feat: structural isDefEq for Sym (#11819)

This PR adds some basic infrastructure for a structural (and cheaper)
`isDefEq` predicate for pattern matching and unification in `Sym`.

src/Lean/Meta/Sym.lean

@@ -14,6 +14,8 @@ public import Lean.Meta.Sym.LooseBVarsS
 public import Lean.Meta.Sym.InstantiateS
 public import Lean.Meta.Sym.IsClass
 public import Lean.Meta.Sym.Intro
+public import Lean.Meta.Sym.InstantiateMVarsS
+public import Lean.Meta.Sym.ProofInstInfo
 public import Lean.Meta.Sym.Pattern
 
 /-!

src/Lean/Meta/Sym/InstantiateMVarsS.lean

@@ -0,0 +1,21 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+module
+prelude
+public import Lean.Meta.Sym.SymM
+namespace Lean.Meta.Sym
+
+/--
+Instantiates metavariables occurring in `e`, and returns a maximally shared term.
+-/
+def instantiateMVarsS (e : Expr) : SymM Expr := do
+  if e.hasMVar then
+    -- **Note**: If this is a bottleneck, write a new function that combines both steps.
+    Grind.shareCommon (← instantiateMVars e)
+  else
+    return e
+
+end Lean.Meta.Sym

src/Lean/Meta/Sym/Pattern.lean

@@ -9,6 +9,8 @@ public import Lean.Meta.Sym.SymM
 import Lean.Util.FoldConsts
 import Lean.Meta.Sym.InstantiateS
 import Lean.Meta.Sym.IsClass
+import Lean.Meta.Sym.ProofInstInfo
+import Lean.Meta.Tactic.Grind.AlphaShareBuilder
 namespace Lean.Meta.Sym
 open Grind
 
@@ -34,67 +36,16 @@ framework (`Sym`). The design prioritizes performance by using a two-phase appro
 - `instantiateRevS` ensures maximal sharing of result expressions
 -/
 
-def preprocessType (type : Expr) : MetaM Expr := do
-  let type ← unfoldReducible type
-  let type ← Core.betaReduce type
-  zetaReduce type
-
 /--
-Information about a single argument position in a function's type signature.
-
-This is used during pattern matching to identify arguments that can be skipped
-or handled specially (e.g., instance arguments can be synthesized, proof arguments
-can be inferred).
--/
-public structure PatternArgInfo where
-  /-- `true` if this argument is a proof (its type is a `Prop`). -/
-  isProof    : Bool
-  /-- `true` if this argument is a type class instance. -/
-  isInstance : Bool
-
-/--
-Information about a function symbol occurring in a pattern.
-
-Stores which argument positions are proofs or instances, enabling optimizations
-during pattern matching such as skipping proof arguments or deferring instance synthesis.
--/
-public structure FunPatternInfo where
-  /-- Information about each argument position. -/
-  argsInfo : Array PatternArgInfo
-
-/--
-Analyzes the type signature of `declName` and returns information about which arguments
-are proofs or instances. Returns `none` if no arguments are proofs or instances.
--/
-def mkFunPatternInfo? (declName : Name) : MetaM (Option FunPatternInfo) := do
-  let info ← getConstInfo declName
-  let type ← preprocessType info.type
-  forallTelescopeReducing type fun xs _ => do
-    let env ← getEnv
-    let mut argsInfo := #[]
-    let mut found := false
-    for x in xs do
-      let type ← inferType x
-      let isInstance := isClass? env type |>.isSome
-      let isProof ← isProp type
-      if isInstance || isProof then
-        found := true
-      argsInfo := argsInfo.push { isInstance, isProof }
-    if found then
-      return some { argsInfo }
-    else
-      return none
-
-/--
-Collects `FunPatternInfo` for all function symbols occurring in `pattern`.
+Collects `ProofInstInfo` for all function symbols occurring in `pattern`.
 
