedNameAction produce just one of the two.
* We create `foo.def_eq` eagerly for well-founded recursion. This is
needed because we need feed in the proof of the rewriting done by
`wf_preprocess`. But if `foo.def_eq` is private in a module, then a
non-module importing it will still expect a non-private `foo.def_eq` to
exist. To patch that, we install a `copyPrivateUnfoldTheorem :
GetUnfoldEqnFn` that declares a theorem aliasing the private one. Seems
to work.
This PR removes the `NatCast (Fin n)` global instance (both the direct
instance, and the indirect one via `Lean.Grind.Semiring`), as that
instance causes causes `x < n` (for `x : Fin k`, `n : Nat`) to be
elaborated as `x < ↑n` rather than `↑x < n`, which is undesirable. Note
however that in Mathlib this happens anyway!
This PR adds a test case / use case example for `grind`, setting up the
very basics of `IndexMap`, modelled on Rust's
[`indexmap`](https://docs.rs/indexmap/latest/indexmap/). It is not
intended as a complete implementation: just enough to exercise `grind`.
(Thanks to @arthurpaulino for suggesting this as a test case.)
This PR fixes a bug in the equality-resolution procedure used by
`grind`.
The procedure now performs a topological sort so that every simplified
theorem declaration is emitted **before** any place where it is
referenced.
Previously, applying equality resolution to
```lean
h : ∀ x, p x a → ∀ y, p y b → x ≠ y
```
in the example
```lean
example
(p : Nat → Nat → Prop)
(a b c : Nat)
(h : ∀ x, p x a → ∀ y, p y b → x ≠ y)
(h₁ : p c a)
(h₂ : p c b) :
False := by
grind
```
caused `grind` to produce the incorrect term
```lean
p ?y a → ∀ y, p y b → False
```
The patch eliminates this error, and the following correct simplified
theorem is generated
```lean
∀ y, p y a → p y b → False
```
This PR fixes (1) an issue where private names are not unresolved when
they are pretty printed, (2) an issue where in `pp.universes` mode names
were allowed to shadow local names, (3) an issue where in `match`
patterns constants shadowing locals wouldn't use `_root_`, and (4) an
issue where tactics might have an incorrect "try this" when
`pp.fullNames` is set. Adds more delaboration tests for name
unresolution.
It also cleans up the `delabConst` delaborator so that it uses
`unresolveNameGlobalAvoidingLocals`, rather than doing any local context
analysis itself. The `inPattern` logic has been removed; it was a
heuristic added back in #575, but it now leads to incorrect results (and
in `match` patterns, local names shadow constants in name resolution).
This PR implements signature help support. When typing a function
application, editors with support for signature help will now display a
popup that designates the current (remaining) function type. This
removes the need to remember the function signature while typing the
function application, or having to constantly cycle between hovering
over the function identifier and typing the application. In VS Code, the
signature help can be triggered manually using `Ctrl+Shift+Space`.
### Other changes
- In order to support signature help for the partial syntax `f a <|` or
`f a $`, these notations now elaborate as `f a`, not `f a .missing`.
- The logic in `delabConstWithSignature` that delaborates parameters is
factored out into a function `delabForallParamsWithSignature` so that it
can be used for arbitrary `forall`s, not just constants.
- The `InfoTree` formatter is adjusted to produce output where it is
easier to identify the kind of `Info` in the `InfoTree`.
- A bug in `InfoTree.smallestInfo?` is fixed so that it doesn't panic
anymore when its predicate `p` does not ensure that both `pos?` and
`tailPos?` of the `Info` are present.
This PR adds support for server-sided `RpcRef` reuse and fixes a bug
where trace nodes in the InfoView would close while the file was still
being processed.
The core of the trace node issue is that the server always serves new
RPC references in every single response to the client, which means that
the client is forced to reset its UI state.
In a previous attempt at fixing this (#8056), the server would memorize
the RPC-encoded JSON of interactive diagnostics (which includes RPC
references) and serve it for as long as it could reuse the snapshot
containing the diagnostics, so that RPC references are reused. The
problem with this was that the client then had multiple finalizers
registered for the same RPC reference (one for every reused RPC
reference that was served), and once the first reference was
garbage-collected, all other reused references would point into the
void.
This PR takes a different approach to resolve the issue: The meaning of
`$/lean/rpc/release` is relaxed from "Free the object pointed to by this
RPC reference" to "Decrement the RPC reference count of the object
pointed to by this RPC reference", and the server now maintains a
reference count to track how often a given `RpcRef` was served. Only
when every single served instance of the `RpcRef` has been released, the
object is freed. Additionally, the reuse mechanism is generalized from
being only supported for interactive diagnostics, to being supported for
any object using `WithRpcRef`. In order to make use of reusable RPC
references, downstream users still need to memorize the `WithRpcRef`
instances accordingly.
Closes#8053.
### Breaking changes
Since `WithRpcRef` is now capable of tracking its identity to decide
which `WithRpcRef` usage constitutes a reuse, the constructor of
`WithRpcRef` has been made `private` to discourage downstream users from
creating `WithRpcRef` instances with manually-set `id`s. Instead,
`WithRpcRef.mk` (which lives in `BaseIO`) is now the preferred way to
create `WithRpcRef` instances.
This PR provides the iterator combinator `drop` that transforms any
iterator into one that drops the first `n` elements.
Additionally, the PR removes the specialized `IteratorLoop` instance on
`Take`. It currently does not have a `LawfulIteratorLoop` instance,
which needs to exist for the loop consumer lemmas to work. Having the
specialized instance is low priority.
