diff --git a/testsuite/tests/typing-misc/deep.ml b/testsuite/tests/typing-misc/deep.ml
new file mode 100644
index 000000000000..1d1a02271952
--- /dev/null
+++ b/testsuite/tests/typing-misc/deep.ml
@@ -0,0 +1,88 @@
+(* TEST
+   * expect
+*)
+
+module M : sig
+  val x : bool * int
+end = struct
+  let x = false , "not an int"
+end
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   let x = false , "not an int"
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig val x : bool * string end
+       is not included in
+         sig val x : bool * int end
+       Values do not match:
+         val x : bool * string
+       is not included in
+         val x : bool * int
+|}]
+
+module T : sig
+  val f : int -> (float * string ref) list
+end = struct
+  let f x = x + List.length [0.0, ref true]
+end
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   let f x = x + List.length [0.0, ref true]
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig val f : int -> int end
+       is not included in
+         sig val f : int -> (float * string ref) list end
+       Values do not match:
+         val f : int -> int
+       is not included in
+         val f : int -> (float * string ref) list
+|}]
+
+(* Alpha-equivalence *)
+module T : sig
+  val f : ('a list * 'b list -> int)
+end = struct
+  let f : ('c list * 'd ref  -> int) = assert false
+end
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   let f : ('c list * 'd ref  -> int) = assert false
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig val f : 'c list * 'd ref -> int end
+       is not included in
+         sig val f : 'a list * 'b list -> int end
+       Values do not match:
+         val f : 'c list * 'd ref -> int
+       is not included in
+         val f : 'a list * 'b list -> int
+|}]
+
+module T : sig
+  type t = int * float
+end = struct
+  type t = bool * float
+end
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   type t = bool * float
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig type t = bool * float end
+       is not included in
+         sig type t = int * float end
+       Type declarations do not match:
+         type t = bool * float
+       is not included in
+         type t = int * float
+|}]
diff --git a/testsuite/tests/typing-modules/inclusion_errors.ml b/testsuite/tests/typing-modules/inclusion_errors.ml
index a20566f55915..f0c258d3fa1c 100644
--- a/testsuite/tests/typing-modules/inclusion_errors.ml
+++ b/testsuite/tests/typing-modules/inclusion_errors.ml
@@ -1053,6 +1053,70 @@ Error: Signature mismatch:
          type t = private [> `A of int ]
 |}];;
 
+module M : sig
+  type t = private [< `A | `B]
+end = struct
+  type t = private [`A | `B]
+end;;
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   type t = private [`A | `B]
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig type t = private [ `A | `B ] end
+       is not included in
+         sig type t = private [< `A | `B ] end
+       Type declarations do not match:
+         type t = private [ `A | `B ]
+       is not included in
+         type t = private [< `A | `B ]
+|}];;
+
+module M : sig
+  type t = [`A | `B]
+end = struct
+  type t = private [`A | `B]
+end;;
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   type t = private [`A | `B]
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig type t = private [ `A | `B ] end
+       is not included in
+         sig type t = [ `A | `B ] end
+       Type declarations do not match:
+         type t = private [ `A | `B ]
+       is not included in
+         type t = [ `A | `B ]
+       A private type would be revealed.
+|}];;
+
+module M : sig
+  type t = private [< `A | `B > `B]
+end = struct
+  type t = private [< `A | `B]
+end;;
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   type t = private [< `A | `B]
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig type t = private [< `A | `B ] end
+       is not included in
+         sig type t = private [< `A | `B > `B ] end
+       Type declarations do not match:
+         type t = private [< `A | `B ]
+       is not included in
+         type t = private [< `A | `B > `B ]
+|}];;
+
 module M : sig
   type t = private <a : int; ..>
 end = struct
diff --git a/testsuite/tests/typing-modules/pr10399.ml b/testsuite/tests/typing-modules/pr10399.ml
new file mode 100644
index 000000000000..0e376da8401f
--- /dev/null
+++ b/testsuite/tests/typing-modules/pr10399.ml
@@ -0,0 +1,44 @@
+(* TEST
+ * expect
+*)
+
+(* From jctis: <https://github.com/ocaml/ocaml/issues/10399> *)
+
+module PR10399 : sig
+  type t = < x : int >
+
+  class c : object method x : int method y : bool end
+
+  val o : t
+end = struct
+  type t = < x : int >
+
+  class c = object method x = 3 method y = true end
+
+  let o = new c
+end
+
+[%%expect{|
+Lines 7-13, characters 6-3:
+ 7 | ......struct
+ 8 |   type t = < x : int >
+ 9 |
+10 |   class c = object method x = 3 method y = true end
+11 |
+12 |   let o = new c
+13 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig
+           type t = < x : int >
+           class c : object method x : int method y : bool end
+           val o : c
+         end
+       is not included in
+         sig
+           type t = < x : int >
+           class c : object method x : int method y : bool end
+           val o : t
+         end
+       Values do not match: val o : c is not included in val o : t
+|}]
diff --git a/testsuite/tests/typing-unboxed/test.ml b/testsuite/tests/typing-unboxed/test.ml
index fb1ecb82b6f9..e57ed3b4e8c4 100644
--- a/testsuite/tests/typing-unboxed/test.ml
+++ b/testsuite/tests/typing-unboxed/test.ml
@@ -122,6 +122,28 @@ Error: Signature mismatch:
 |}]
 