 Only includes functions that have at least one proof or instance argument.
 -/
-def mkFunInfosFor (pattern : Expr) : MetaM (AssocList Name FunPatternInfo) := do
+def mkProofInstInfoMapFor (pattern : Expr) : MetaM (AssocList Name ProofInstInfo) := do
   let cs := pattern.getUsedConstants
   let mut fnInfos := {}
   for declName in cs do
-    if let some info ← mkFunPatternInfo? declName then
+    if let some info ← mkProofInstInfo? declName then
       fnInfos := fnInfos.insertNew declName info
   return fnInfos
 
@@ -102,7 +53,7 @@ public structure Pattern where
   levelParams  : List Name
   varTypes     : Array Expr
   pattern      : Expr
-  fnInfos      : AssocList Name FunPatternInfo
+  fnInfos      : AssocList Name ProofInstInfo
   deriving Inhabited
 
 def uvarPrefix : Name := `_uvar
@@ -124,7 +75,7 @@ public def mkPatternFromTheorem (declName : Name) : MetaM Pattern := do
     | .forallE _ d b _ => go b (varTypes.push d)
     | _ =>
       let pattern := type
-      let fnInfos ← mkFunInfosFor pattern
+      let fnInfos ← mkProofInstInfoMapFor pattern
       return { levelParams, varTypes, pattern, fnInfos }
   go type #[]
 
@@ -248,7 +199,7 @@ where
     let numArgs := p.getAppNumArgs
     processAppWithInfo p e (numArgs - 1) info
 
-  processAppWithInfo (p : Expr) (e : Expr) (i : Nat) (info : FunPatternInfo) : UnifyM Bool := do
+  processAppWithInfo (p : Expr) (e : Expr) (i : Nat) (info : ProofInstInfo) : UnifyM Bool := do
     let .app fp ap := p | process p e
     let .app fe ae := e | return false
     unless (← processAppWithInfo fp fe (i - 1) info) do return false
@@ -283,6 +234,86 @@ where
     let .sort v := e | return false
     processLevel u v
 
+def isLevelDefEqS (u : Level) (v : Level) : MetaM Bool := do
+  match u, v with
+  | .param u, .param v => return u == v
+  | .zero, .zero => return true
+  | .succ u, .succ v => isLevelDefEqS u v
+  | .zero, .succ _ => return false
+  | .succ _, .zero => return false
+  | .zero, .max v₁ v₂ => isLevelDefEqS .zero v₁ <&&> isLevelDefEqS .zero v₂
+  | .max u₁ u₂, .zero => isLevelDefEqS u₁ .zero <&&> isLevelDefEqS u₂ .zero
+  | .zero, .imax _ v => isLevelDefEqS .zero v
+  | .imax _ u, .zero => isLevelDefEqS u .zero
+  | .max u₁ u₂, .max v₁ v₂ => isLevelDefEqS u₁ v₁ <&&> isLevelDefEqS u₂ v₂
+  | .imax u₁ u₂, .imax v₁ v₂ => isLevelDefEqS u₁ v₁ <&&> isLevelDefEqS u₂ v₂
+  | .mvar mvarId, v => assignLevelMVar mvarId v; return true
+  | u, .mvar mvarId => assignLevelMVar mvarId u; return true
+  | _, _ => return false
+
+structure DefEqM.Context where
+  unify     : Bool := true
+  zetaDelta : Bool := true
+  /--
+  If `unit
+  -/
+  mvarsNew  : Array MVarId := #[]
+
+abbrev DefEqM := ReaderT DefEqM.Context SymM
+
+/--
+Structural definitional equality. It is much cheaper than `isDefEq`.
+-/
+@[extern "lean_sym_def_eq"] -- Forward definition
+opaque isDefEqS : Expr → Expr → DefEqM Bool
+
+/--
+Structural definitional equality for `forall` and `lambda` binders.
+-/
+def isDefEqBindingS (a b : Expr) : DefEqM Bool := do
+  let lctx ← getLCtx
+  let localInsts ← getLocalInstances
+  go lctx localInsts #[] a b #[]
+where
+  checkDomains (fvars : Array Expr) (ds₂ : Array Expr) : DefEqM Bool := do
+    for fvar in fvars, d in ds₂ do
+      let fvarType ← fvar.fvarId!.getType
+      unless (← isDefEqS fvarType d) do return false
+    return true
+
+  go (lctx : LocalContext) (localInsts : LocalInstances) (fvars : Array Expr) (e₁ e₂ : Expr) (ds₂ : Array Expr) : DefEqM Bool := do
+    match e₁, e₂ with
+    | .forallE n d₁ b₁ _, .forallE _ d₂ b₂ _
+    | .lam     n d₁ b₁ _, .lam     _ d₂ b₂ _ =>
+      let d₁     ← instantiateRevS d₁ fvars
+      let d₂     ← instantiateRevS d₂ fvars
+      let fvarId ← mkFreshFVarId
+      let fvar   ← mkFVarS fvarId
+      let lctx   := lctx.mkLocalDecl fvarId n d₁
+      let localInsts := if let some className := isClass? (← getEnv) d₁ then
+        localInsts.push { className, fvar }
+      else
+        localInsts
+      go lctx localInsts (fvars.push fvar) b₁ b₂ (ds₂.push d₂)
+    | _, _ => withLCtx lctx localInsts do
+      unless (← checkDomains fvars ds₂) do return false
+      isDefEqS (← instantiateRevS e₁ fvars) (← instantiateRevS e₂ fvars)
+
+/--
+`isDefEqS` implementation.
+-/
+@[export lean_sym_def_eq]
+def isDefEqSImpl (t : Expr) (s : Expr) : DefEqM Bool := do
+  if isSameExpr t s then return true
+  match t, s with
+  | .lit  l₁,      .lit l₂     => return l₁ == l₂
+  | .sort u,       .sort v     => isLevelDefEqS u v
+  | .lam ..,       .lam ..     => isDefEqBindingS t s
+  | .forallE ..,   .forallE .. => isDefEqBindingS t s
+  | _, _ =>
+    -- **TODO**
+    return false
+
 def noPending : UnifyM Bool := do
   let s ← get
   return s.ePending.isEmpty && s.uPending.isEmpty && s.iPending.isEmpty

