isErrorModel check for base models (#2968)

fix #2957

.chronus/changes/is-error-model-2024-1-29-0-44-17.md

@@ -0,0 +1,8 @@
+---
+# Change versionKind to one of: internal, fix, dependencies, feature, deprecation, breaking
+changeKind: feature
+packages:
+  - "@typespec/compiler"
+---
+
+Any subtype of an error(marked with `@error`) is now an error.

packages/compiler/src/lib/decorators.ts

@@ -350,16 +350,28 @@ const errorKey = createStateSymbol("error");
 
 /**
  * `@error` decorator marks a model as an error type.
- *
- * `@error` can only be specified on a model.
+ *  Any derived models (using extends) will also be seen as error types.
  */
 export function $error(context: DecoratorContext, entity: Model) {
   validateDecoratorUniqueOnNode(context, entity, $error);
   context.program.stateSet(errorKey).add(entity);
 }
 
+/**
+ * Check if the type is an error model or a descendant of an error model.
+ */
 export function isErrorModel(program: Program, target: Type): boolean {
-  return program.stateSet(errorKey).has(target);
+  if (target.kind !== "Model") {
+    return false;
+  }
+  let current: Model | undefined = target;
+  while (current) {
+    if (program.stateSet(errorKey).has(current)) {
+      return true;
+    }
+    current = current.baseModel;
+  }
+  return false;
 }
 
 // -- @format decorator ---------------------

packages/compiler/test/decorators/decorators.test.ts

@@ -387,6 +387,16 @@ describe("compiler: built-in decorators", () => {
       ok(isErrorModel(runner.program, A), "isError should be true");
     });
 
+    it("applies @error on derived models", async () => {
+      const { B, C } = await runner.compile(`
+        @error model A { }
+        @test model B extends A { }
+        @test model C extends B { }
+      `);
+      ok(isErrorModel(runner.program, B), "isError should be true");
+      ok(isErrorModel(runner.program, C), "isError should be true");
+    });
+
     it("emit diagnostic if error is not applied to a model", async () => {
       const diagnostics = await runner.diagnose(`
         @error