fix: grind preprocessor (#10177)

This PR fixes a bug in the `grind` preprocessor exposed by #10160.

Closes #10160

src/Lean/Meta/Tactic/Grind/Arith/Linear/DenoteExpr.lean

@@ -5,13 +5,13 @@ Authors: Leonardo de Moura
 -/
 module
 prelude
-public import Lean.Meta.Tactic.Grind.ProveEq
-public import Lean.Meta.Tactic.Grind.Arith.CommRing.DenoteExpr
+public import Lean.Meta.Tactic.Grind.Types
 public import Lean.Meta.Tactic.Grind.Arith.Linear.Util
-public import Lean.Meta.Tactic.Grind.Arith.Linear.Var
+import Lean.Meta.Tactic.Grind.Simp
+import Lean.Meta.Tactic.Grind.Arith.CommRing.DenoteExpr
+import Lean.Meta.Tactic.Grind.Arith.Linear.Var
 import Lean.Meta.Tactic.Grind.Arith.CommRing.Functions
 public section
-
 namespace Lean.Meta.Grind.Arith.Linear
 /-!
 Helper functions for converting reified terms back into their denotations.

src/Lean/Meta/Tactic/Grind/Arith/Linear/Proof.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 module
 prelude
 public import Lean.Meta.Tactic.Grind.Arith.Linear.Util
+import Lean.Data.RArray
 import Lean.Meta.Tactic.Grind.Arith.Util
 import Lean.Meta.Tactic.Grind.Arith.Linear.ToExpr
 import Lean.Meta.Tactic.Grind.Arith.Linear.DenoteExpr

src/Lean/Meta/Tactic/Grind/CasesMatch.lean

@@ -4,15 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 module
-
 prelude
 public import Lean.Meta.Tactic.Util
-public import Lean.Meta.Tactic.Cases
-public import Lean.Meta.Match.MatcherApp
-public import Lean.Meta.Tactic.Grind.MatchCond
-
+import Lean.Meta.Tactic.Grind.Types
+import Lean.Meta.Tactic.Cases
+import Lean.Meta.Match.MatcherApp
+import Lean.Meta.Tactic.Grind.MatchCond
+import Lean.Meta.Tactic.Grind.Simp
 public section
-
 namespace Lean.Meta.Grind
 
 /-- Returns `true` if `e` is of the form `∀ ..., _ = _ ... -> False` -/

src/Lean/Meta/Tactic/Grind/Ctor.lean

@@ -7,10 +7,8 @@ module
 
 prelude
 public import Lean.Meta.Tactic.Grind.Types
-public import Lean.Meta.Tactic.Grind.ProveEq
-
+import Lean.Meta.Tactic.Grind.Simp
 public section
-
 namespace Lean.Meta.Grind
 
 private partial def propagateInjEqs (eqs : Expr) (proof : Expr) : GoalM Unit := do

src/Lean/Meta/Tactic/Grind/EMatch.lean

@@ -7,6 +7,8 @@ module
 prelude
 public import Lean.Meta.Tactic.Grind.Types
 import Lean.Meta.Tactic.Grind.Core
+import Lean.Meta.Tactic.Grind.MatchDiscrOnly
+import Lean.Meta.Tactic.Grind.ProveEq
 import Lean.Meta.Tactic.Grind.SynthInstance
 public section
 namespace Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/ForallProp.lean

@@ -4,17 +4,17 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 module
-
 prelude
-public import Init.Grind.Lemmas
 public import Lean.Meta.Tactic.Grind.Types
-public import Lean.Meta.Tactic.Grind.Internalize
-public import Lean.Meta.Tactic.Grind.Simp
-public import Lean.Meta.Tactic.Grind.EqResolution
+public import Init.Grind.Propagator
+import Init.Grind.Lemmas
+import Init.Grind.Norm
+import Lean.Meta.Tactic.Grind.Propagate
+import Lean.Meta.Tactic.Grind.Internalize
+import Lean.Meta.Tactic.Grind.Simp
+import Lean.Meta.Tactic.Grind.EqResolution
 import Lean.Meta.Tactic.Grind.SynthInstance
-
 public section
-
 namespace Lean.Meta.Grind
 /--
 If `parent` is a projection-application `proj_i c`,

src/Lean/Meta/Tactic/Grind/Internalize.lean

@@ -4,22 +4,21 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 module
-
 prelude
 public import Init.Grind.Util
 public import Init.Grind.Lemmas
-public import Lean.Meta.LitValues
-public import Lean.Meta.Match.MatcherInfo
-public import Lean.Meta.Match.MatchEqsExt
-public import Lean.Meta.Match.MatchEqs
-public import Lean.Util.CollectLevelParams
 public import Lean.Meta.Tactic.Grind.Types
-public import Lean.Meta.Tactic.Grind.Util
-public import Lean.Meta.Tactic.Grind.Beta
-public import Lean.Meta.Tactic.Grind.MatchCond
-
+import Lean.Meta.LitValues
+import Lean.Meta.Match.MatcherInfo
+import Lean.Meta.Match.MatchEqsExt
+import Lean.Meta.Match.MatchEqs
+import Lean.Util.CollectLevelParams
+import Lean.Meta.Tactic.Grind.Util
+import Lean.Meta.Tactic.Grind.Beta
+import Lean.Meta.Tactic.Grind.MatchCond
+import Lean.Meta.Tactic.Grind.Simp
+import Lean.Meta.Tactic.Grind.MarkNestedSubsingletons
 public section
-
 namespace Lean.Meta.Grind
 