src/Lean/Meta/Sym/ProofInstInfo.lean

@@ -0,0 +1,55 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+module
+prelude
+public import Lean.Meta.Sym.SymM
+import Lean.Meta.Sym.IsClass
+namespace Lean.Meta.Sym
+
+/--
+Preprocesses types that used for pattern matching and unification.
+-/
+public def preprocessType (type : Expr) : MetaM Expr := do
+  let type ← Grind.unfoldReducible type
+  let type ← Core.betaReduce type
+  zetaReduce type
+
+/--
+Analyzes the type signature of `declName` and returns information about which arguments
+are proofs or instances. Returns `none` if no arguments are proofs or instances.
+-/
+public def mkProofInstInfo? (declName : Name) : MetaM (Option ProofInstInfo) := do
+  let info ← getConstInfo declName
+  let type ← preprocessType info.type
+  forallTelescopeReducing type fun xs _ => do
+    let env ← getEnv
+    let mut argsInfo := #[]
+    let mut found := false
+    for x in xs do
+      let type ← inferType x
+      let isInstance := isClass? env type |>.isSome
+      let isProof ← isProp type
+      if isInstance || isProof then
+        found := true
+      argsInfo := argsInfo.push { isInstance, isProof }
+    if found then
+      return some { argsInfo }
+    else
+      return none
+
+/--
+Returns information about the type signature of `declName`. It contains information about which arguments
+are proofs or instances. Returns `none` if no arguments are proofs or instances.
+-/
+public def getProofInstInfo? (declName : Name) : SymM (Option ProofInstInfo) := do
+  if let some r := (← get).proofInstInfo.find? declName then
+    return r
+  else
+    let r ← mkProofInstInfo? declName
+    modify fun s => { s with proofInstInfo := s.proofInstInfo.insert declName r }
+    return r
+
+end Lean.Meta.Sym

src/Lean/Meta/Sym/SymM.lean

@@ -11,8 +11,33 @@ public section
 namespace Lean.Meta.Sym
 export Grind (ExprPtr Goal)
 
+/--
+Information about a single argument position in a function's type signature.
+
+This is used during pattern matching and structural definitional equality tests
+to identify arguments that can be skipped or handled specially
+(e.g., instance arguments can be synthesized, proof arguments can be inferred).
+-/
+public structure ProofInstArgInfo where
+  /-- `true` if this argument is a proof (its type is a `Prop`). -/
+  isProof    : Bool
+  /-- `true` if this argument is a type class instance. -/
+  isInstance : Bool
+  deriving Inhabited
+
+/--
+Information about a function symbol. It stores which argument positions are proofs or instances,
+enabling optimizations during pattern matching and structural definitional equality tests
+such as skipping proof arguments or deferring instance synthesis.
+-/
+public structure ProofInstInfo where
+  /-- Information about each argument position. -/
+  argsInfo : Array ProofInstArgInfo
+  deriving Inhabited
+
 structure State where
   maxFVar : PHashMap ExprPtr (Option FVarId) := {}
+  proofInstInfo : PHashMap Name (Option ProofInstInfo) := {}
 
 abbrev SymM := ReaderT Grind.Params StateRefT State Grind.GrindM