 module Bad2 : sig
+  external f : int -> int = "f" "f_nat"
+end = struct
+  external f : (int [@untagged]) -> int = "f" "f_nat"
+end;;
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : (int [@untagged]) -> int = "f" "f_nat"
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : (int [@untagged]) -> int = "f" "f_nat" end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : (int [@untagged]) -> int = "f" "f_nat"
+       is not included in
+         external f : int -> int = "f" "f_nat"
+|}]
+
+module Bad3 : sig
   external f : int -> int = "a" "a_nat"
 end = struct
   external f : (int [@untagged]) -> int = "f" "f_nat"
@@ -143,7 +165,7 @@ Error: Signature mismatch:
          external f : int -> int = "a" "a_nat"
 |}]
 
-module Bad3 : sig
+module Bad4 : sig
   external f : float -> float = "f" "f_nat"
 end = struct
   external f : float -> (float [@unboxed]) = "f" "f_nat"
@@ -165,7 +187,29 @@ Error: Signature mismatch:
          external f : float -> float = "f" "f_nat"
 |}]
 
-module Bad4 : sig
+module Bad5 : sig
+  external f : float -> float = "f" "f_nat"
+end = struct
+  external f : (float [@unboxed]) -> float = "f" "f_nat"
+end;;
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : (float [@unboxed]) -> float = "f" "f_nat"
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : (float [@unboxed]) -> float = "f" "f_nat" end
+       is not included in
+         sig external f : float -> float = "f" "f_nat" end
+       Values do not match:
+         external f : (float [@unboxed]) -> float = "f" "f_nat"
+       is not included in
+         external f : float -> float = "f" "f_nat"
+|}]
+
+module Bad6 : sig
   external f : float -> float = "a" "a_nat"
 end = struct
   external f : (float [@unboxed]) -> float = "f" "f_nat"
@@ -187,9 +231,31 @@ Error: Signature mismatch:
          external f : float -> float = "a" "a_nat"
 |}]
 
+module Bad7 : sig
+  external f : int -> int = "f" "f_nat"
+end = struct
+  external f : int -> int = "f" "f_nat" [@@noalloc]
+end;;
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : int -> int = "f" "f_nat" [@@noalloc]
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int = "f" "f_nat" [@@noalloc] end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int = "f" "f_nat" [@@noalloc]
+       is not included in
+         external f : int -> int = "f" "f_nat"
+|}]
+
 (* Bad: attributes in the interface but not in the implementation *)
 
-module Bad5 : sig
+module Bad8 : sig
   external f : int -> (int [@untagged]) = "f" "f_nat"
 end = struct
   external f : int -> int = "f" "f_nat"
@@ -211,7 +277,29 @@ Error: Signature mismatch:
          external f : int -> (int [@untagged]) = "f" "f_nat"
 |}]
 
-module Bad6 : sig
+module Bad9 : sig
+  external f : (int [@untagged]) -> int = "f" "f_nat"
+end = struct
+  external f : int -> int = "f" "f_nat"
+end;;
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : int -> int = "f" "f_nat"
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int = "f" "f_nat" end
+       is not included in
+         sig external f : (int [@untagged]) -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int = "f" "f_nat"
+       is not included in
+         external f : (int [@untagged]) -> int = "f" "f_nat"
+|}]
+
+module Bad10 : sig
   external f : (int [@untagged]) -> int = "f" "f_nat"
 end = struct
   external f : int -> int = "a" "a_nat"
@@ -233,7 +321,7 @@ Error: Signature mismatch:
          external f : (int [@untagged]) -> int = "f" "f_nat"
 |}]
 
-module Bad7 : sig
+module Bad11 : sig
   external f : float -> (float [@unboxed]) = "f" "f_nat"
 end = struct
   external f : float -> float = "f" "f_nat"
@@ -255,7 +343,29 @@ Error: Signature mismatch:
          external f : float -> (float [@unboxed]) = "f" "f_nat"
 |}]
 
-module Bad8 : sig
+module Bad12 : sig
+  external f : (float [@unboxed]) -> float = "f" "f_nat"
+end = struct
+  external f : float -> float = "f" "f_nat"
+end;;
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : float -> float = "f" "f_nat"
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : float -> float = "f" "f_nat" end
+       is not included in
+         sig external f : (float [@unboxed]) -> float = "f" "f_nat" end
+       Values do not match:
+         external f : float -> float = "f" "f_nat"
+       is not included in
+         external f : (float [@unboxed]) -> float = "f" "f_nat"
+|}]
+
+module Bad13 : sig
   external f : (float [@unboxed]) -> float = "f" "f_nat"
 end = struct
   external f : float -> float = "a" "a_nat"
@@ -277,6 +387,215 @@ Error: Signature mismatch:
          external f : (float [@unboxed]) -> float = "f" "f_nat"
 |}]
 