 @[extern "lean_grind_ac_internalize"] -- forward definition

src/Lean/Meta/Tactic/Grind/Intro.lean

@@ -4,20 +4,18 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 module
-
 prelude
 public import Init.Grind.Lemmas
-public import Lean.Meta.Tactic.Assert
-public import Lean.Meta.Tactic.Grind.Simp
 public import Lean.Meta.Tactic.Grind.Types
-public import Lean.Meta.Tactic.Grind.Cases
-public import Lean.Meta.Tactic.Grind.CasesMatch
-public import Lean.Meta.Tactic.Grind.Injection
-public import Lean.Meta.Tactic.Grind.Core
 public import Lean.Meta.Tactic.Grind.SearchM
-
+import Lean.Meta.Tactic.Assert
+import Lean.Meta.Tactic.Apply
+import Lean.Meta.Tactic.Grind.Simp
+import Lean.Meta.Tactic.Grind.Cases
+import Lean.Meta.Tactic.Grind.CasesMatch
+import Lean.Meta.Tactic.Grind.Injection
+import Lean.Meta.Tactic.Grind.Core
 public section
-
 namespace Lean.Meta.Grind
 
 private inductive IntroResult where

src/Lean/Meta/Tactic/Grind/Main.lean

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 module
-
 prelude
-public import Init.Grind.Lemmas
 public import Lean.Meta.Tactic.Util
-public import Lean.Meta.Tactic.ExposeNames
-public import Lean.Meta.Tactic.Simp.Diagnostics
-public import Lean.Meta.Tactic.Grind.Split  -- TODO: not minimal yet
+public import Lean.Meta.Tactic.Grind.Types
+import Init.Grind.Lemmas
+import Lean.Meta.Tactic.ExposeNames
+import Lean.Meta.Tactic.Simp.Diagnostics
+import Lean.Meta.Tactic.Grind.Split
 import Lean.Meta.Tactic.Grind.RevertAll
 import Lean.Meta.Tactic.Grind.PropagatorAttr
 import Lean.Meta.Tactic.Grind.Proj
@@ -24,9 +24,8 @@ import Lean.Meta.Tactic.Grind.SimpUtil
 import Lean.Meta.Tactic.Grind.Cases
 import Lean.Meta.Tactic.Grind.LawfulEqCmp
 import Lean.Meta.Tactic.Grind.ReflCmp
-
+import Lean.Meta.Tactic.Grind.PP
 public section
-
 namespace Lean.Meta.Grind
 
 structure Params where

src/Lean/Meta/Tactic/Grind/ProveEq.lean

@@ -7,18 +7,11 @@ module
 
 prelude
 public import Lean.Meta.Tactic.Grind.Types
-public import Lean.Meta.Tactic.Grind.Simp
+import Lean.Meta.Tactic.Grind.Simp
 
 public section
 
 namespace Lean.Meta.Grind
-/--
-A lighter version of `preprocess` which produces a definitionally equal term,
-but ensures assumptions made by `grind` are satisfied.
--/
-def preprocessLight (e : Expr) : GoalM Expr := do
-  shareCommon (← canon (← normalizeLevels (← foldProjs (← eraseIrrelevantMData (← markNestedSubsingletons (← unfoldReducible e))))))
-
 /--
 If `e` has not been internalized yet, instantiate metavariables, unfold reducible, canonicalize,
 and internalize the result.

src/Lean/Meta/Tactic/Grind/Simp.lean

@@ -6,12 +6,12 @@ Authors: Leonardo de Moura
 module
 prelude
 public import Init.Grind.Lemmas
-public import Lean.Meta.Tactic.Assert
 public import Lean.Meta.Tactic.Simp.Main
-public import Lean.Meta.Tactic.Grind.Util
 public import Lean.Meta.Tactic.Grind.Types
-public import Lean.Meta.Tactic.Grind.MatchDiscrOnly
-public import Lean.Meta.Tactic.Grind.MarkNestedSubsingletons
+import Lean.Meta.Tactic.Assert
+import Lean.Meta.Tactic.Grind.Util
+import Lean.Meta.Tactic.Grind.MatchDiscrOnly
+import Lean.Meta.Tactic.Grind.MarkNestedSubsingletons
 public section
 namespace Lean.Meta.Grind
 
