fix: use eta reduction at DiscrTree

@kha @dselsam

Suppose we are trying to retrieve the global instances for
`(Monad (StateM Nat))`.
During retrieval, we reducde `StateM Nat` into `fun x => StateT Nat Id x`
However, the `DiscrTree` contains an entry for `Monad (StateT * *)`.
Thus, we fail to retrieve any instance.
I fixed the particular issue by using eta reduction.
Not sure we will encounter other definitional-equality related problems .

src/Init/Lean/Meta/DiscrTree.lean

@@ -141,9 +141,16 @@ private partial def pushArgsAux (infos : Array ParamInfo) : Nat → Expr → Arr
     (pushArgsAux (i-1) f (todo.push a))
 | _, _, todo => pure todo
 
+private partial def whnfEta : Expr → MetaM Expr
+| e => do
+  e ← whnf e;
+  match e.etaExpandedStrict? with
+  | some e => whnfEta e
+  | none   => pure e
+
 private def pushArgs (todo : Array Expr) (e : Expr) : MetaM (Key × Array Expr) :=
-do e ← whnf e;
-   let fn    := e.getAppFn;
+do e ← whnfEta e;
+   let fn := e.getAppFn;
    let push (k : Key) (nargs : Nat) : MetaM (Key × Array Expr) := do {
      info ← getFunInfoNArgs fn nargs;
      todo ← pushArgsAux info.paramInfo (nargs-1) e todo;
@@ -238,7 +245,7 @@ Format.group r
 instance DiscrTree.hasFormat {α} [HasFormat α] : HasFormat (DiscrTree α) := ⟨format⟩
 
 private def getKeyArgs (e : Expr) (isMatch? : Bool) : MetaM (Key × Array Expr) :=
-do e ← whnf e;
+do e ← whnfEta e;
    match e.getAppFn with
    | Expr.lit v _       => pure (Key.lit v, #[])
    | Expr.const c _ _   => let nargs := e.getAppNumArgs; pure (Key.const c nargs, e.getAppRevArgs)

tests/lean/run/meta2.lean

@@ -300,6 +300,23 @@ do u ← getLevel σ;
    check r;
    pure r
 
+def mkMonad (m : Expr) : MetaM Expr :=
+do u ← mkFreshLevelMVar;
+   v ← mkFreshLevelMVar;
+   let arrow := mkArrow (mkSort (mkLevelSucc u)) (mkSort (mkLevelSucc v));
+   mType ← inferType m;
+   mType ← whnf mType;
+   print arrow;
+   print mType;
+   condM (isDefEq arrow mType)
+     (do u ← instantiateLevelMVars u;
+         v ← instantiateLevelMVars v;
+         let r := mkApp (mkConst `Monad [u, v]) m;
+         print r;
+         check r;
+         pure r)
+     (throw $ Exception.other "failed to create Monad application")
+
 def mkMonadState (σ m : Expr) : MetaM Expr :=
 do u ← getLevel σ;
    (some u) ← pure u.dec | throw $ Exception.other "failed to create MonadState application";
@@ -320,10 +337,31 @@ do u ← getLevel σ;
 
 def tst14 : MetaM Unit :=
 do print "----- tst14 -----";
-   decEqNat ← mkDecEq nat;
-   c ← synthInstance decEqNat;
    stateM ← mkStateM nat;
    print stateM;
+   monad ← mkMonad stateM;
+   globalInsts ← getGlobalInstances;
+   insts ← globalInsts.getUnify monad;
+   print insts;
+   pure ()
+
+#eval run [`Init.Control.State] tst14
+
+#exit
+
+def tst15 : MetaM Unit :=
+do print "----- tst15 -----";
+   stateM ← mkStateM nat;
+   print stateM;
+   monad ← mkMonad stateM;
+   print monad;
+   c ← synthInstance monad;
+   pure ()
+
+
+#exit
+   decEqNat ← mkDecEq nat;
+   c ← synthInstance decEqNat;
    monadState ← mkMonadState nat stateM;
    print monadState;
    c ← synthInstance monadState;