+module Bad14 : sig
+  external f : int -> int = "f" "f_nat" [@@noalloc]
+end = struct
+  external f : int -> int = "f" "f_nat"
+end;;
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : int -> int = "f" "f_nat"
+5 | end..
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int = "f" "f_nat" end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" [@@noalloc] end
+       Values do not match:
+         external f : int -> int = "f" "f_nat"
+       is not included in
+         external f : int -> int = "f" "f_nat" [@@noalloc]
+|}]
+
+(* Bad: claiming something is a primitive when it isn't *)
+
+module Bad15 : sig
+  external f : int -> int = "f" "f_nat"
+end = struct
+  let f x = x + 1
+end
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   let f x = x + 1
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig val f : int -> int end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" end
+       Values do not match:
+         val f : int -> int
+       is not included in
+         external f : int -> int = "f" "f_nat"
+|}]
+
+(* Good: not claiming something is a primitive when it is *)
+
+module Good16 : sig
+  val f : int -> int
+end = struct
+  external f : int -> int = "f" "f_nat"
+end
+(* The expected error here is that "f" isn't defined -- that means typechecking
+   succeeded *)
+
+[%%expect{|
+Line 1:
+Error: The external function `f' is not available
+|}]
+
+(* Bad: mismatched names and native names *)
+
+module Bad17 : sig
+  external f : int -> int = "f" "f_nat"
+end = struct
+  external f : int -> int = "gg" "f_nat"
+end
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : int -> int = "gg" "f_nat"
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int = "gg" "f_nat" end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int = "gg" "f_nat"
+       is not included in
+         external f : int -> int = "f" "f_nat"
+|}]
+
+module Bad18 : sig
+  external f : int -> int = "f" "f_nat"
+end = struct
+  external f : int -> int = "f" "gg_nat"
+end
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : int -> int = "f" "gg_nat"
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int = "f" "gg_nat" end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int = "f" "gg_nat"
+       is not included in
+         external f : int -> int = "f" "f_nat"
+|}]
+
+module Bad19 : sig
+  external f : int -> int = "f" "f_nat"
+end = struct
+  external f : int -> int = "gg" "gg_nat"
+end
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : int -> int = "gg" "gg_nat"
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int = "gg" "gg_nat" end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int = "gg" "gg_nat"
+       is not included in
+         external f : int -> int = "f" "f_nat"
+|}]
+
+(* Bad: mismatched arities *)
+
+(* NB: The compiler checks primitive arities *syntactically*, based on the
+   number of arrows it sees.  Thus, hiding function types behind type synonyms
+   will produce an error about the primitive arities not matching, even when the
+   types agree. *)
+
+module Bad20 : sig
+  type int_int := int -> int
+  external f : int -> int_int = "f" "f_nat"
+end = struct
+  external f : int -> int -> int = "f" "f_nat"
+end
+
+[%%expect{|
+Lines 4-6, characters 6-3:
+4 | ......struct
+5 |   external f : int -> int -> int = "f" "f_nat"
+6 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int -> int = "f" "f_nat" end
+       is not included in
+         sig external f : int -> int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int -> int = "f" "f_nat"
+       is not included in
+         external f : int -> int -> int = "f" "f_nat"
+|}]
+
+module Bad21 : sig
+  external f : int -> int -> int = "f" "f_nat"
+end = struct
+  type int_int = int -> int
+  external f : int -> int_int = "f" "f_nat"
+end
+
+[%%expect{|
+Lines 3-6, characters 6-3:
+3 | ......struct
+4 |   type int_int = int -> int
+5 |   external f : int -> int_int = "f" "f_nat"
+6 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig
+           type int_int = int -> int
+           external f : int -> int_int = "f" "f_nat"
+         end
+       is not included in
+         sig external f : int -> int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int_int = "f" "f_nat"
+       is not included in
+         external f : int -> int -> int = "f" "f_nat"
+|}]
+
+(* This will fail with a *type* error, instead of an arity mismatch *)
+module Bad22 : sig
+  external f : int -> int = "f" "f_nat"
+end = struct
+  external f : int -> int -> int = "f" "f_nat"
+end
+
+[%%expect{|
+Lines 3-5, characters 6-3:
+3 | ......struct
+4 |   external f : int -> int -> int = "f" "f_nat"
+5 | end
+Error: Signature mismatch:
+       Modules do not match:
+         sig external f : int -> int -> int = "f" "f_nat" end
+       is not included in
+         sig external f : int -> int = "f" "f_nat" end
+       Values do not match:
+         external f : int -> int -> int = "f" "f_nat"
+       is not included in
+         external f : int -> int = "f" "f_nat"
+|}]
+
 (* Bad: unboxed or untagged with the wrong type *)
 
 external g : (float [@untagged]) -> float = "g" "g_nat";;