Register module types of an applied functor's signature

Codex review on #9084: the applied signature's module types were dropped,
because the signature walk handled modules but not module types, so a
member declared with one, such as `Applied.Nested.value` with
`module Nested: S`, no longer resolved. Module types are registered like
those of a structure now.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Kbf3gLMawVgtmiKy3TMBc3
Claude-Session: https://claude.ai/code/session_01Kr4cjoUi2f5VpMvE6wT9bo
Signed-off-by: Christoph Knittel <ck@cca.io>

Author: cknitt

analysis/src/process_cmt.ml

@@ -165,6 +165,28 @@ let rec for_type_signature_item ~(env : Shared_types.Env.t)
         loc = declared.extent_loc;
       };
     ]
+  | Sig_modtype (ident, {mtd_type = Some mod_type; mtd_attributes; mtd_loc}) ->
+    let name = Ident.name ident in
+    let env = env |> Env.add_module_type ~name in
+    let declared =
+      add_declared ~extent:mtd_loc
+        ~item:(for_type_module ~name ~env mod_type)
+        ~name:(Location.mkloc name mtd_loc)
+        ~stamp:(Ident.binding_time ident) ~env mtd_attributes
+        (Exported.add exported Exported.Module)
+        Stamps.add_module
+    in
+    [
+      {
+        Module.kind =
+          Module
+            {type_ = declared.item; is_module_type = is_module_type declared};
+        name = declared.name.txt;
+        docstring = declared.docstring;
+        deprecated = declared.deprecated;
+        loc = declared.extent_loc;
+      };
+    ]
   | _ -> []
 
 and for_type_signature ~name ~env signature =

tests/analysis_tests/tests/src/AppliedFunctor.res

@@ -62,3 +62,20 @@ let shape = Shapes.Box(1)
 
 let py = p.x
 //         ^ren y
+
+module WithModType = (O: Ord) => {
+  module type S = {
+    let value: int
+  }
+  module Nested: S = {
+    let value = 1
+  }
+}
+
+module Applied = WithModType(IntOrd)
+
+let nv = Applied.Nested.value
+//                      ^hov
+
+// let nv2 = Applied.Nested.
+//                          ^com

tests/analysis_tests/tests/src/expected/AppliedFunctor.res.txt

@@ -223,3 +223,16 @@ Rename src/AppliedFunctor.res 62:11 y
   }
 ]
 
+Hover src/AppliedFunctor.res 76:24
+{ "contents": { "kind": "markdown", "value": "```rescript\nint\n```" } }
+
+Complete src/AppliedFunctor.res 79:28
+pos_cursor:[79:28] pos_no_white:[79:27] Found expr:[79:13->79:28]
+Pexp_ident Applied.Nested.:[79:13->79:28]
+Completable: Cpath Value[Applied, Nested, ""]
+Package opens Stdlib.place holder Pervasives.JsxModules.place holder
+Resolved opens 1 Stdlib
+ContextPath Value[Applied, Nested, ""]
+Path Applied.Nested.
+[ { "detail": "int", "kind": 12, "label": "value", "tags": [] } ]
+