This PR allows Lean's parser to run with a final position prior to the
end of the string, so it can be invoked on a sub-region of the input.
This has applications in Verso proper, which parses Lean syntax in
contexts such as code blocks and docstrings, and it is a prerequisite to
parsing the contents of Lean docstrings.
This PR fixes the compilation of `noConfusion` by repairing an oversight
made when porting this code from the old compiler. The old compiler only
repeatedly expanded the major for each non-`Prop` field of the inductive
under consideration, mirroring the construction of `noConfusion` itself,
whereas the new compiler erroneously counted all fields.
Fixes#9971.
This PR improves support for `a^n` in `grind cutsat`. For example, if
`cutsat` discovers that `a` and `b` are equal to numerals, it now
propagates the equality. This PR is similar to #9996, but `a^b`.
Example:
```lean
example (n : Nat) : n = 2 → 2 ^ (n+1) = 8 := by
grind
```
With #10022, it also improves the support for `BitVec n` when `n` is not
numeral. Example:
```lean
example {n m : Nat} (x : BitVec n)
: 2 ≤ n → n ≤ m → m = 2 → x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 := by
grind
```
This PR implements the necessary typeclasses so that range notation
works for integers. For example, `((-2)...3).toList = [-2, -1, 0, 1, 2]
: List Int`.
This PR changes macro scope numbering from per-module to per-command,
ensuring that unrelated changes to other commands do not affect macro
scopes generated by a command, which improves `prefer_native` hit rates
on bootstrapping as well as avoids further rebuilds under the module
system.
In detail, instead of always using the current module name as a macro
scope prefix, each command now introduces a new macro scope prefix
(called "context") of the shape `<main module>._hygCtx_<uniq>` where
`uniq` is a `UInt32` derived from the command but automatically
incremented in case of conflicts (which must be local to the current
module). In the current implementation, `uniq` is the hash of the
declaration name, if any, or else the hash of the full command's syntax.
Thus, it is always independent of syntactic changes to other commands
(except in case of hash conflicts, which should only happen in practice
for syntactically identical commands) and, in the case of declarations,
also independent of syntactic changes to any private parts of the
declaration.
This PR adds useful declarations to the `LawfulOrderMin/Max` and
`LawfulOrderLeftLeaningMin/Max` API. In particular, it introduces
`.leftLeaningOfLE` factories for `Min` and `Max`. It also renames
`LawfulOrderMin/Max.of_le` to .of_le_min_iff` and `.of_max_le_iff` and
introduces a second variant with different arguments.
This PR changes the `toMono` pass to replace decls with their `_redArg`
equivalent, which has the consequence of not considering arguments
deemed useless by the `reduceArity` pass for the purposes of the
`noncomputable` check.
This PR adds support for correctly handling computations on fields in
`casesOn` for inductive predicates that support large elimination. In
any such predicate, the only relevant fields allowed are those that are
also used as an index, in which case we can find the supplied index and
use that term instead.
This PR improves support for `Fin n` in `grind cutsat` when `n` is not a
numeral. For example, the following goals can now be solved
automatically:
```lean
example (p d : Nat) (n : Fin (p + 1))
: 2 ≤ p → p ≤ d + 1 → d = 1 → n = 0 ∨ n = 1 ∨ n = 2 := by
grind
example (s : Nat) (i j : Fin (s + 1)) (hn : i ≠ j) (hl : ¬i < j) : j < i := by
grind
example {n : Nat} (j : Fin (n + 1)) : j ≤ j := by
grind
example {n : Nat} (x y : Fin ((n + 1) + 1)) (h₂ : ¬x = y) (h : ¬x < y) : y < x := by
grind
```
This PR changes the handling of overapplied constructors when lowering
LCNF to IR from a (slightly implicit) assertion failure to producing
`unreachable`. Transformations on inlined unreachable code can produce
constructor applications with additional arguments.
In the old compiler, these additional arguments were silently ignored,
but it seems more sensible to replace them with `unreachable`, just in
case they arise due to a compiler error.
Fixes#9937.
This PR improves support for nonlinear `/` and `%` in `grind cutsat`.
For example, given `a / b`, if `cutsat` discovers that `b = 2`, it now
propagates that `a / b = b / 2`. This PR is similar to #9996, but for
`/` and `%`. Example:
```lean
example (a b c d : Nat)
: b > 1 → d = 1 → b ≤ d + 1 → a % b = 1 → a = 2 * c → False := by
grind
```
This PR fixes a bug in `#eval` where clicking on the evaluated
expression could show errors in the Infoview. This was caused by `#eval`
not saving the temporary environment that is used when elaborating the
expression.