@@ -50,6 +50,9 @@ def preprocess (e : Expr) : GoalM Simp.Result := do
   let e ← instantiateMVars e
   let r ← simpCore e
   let e' := r.expr
+  -- Remark: `simpCore` unfolds reducible constants, but it does not consistently visit all possible subterms.
+  -- So, we must use the following `unfoldReducible` step. It is non-op in most cases
+  let e' ← unfoldReducible e'
   let e' ← abstractNestedProofs e'
   let e' ← markNestedSubsingletons e'
   let e' ← eraseIrrelevantMData e'
@@ -83,4 +86,11 @@ def pushNewFact (proof : Expr) (generation : Nat := 0) : GoalM Unit := do
   trace[grind.debug.pushNewFact] "{prop}"
   pushNewFact' prop proof generation
 
+/--
+A lighter version of `preprocess` which produces a definitionally equal term,
+but ensures assumptions made by `grind` are satisfied.
+-/
+def preprocessLight (e : Expr) : GoalM Expr := do
+  shareCommon (← canon (← normalizeLevels (← foldProjs (← eraseIrrelevantMData (← markNestedSubsingletons (← unfoldReducible e))))))
+
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Solve.lean

@@ -4,16 +4,15 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 module
-
 prelude
-public import Lean.Meta.Tactic.Grind.Split
-public import Lean.Meta.Tactic.Grind.EMatch
-public import Lean.Meta.Tactic.Grind.Arith
-public import Lean.Meta.Tactic.Grind.Lookahead
+public import Lean.Meta.Tactic.Grind.Types
 public import Lean.Meta.Tactic.Grind.SearchM
-
+import Lean.Meta.Tactic.Grind.Split
+import Lean.Meta.Tactic.Grind.EMatch
+import Lean.Meta.Tactic.Grind.Arith
+import Lean.Meta.Tactic.Grind.Lookahead
+import Lean.Meta.Tactic.Grind.Intro
 public section
-
 namespace Lean.Meta.Grind
 def tryFallback : GoalM Bool := do
   (← getMethods).fallback

src/Lean/Meta/Tactic/Grind/Split.lean

@@ -4,16 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 module
-
 prelude
 public import Lean.Meta.Tactic.Grind.Types
-public import Lean.Meta.Tactic.Grind.Intro
-public import Lean.Meta.Tactic.Grind.Cases
-public import Lean.Meta.Tactic.Grind.CasesMatch
 public import Lean.Meta.Tactic.Grind.SearchM
-
+import Lean.Meta.Tactic.Grind.Intro
+import Lean.Meta.Tactic.Grind.Cases
+import Lean.Meta.Tactic.Grind.CasesMatch
+import Lean.Meta.Tactic.Grind.Internalize
 public section
-
 namespace Lean.Meta.Grind
 
 inductive SplitStatus where

tests/lean/run/grind_10160.lean

@@ -0,0 +1,47 @@
+structure PreInt where
+  minuend : Nat
+  subtrahend : Nat
+
+/-- Definition 4.1.1 -/
+instance PreInt.instSetoid : Setoid PreInt where
+  r a b := a.minuend + b.subtrahend = b.minuend + a.subtrahend
+  iseqv := {
+    refl := by grind
+    symm := by grind
+    trans := by grind
+  }
+
+abbrev MyInt := Quotient PreInt.instSetoid
+
+abbrev MyInt.formalDiff (a b : Nat) : MyInt := Quotient.mk PreInt.instSetoid ⟨ a, b ⟩
+
+theorem MyInt.eq (a b c d : Nat) : formalDiff a b = formalDiff c d ↔ a + d = c + b :=
+  ⟨ Quotient.exact, by intro h; exact Quotient.sound h ⟩
+
+instance MyInt.instOfNat {n : Nat} : OfNat MyInt n where
+  ofNat := formalDiff n 0
+
+instance MyInt.instNatCast : NatCast MyInt where
+  natCast n := formalDiff n 0
+
+theorem MyInt.natCast_eq (n : Nat) : (n : MyInt) = formalDiff n 0 := rfl
+
+theorem MyInt.natCast_inj (n m : Nat) :
+  (n : MyInt) = (m : MyInt) ↔ n = m := by
+  rw [natCast_eq, natCast_eq, eq]
+  grind
+
+example (n m : Nat) : (n : MyInt) = (m : MyInt) ↔ n = m := by
+  grind [MyInt.natCast_eq, MyInt.eq]
+
+@[grind]
+theorem MyInt.eq_0_of_cast_eq_0 (n : Nat) (h : (n : MyInt) = 0) : n = 0 := by
+  rw [show (0 : MyInt) = ((0 : Nat) : MyInt) by rfl] at h
+  rwa [natCast_inj] at h
+
+theorem MyInt.pos_iff_gt_0 {a : MyInt} : (∃ (n:Nat), n > 0 ∧ a = n) → a ≠ 0 := by
+  intro ⟨ w, hw ⟩ h
+  grind
+
+example {a : MyInt} : (∃ (n:Nat), n > 0 ∧ a = n) → a ≠ 0 := by
+  grind