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 sets `ring := true` by default in `grind`. It also fixes a bug
in the reification procedure, and improves the term internalization in
the ring and cutsat modules.
This PR simplifies the interface between the `grind` core and the cutsat
procedure. Before this PR, core would try to minimize the number of
numeric literals that have to be internalized in cutsat. This
optimization was buggy (see `grind_cutsat_zero.lean` test), and produced
counterintuitive counterexamples.
This PR fixes the hash function used to implement congruence closure in
`grind`. The hash of an `Expr` must not depend on whether the expression
has been internalized or not.
This PR fixes two inappropriate uses of `whnfD` in `grind`. They were
potential performance foot guns, and were producing unexpected errors
since `whnfD` is not consistently used (and it should not be) in all
modules.
This PR implements `match`-expressions in `grind` using `match`
congruence equations. The goal is to minimize the number of `cast`
operations that need to be inserted, and avoid `cast` over functions.
The new approach support `match`-expressions of the form `match h : ...
with ...`.
This PR upstreams and extends the Mathlib `clear_value` tactic. Given a
local definition `x : T := v`, the tactic `clear_value x` replaces it
with a hypothesis `x : T`, or throws an error if the goal does not
depend on the value `v`. The syntax `clear_value x with h` creates a
hypothesis `h : x = v` before clearing the value of `x`. Furthermore,
`clear_value *` clears all values that can be cleared, or throws an
error if none can be cleared.
This PR adds `seal` commands at `grind_ite.lean` to workaround expensive
definitionally equality tests in the canonicalizer. The new module
system will automatically hide definitions such as `HashMap.insert` and
`TreeMap.insert` which are being unfolded by the canonicalizer in this
test.
This PR also adds a `profileItM` for tracking the time spent in the
`grind` canonicalizer.
This PR implements non-chronological backtracking for the `grind`
tactic. This feature ensures that `grind` does not need to process
irrelevant branches after performing a case-split that is not relevant.
It is not just about performance, but also the size of the final proof
term. The new test demonstrates this feature in practice.
```lean
-- In the following test, the first 8 case-splits are irrelevant,
-- and non-choronological backtracking is used to avoid searching
-- (2^8 - 1) irrelevant branches
/--
trace:
[grind.split] p8 ∨ q8, generation: 0
[grind.split] p7 ∨ q7, generation: 0
[grind.split] p6 ∨ q6, generation: 0
[grind.split] p5 ∨ q5, generation: 0
[grind.split] p4 ∨ q4, generation: 0
[grind.split] p3 ∨ q3, generation: 0
[grind.split] p2 ∨ q2, generation: 0
[grind.split] p1 ∨ q1, generation: 0
[grind.split] ¬p ∨ ¬q, generation: 0
-/
#guard_msgs (trace) in
set_option trace.grind.split true in
theorem ex
: p ∨ q →
¬ p ∨ q →
p ∨ ¬ q →
¬ p ∨ ¬ q →
p1 ∨ q1 →
p2 ∨ q2 →
p3 ∨ q3 →
p4 ∨ q4 →
p5 ∨ q5 →
p6 ∨ q6 →
p7 ∨ q7 →
p8 ∨ q8 →
False := by
grind (splits := 10)
```
This PR fixes `split` in the presence of metavariables in the target.
The fix consists of replacing an internal use of `apply` for
instantiating match splitters by a new, simpler variant `applyN`. This
new `applyN` is not prone to #8436, which is the ultimate cause for
`split` failing on targets containing metavariables.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR adds the attribute `[grind?]`. It is like `[grind]` but displays
inferred E-matching patterns. It is a more convinient than writing.
Thanks @kim-em for suggesting this feature.
```lean
set_option trace.grind.ematch.pattern true
```
This PR also improves some tests, and adds helper function
`ENode.isRoot`.
This PR unifies various ways of naming auxiliary declarations in a
conflict-free way and ensures the method is compatible with diverging
branches of elaboration such as parallelism or Aesop-like
backtracking+replaying search.
This PR ensures that using `mapError` to expand an error message uses
`addMessageContext` to include the current context, so that expressions
are rendered correctly. Also adds a `preprendError` variant with a more
convenient argument order for the common cases of
prepending-and-indenting.
This PR improves the functional cases principles, by making a more
educated guess which function parameters should be targets and which
should remain parameters (or be dropped). This simplifies the
principles, and increases the chance that `fun_cases` can unfold the
function call.
Fixes#8296 (at least for the common cases, I hope.)
This PR fixes a type error at `instantiateTheorem` function used in
`grind`. It was failing to instantiate theorems such as
```lean
theorem getElem_reverse {xs : Array α} {i : Nat} (hi : i < xs.reverse.size)
: (xs.reverse)[i] = xs[xs.size - 1 - i]'(by simp at hi; omega)
```
in examples such as
```lean
example (xs : Array Nat) (w : xs.reverse = xs) (j : Nat) (hj : 0 ≤ j) (hj' : j < xs.size / 2)
: xs[j] = xs[xs.size - 1 - j]
```
generating the issue
```lean
[issue] type error constructing proof for Array.getElem_reverse
when assigning metavariable ?hi with
‹j < xs.toList.length›
has type
j < xs.toList.length : Prop
but is expected to have type
j < xs.reverse.size : Prop
```
This PR fixes the transparency mode for ground patterns. This is
important for implicit instances. Here is a mwe for an issue detected
while testing `grind` in Mathlib.
```lean
example (a : Nat) : max a a = a := by
grind
instance : Max Nat where
max := Nat.max
example (a : Nat) : max a a = a := by
grind -- Should work
```
This PR adds basic support for eta-reduction to `grind`.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
This PR fixes a bug in the `cases` tacic introduced in #3188 that arises
when cases (not induction) is used with a non-atomic expression in using
and the argument indexing gets confused.
This fixes#8360.
This PR tries harder to clean internals of the argument packing of n-ary
functions from the functional induction theorem, in particular the
unfolding variant
This PR adjusts the experimental module system to not export the bodies
of `def`s unless opted out by the new attribute `@[expose]` on the `def`
or on a surrounding `section`.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This PR splits `Lean.Grind.CommRing` into 4 typeclasses, for semirings
and noncommutative rings. This does not yet change the behaviour of
`grind`, which expects to find all 4 typeclasses. Later we will make
some generalizations.
This PR stops `dsimp` from visiting proof terms, which should make
`simp` and `dsimp` more efficient.
In this attempt I have `dsimp` leave the proofs in place as-is, instead
of simplifying the proof type.
Closes#6960
This PR improves support for structure extensionality in `grind`. It now
uses eta expansion for structures instead of the extensionality theorems
generated by `[ext]`. Examples:
```lean
opaque f (a : Nat) : Nat × Bool
attribute [grind ext] Prod Subtype
example (a b : Nat) : (f a).1 = (f b).1 → (f a).2 = (f b).2 → f a = f b := by
grind
def g (a : Nat) : { x : Nat // x > 1 } :=
⟨a + 2, by grind⟩
example (a b : Nat) : (g a).1 = (g b).1 → g a = g b := by
grind
@[grind ext] structure S where
x : Nat
y : Int
example (x y : S) : x.1 = y.1 → x.2 = y.2 → x = y := by
grind
```
This PR makes `fun_induction` and `fun_cases` (try to) unfold the
function application of interest in the goal. The old behavior can be
enabled with `set_option tactic.fun_induction.unfolding false`. For
`fun_cases` this does not work yet when the function’s result type
depends on one of the arguments, see issue #8296.