This PR provides factories that derive order typeclasses in bulk, given
an `Ord` instance. If present, existing instances are preferred over
those derived from `Ord`. It is possible to specify any instance
manually if desired.
This PR reduces the number of `Nat.Bitwise` grind annotations we have
the deal with distributivity. The new smaller set encourages `grind` to
rewrite into DNF. The old behaviour just resulted in saturating up to
the instantiation limits.
This PR improves support for nonlinear monomials in `grind cutsat`. For
example, given a monomial `a * b`, if `cutsat` discovers that `a = 2`,
it now propagates that `a * b = 2 * b`.
Recall that nonlinear monomials like `a * b` are treated as variables in
`cutsat`, a procedure designed for linear integer arithmetic.
Example:
```lean
example (a : Nat) (ha : a < 8) (b c : Nat) : 2 ≤ b → c = 1 → b ≤ c + 1 → a * b < 8 * b := by
grind
example (x y z w : Int) : z * x * y = 4 → x = z + w → z = 1 → w = 2 → False := by
grind
```
This PR provides the means to quickly provide all the order instances
associated with some high-level order structure (preorder, partial
order, linear preorder, linear order). This can be done via the factory
functions `PreorderPackage.ofLE`, `PartialOrderPackage.ofLE`,
`LinearPreorderPackage.ofLE` and `LinearOrderPackage.ofLE`.
This PR eliminates uses of `intros x y z` (with arguments) and updates
the `intros` docstring to suggest that `intro x y z` should be used
instead. The `intros` tactic is historical, and can be traced all the
way back to Lean 2, when `intro` could only introduce a single
hypothesis. Since 2020, the `intro` tactic has superceded it. The
`intros` tactic (without arguments) is currently still useful.
This PR upstreams the definition of Rat from Batteries, for use in our
planned interval arithmetic tactic.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR adds two test cases extracted from Mathlib, that `grind` cannot
solve but `omega` can. Originally the multiplication instance came from
`Nat.instSemiring` and `Int.instSemiring`, in minimizing I found that
`Distrib` is already enough.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This PR fixes an issue when running Mathlib's `FintypeCat` as code,
where an erased type former is passed to a polymorphic function. We were
lowering the arrow type to`object`, which conflicts with the runtime
representation of an erased value as a tagged scalar.
This PR modifies the generation of induction and partial correctness
lemmas for `mutual` blocks defined via `partial_fixpoint`. Additionally,
the generation of lattice-theoretic induction principles of functions
via `mutual` blocks is modified for consistency with `partial_fixpoint`.
The lemmas now come in two variants:
1. A conjunction variant that combines conclusions for all elements of
the mutual block. This is generated only for the first function inside
of the mutual block.
2. Projected variants for each function separately
## Example 1
```lean4
axiom A : Type
axiom B : Type
axiom A.toB : A → B
axiom B.toA : B → A
mutual
noncomputable def f : A := g.toA
partial_fixpoint
noncomputable def g : B := f.toB
partial_fixpoint
end
```
Generated `fixpoint_induct` lemmas:
```lean4
f.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_1 f
g.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_2 g
```
Mutual (conjunction) variant:
```lean4
f.mutual_fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1) (adm_2 : admissible motive_2)
(h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA) (h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) :
motive_1 f ∧ motive_2 g
```
## Example 2
```lean4
mutual
def f (n : Nat) : Option Nat :=
g (n + 1)
partial_fixpoint
def g (n : Nat) : Option Nat :=
if n = 0 then .none else f (n + 1)
partial_fixpoint
end
```
Generated `partial_correctness` lemmas (in a projected variant):
```lean4
f.partial_correctness (motive_1 motive_2 : Nat → Nat → Prop)
(h_1 :
∀ (g : Nat → Option Nat),
