This PR ensures users can select the "minimal indexable subexpression"
condition in `grind` parameters. Example, they can now write `grind [!
-> thmName]`. `grind?` will include the `!` modifier whenever users had
used `@[grind!]`. This PR also fixes a missing case in the new pattern
inference procedure.
It also adjusts some `grind` annotations and tests in preparation for
setting the new pattern inference heuristic as the new default.
This PR changes the order of steps tried when proving equational
theorems for structural recursion. In order to avoid goals that `split`
cannot handle, avoid unfolding the LHS of the equation to `.brecOn` and
`.rec` until after the RHS has been split into its final cases.
Fixes: #10195
This PR implements the new E-matching pattern inference heuristic for
`grind`. It is not enabled yet. You can activate the new behavior using
`set_option backward.grind.inferPattern false`. Here is a summary of the
new behavior.
* `[grind =]`, `[grind =_]`, `[grind _=_]`, `[grind <-=]`: no changes;
we keep the current behavior.
* `[grind ->]`, `[grind <-]`, `[grind =>]`, `[grind <=]`: we stop using
the *minimal indexable subexpression* and instead use the first
indexable one.
* `[grind! <mod>]`: behaves like `[grind <mod>]` but uses the minimal
indexable subexpression restriction. We generate an error if the user
writes `[grind! =]`, `[grind! =_]`, `[grind! _=_]`, or `[grind! <-=]`,
since there is no pattern search in these cases.
* `[grind]`: it tries `=`, `=_`, `<-`, `->`, `<=`, `=>` with and without
the minimal indexable subexpression restriction. For the ones that work,
we generate a code action to encourage users to select the one they
prefer.
* `[grind!]`: it tries `<-`, `->`, `<=`, `=>` using the minimal
indexable subexpression restriction. For the ones that work, we generate
a code action to encourage users to select the one they prefer.
* `[grind? <mod>]`: where `<mod>` is one of the modifiers above, it
behaves like `[grind <mod>]` but also displays the pattern.
Example:
```lean
/--
info: Try these:
• [grind =] for pattern: [f (g #0)]
• [grind =_] for pattern: [r #0#0]
• [grind! ←] for pattern: [g #0]
-/
#guard_msgs in
@[grind] axiom fg₇ : f (g x) = r x x
```
This PR adds the ability to do `deriving ReflBEq, LawfulBEq`. Both
classes have to listed in the `deriving` clause. For `ReflBEq`, a simple
`simp`-based proof is used. For `LawfulBEq`, a dedicated,
syntax-directed tactic is used that should work for derived `BEq`
instances. This is meant to work with `deriving BEq` (but you can try to
use it on hand-rolled `@[methods_specs] instance : BEq…` instances).
Does not support mutual or nested inductives.
This PR adds the `reduceBEq` and `reduceOrd` simprocs. They rewrite
occurrences of `_ == _` resp. `Ord.compare _ _` if both arguments are
constructors and the corresponding instance has been marked with
`@[method_specs]` (introduced in #10302), which now by default is the
case for derived instances.
This PR makes the builtin Verso docstring elaborators bootstrap
correctly, adds the ability to postpone checks (which is necessary for
resolving forward references and bootstrapping issues), and fixes a
minor parser bug.
This PR implements a new E-matching pattern inference procedure that is
faithful to the behavior documented in the reference manual regarding
minimal indexable subexpressions. The old inference procedure was
failing to enforce this condition. For example, the manual documents
`[grind ->]` as follows
`[@grind →]` selects a multi-pattern from the hypotheses of the theorem.
In other words, `grind` will use the theorem for forwards reasoning.
To generate a pattern, it traverses the hypotheses of the theorem from
left to right. Each time it encounters a **minimal indexable
subexpression** which covers an argument which was not previously
covered, it adds that subexpression as a pattern, until all arguments
have been covered.
That said, the new procedure is currently disabled, and the following
option must be used to enable it.
```
set_option backward.grind.inferPattern false
```
Users can inspect differences between the old a new procedures using the
option
```
set_option backward.grind.checkInferPatternDiscrepancy true
```
Example:
```lean
/--
warning: found discrepancy between old and new `grind` pattern inference procedures, old:
[@List.length #2 (@toList _ #1#0)]
new:
[@toList #2#1#0]
use `set_option backward.grind.inferPattern true` to force old procedure
-/
#guard_msgs in
set_option backward.grind.checkInferPatternDiscrepancy true in
@[grind] theorem Vector.length_toList' (xs : Vector α n) : xs.toList.length = n := by sorry
```
This PR upstreams the Verso parser and adds preliminary support for
Verso in docstrings. This will allow the compiler to check examples and
cross-references in documentation.
After a `stage0` update, a follow-up PR will add the appropriate
attributes that allow the feature to be used. The parser tests from
Verso also remain to be upstreamed, and user-facing documentation will
be added once the feature has been used on more internals.
This PR completes the `grind` solver extension design and ports the
`grind ac` solver to the new framework. Future PRs will document the API
and port the remaining solvers. An additional benefit of the new design
is faster build times.
This PR adds infrastructure for registering new `grind` solvers. `grind`
already includes many solvers, and this PR is the first step toward
modularizing the design and supporting user-defined solvers.
This PR adds “non-branching case statements”: For each inductive
constructor `T.con` this adds a function `T.con.with` that is similar
`T.casesOn`, but has only one arm (the one for `con`), and an additional
`t.toCtorIdx = 12` assumption.
For example:
```lean
inductive Vec (α : Type) : Nat → Type where
| nil : Vec α 0
| cons {n} : α → Vec α n → Vec α (n + 1)
/--
info: @[reducible] protected def Vec.cons.elim.{u} : {α : Type} →
{motive : (a : Nat) → Vec α a → Sort u} →
{a : Nat} →
(t : Vec α a) →
t.ctorIdx = 1 → ({n : Nat} → (a : α) → (a_1 : Vec α n) → motive (n + 1) (Vec.cons a a_1)) → motive a t
-/
#guard_msgs in
#print sig Vec.cons.elim
```
This is a building block for non-quadratic implementations of `BEq` and
`DecidableEq` etc.
Builds on top of #9951.
The compiled code for a these functions could presumably, without
branching on the inductive value, directly access the fields. Achieving
this optimization (and achieving it without a quadratic compilation
cost) is not in scope for this PR.
This PR adds a private `Lean.Name.getUtf8Byte'` to `Init.Meta` for a
future PR that optimizes `Lean.Name.escapePart`.
`Lean.Name.getUtf8Byte'` should be replaced with `String.getUtf8Byte`
once the string refactor is through.
This PR makes the generation of functional induction principles more
robust when the user `let`-binds a variable that is then `match`'ed on.
Fixes#10132.
