diff --git a/src/Init/Data/Array/BinSearch.lean b/src/Init/Data/Array/BinSearch.lean
index 530c5938b5..5656bcaab8 100644
--- a/src/Init/Data/Array/BinSearch.lean
+++ b/src/Init/Data/Array/BinSearch.lean
@@ -29,37 +29,38 @@ binSearchAux lt id as k lo hi
 @[inline] def binSearchContains {α : Type} [Inhabited α] (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Bool :=
 binSearchAux lt Option.isSome as k lo hi
 
-@[specialize] partial def binInsertAuxAux {α : Type u} [Inhabited α]
+@[specialize] private partial def binInsertAux {α : Type u} {m : Type u → Type v} [Monad m] [Inhabited α]
     (lt : α → α → Bool)
-    (merge : α → α)
-    (add : Unit → α)
+    (merge : α → m α)
+    (add : Unit → m α)
     (as : Array α)
-    (k : α) : Nat → Nat → Array α
+    (k : α) : Nat → Nat → m (Array α)
 | lo, hi =>
   -- as[lo] < k < as[hi]
-  let m := (lo + hi)/2;
-  if lt (as.get! m) k then
-    if m == lo then as.insertAt (lo+1) (add ())
-    else binInsertAuxAux m hi
-  else if lt k (as.get! m) then
-    binInsertAuxAux lo m
-  else
-    as.modify m $ fun a => merge a
+  let mid    := (lo + hi)/2;
+  let midVal := as.get! mid;
+  if lt midVal k then
+    if mid == lo then do v ← add (); pure $ as.insertAt (lo+1) v
+    else binInsertAux mid hi
+  else if lt k midVal then
+    binInsertAux lo mid
+  else do
+    as.modifyM mid $ fun v => merge v
 
-@[specialize] partial def binInsertAux {α : Type u} [Inhabited α]
+@[specialize] partial def binInsertM {α : Type u} {m : Type u → Type v} [Monad m] [Inhabited α]
     (lt : α → α → Bool)
-    (merge : α → α)
-    (add : Unit → α)
+    (merge : α → m α)
+    (add : Unit → m α)
     (as : Array α)
-    (k : α) : Array α :=
-if as.isEmpty then as.push (add ())
-else if lt k (as.get! 0) then as.insertAt 0 (add ())
-else if !lt (as.get! 0) k then as.modify 0 $ fun a => merge a
-else if lt as.back k then as.push (add ())
-else if !lt k as.back then as.modify (as.size - 1) $ fun a => merge a
-else binInsertAuxAux lt merge add as k 0 (as.size - 1)
+    (k : α) : m (Array α) :=
+if as.isEmpty then do v ← add (); pure $ as.push v
+else if lt k (as.get! 0) then do v ← add (); pure $ as.insertAt 0 v
+else if !lt (as.get! 0) k then as.modifyM 0 $ merge
+else if lt as.back k then do v ← add (); pure $ as.push v
+else if !lt k as.back then as.modifyM (as.size - 1) $ merge
+else binInsertAux lt merge add as k 0 (as.size - 1)
 
 @[inline] def binInsert {α : Type u} [Inhabited α] (lt : α → α → Bool) (as : Array α) (k : α) : Array α :=
-binInsertAux lt (fun _ => k) (fun _ => k) as k
+Id.run $ binInsertM lt (fun _ => k) (fun _ => k) as k
 
 end Array
diff --git a/tests/playground/DiscrTree.lean b/tests/playground/DiscrTree.lean
index 08a870d610..c8d22fbd4d 100644
--- a/tests/playground/DiscrTree.lean
+++ b/tests/playground/DiscrTree.lean
@@ -79,8 +79,8 @@ partial def insertAux {α} [HasBeq α] (v : α) : Array Term → Trie α → Tri
     let todo := todo.pop;
     let todo := appendTodo todo t.args;
     let k    := t.key;
-    node vs $
-      cs.binInsertAux
+    node vs $ Id.run $
+      cs.binInsertM
         (fun a b => a.1 < b.1)
         (fun ⟨_, s⟩ => (k, insertAux todo s)) -- merge with existing
         (fun _ => (k, createNodes v todo))  -- add new node