(∀ (n r : Nat), g n = some r → motive_2 n r) → ∀ (n r : Nat), g (n + 1) = some r → motive_1 n r)
(h_2 :
∀ (f : Nat → Option Nat),
(∀ (n r : Nat), f n = some r → motive_1 n r) →
∀ (n r : Nat), (if n = 0 then none else f (n + 1)) = some r → motive_2 n r)
(n r✝ : Nat) : f n = some r✝ → motive_1 n r✝
g.partial_correctness (motive_1 motive_2 : Nat → Nat → Prop)
(h_1 :
∀ (g : Nat → Option Nat),
(∀ (n r : Nat), g n = some r → motive_2 n r) → ∀ (n r : Nat), g (n + 1) = some r → motive_1 n r)
(h_2 :
∀ (f : Nat → Option Nat),
(∀ (n r : Nat), f n = some r → motive_1 n r) →
∀ (n r : Nat), (if n = 0 then none else f (n + 1)) = some r → motive_2 n r)
(n r✝ : Nat) : g n = some r✝ → motive_2 n r✝
```
Mutual (conjunction) variant:
```
f.mutual_partial_correctness (motive_1 motive_2 : Nat → Nat → Prop)
(h_1 :
∀ (g : Nat → Option Nat),
(∀ (n r : Nat), g n = some r → motive_2 n r) → ∀ (n r : Nat), g (n + 1) = some r → motive_1 n r)
(h_2 :
∀ (f : Nat → Option Nat),
(∀ (n r : Nat), f n = some r → motive_1 n r) →
∀ (n r : Nat), (if n = 0 then none else f (n + 1)) = some r → motive_2 n r) :
(∀ (n r : Nat), f n = some r → motive_1 n r) ∧ ∀ (n r : Nat), g n = some r → motive_2 n r
```
This PR modifies `intro` to create tactic info localized to each
hypothesis, making it possible to see how `intro` works
variable-by-variable. Additionally:
- The tactic supports `intro rfl` to introduce an equality and
immediately substitute it, like `rintro rfl` (recall: the `rfl` pattern
is like doing `intro h; subst h`). The `rintro` tactic can also now
support `HEq` in `rfl` patterns if `eq_of_heq` applies.
- In `intro (h : t)`, elaboration of `t` is interleaved with unification
with the type of `h`, which prevents default instances from causing
unification to fail.
- Tactics that change types of hypotheses (including `intro (h : t)`,
`delta`, `dsimp`) now update the local instance cache.
In `intro x y z`, tactic info ranges are `intro x`, `y`, and `z`. The
reason for including `intro` with `x` is to make sure the info range is
"monotonic" while adding the first argument to `intro`.
This PR cleans up `optParam`/`autoParam`/etc. annotations before
elaborating definition bodies, theorem bodies, `fun` bodies, and `let`
function bodies. Both `variable`s and binders in declaration headers are
supported.
There are no changes to `inductive`/`structure`/`axiom`/etc. processing,
just `def`/`theorem`/`example`/`instance`.
This PR removes the option `grind +ringNull`. It provided an alternative
proof term construction for the `grind ring` module, but it was less
effective than the default proof construction mode and had effectively
become dead code.
This PR also optimizes semiring normalization proof terms using the
infrastructure added in #9946.
**Remark:** After updating stage0, we can remove several background
theorems from the `Init/Grind` folder.
This PR optimizes the proof terms produced by `grind linarith`. It is
similar to #9945, but for the `linarith` module in `grind`.
It removes unused entries from the context objects when generating the
final proof, significantly reducing the amount of junk in the resulting
terms.
This PR optimizes the proof terms produced by `grind cutsat`. It removes
unused entries from the context objects when generating the final proof,
significantly reducing the amount of junk in the resulting terms.
Example:
```lean
/--
trace: [grind.debug.proof] fun h h_1 h_2 h_3 h_4 h_5 h_6 h_7 h_8 =>
let ctx := RArray.leaf (f 2);
let p_1 := Poly.add 1 0 (Poly.num 0);
let p_2 := Poly.add (-1) 0 (Poly.num 1);
let p_3 := Poly.num 1;
le_unsat ctx p_3 (eagerReduce (Eq.refl true)) (le_combine ctx p_2 p_1 p_3 (eagerReduce (Eq.refl true)) h_8 h_1)
-/
#guard_msgs in -- Context should contain only `f 2`
open Lean Int Linear in
set_option trace.grind.debug.proof true in
example (f : Nat → Int) :
f 1 <= 0 → f 2 <= 0 → f 3 <= 0 → f 4 <= 0 → f 5 <= 0 →
f 6 <= 0 → f 7 <= 0 → f 8 <= 0 → -1 * f 2 + 1 <= 0 → False := by
grind
```
