feat(genui): support functions in prompts and verify rendering

packages/genui/lib/src/facade/prompt_builder.dart

@@ -370,6 +370,19 @@ final class _BasicPromptBuilder extends PromptBuilder {
       ...catalog.systemPromptFragments,
       ...allowedOperations.systemPromptFragments,
       _fenced(a2uiSchema, sectionName: 'A2UI JSON SCHEMA'),
+      if (catalog.functions.isNotEmpty)
+        _fenced(
+          const JsonEncoder.withIndent('  ').convert([
+            for (final func in catalog.functions)
+              {
+                'name': func.name,
+                'description': func.description,
+                'parameters': func.argumentSchema.value,
+                'returnType': func.returnType.value,
+              },
+          ]),
+          sectionName: 'AVAILABLE FUNCTIONS',
+        ),
       ?_encodedDataModel(clientDataModel),
     ];
 

packages/genui/test/catalog/functions_rendering_test.dart

@@ -0,0 +1,85 @@
+// Copyright 2025 The Flutter Authors.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+import 'package:flutter/material.dart';
+import 'package:flutter_test/flutter_test.dart';
+import 'package:genui/genui.dart';
+
+void main() {
+  late SurfaceController controller;
+  final testCatalog = Catalog(
+    [BasicCatalogItems.text, BasicCatalogItems.column],
+    functions: BasicFunctions.all,
+    catalogId: 'test_catalog',
+  );
+
+  setUp(() {
+    controller = SurfaceController(catalogs: [testCatalog]);
+  });
+
+  tearDown(() {
+    controller.dispose();
+  });
+
+  testWidgets('Surface renders function output correctly', (
+    WidgetTester tester,
+  ) async {
+    const surfaceId = 'testSurface';
+
+    // 1. Create surface
+    controller.handleMessage(
+      const CreateSurface(surfaceId: surfaceId, catalogId: 'test_catalog'),
+    );
+
+    // 2. Update data model
+    controller.handleMessage(
+      const UpdateDataModel(
+        surfaceId: surfaceId,
+        path: DataPath.root,
+        value: {'count': 2},
+      ),
+    );
+
+    // 3. Update components with a function call
+    final components = [
+      const Component(
+        id: 'root',
+        type: 'Column',
+        properties: {
+          'children': ['cartSummaryText'],
+        },
+      ),
+      const Component(
+        id: 'cartSummaryText',
+        type: 'Text',
+        properties: {
+          'text': {
+            'call': 'pluralize',
+            'args': {
+              'count': {'path': '/count'},
+              'zero': 'No items',
+              'one': 'One item',
+              'other': 'Multiple items',
+            },
+            'returnType': 'string',
+          },
+        },
+      ),
+    ];
+
+    controller.handleMessage(
+      UpdateComponents(surfaceId: surfaceId, components: components),
+    );
+
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Surface(surfaceContext: controller.contextFor(surfaceId)),
+      ),
+    );
+    await tester.pumpAndSettle();
+
+    // We expect "Multiple items" because count is 2.
+    expect(find.text('Multiple items'), findsOneWidget);
+  });
+}

packages/genui/test/facade/prompt_builder_test.dart

@@ -123,4 +123,28 @@ void main() {
       });
     }
   });
+
+  group('Prompt with functions', () {
+    test('includes functions section when catalog has functions', () {
+      final catalogWithFunctions = Catalog(
+        [BasicCatalogItems.text],
+        functions: [BasicFunctions.pluralizeFunction],
+        catalogId: 'test_catalog',
+      );
+
+      final String prompt = PromptBuilder.chat(
+        catalog: catalogWithFunctions,
+      ).systemPromptJoined();
+
+      expect(prompt, contains('AVAILABLE_FUNCTIONS'));
+      expect(prompt, contains('pluralize'));
+      expect(
+        prompt,
+        contains(
+          'Returns a localized string based on the Common Locale Data '
+          'Repository',
+        ),
+      );
+    });
+  });
 }