diff --git a/vgi/examples/table.py b/vgi/examples/table.py
index eecdf61..ca98763 100644
--- a/vgi/examples/table.py
+++ b/vgi/examples/table.py
@@ -700,7 +700,7 @@ def output_schema(self) -> pa.Schema:
         When vgi_verbose_mode is "true", includes an extra "details" column.
         This demonstrates how settings can affect the bind result.
         """
-        fields: list[pa.Field] = [
+        fields: list[pa.Field[pa.DataType]] = [
             pa.field("id", pa.int64()),
             pa.field("value", pa.float64()),
         ]
diff --git a/vgi/output_complete.py b/vgi/output_complete.py
new file mode 100644
index 0000000..7395029
--- /dev/null
+++ b/vgi/output_complete.py
@@ -0,0 +1,72 @@
+"""Internal output normalization for VGI function generators.
+
+This module provides the _OutputComplete class used by all function types
+to normalize generator yields into a consistent format with guaranteed
+non-None batches.
+
+This is an internal module - users should not import from here directly.
+"""
+
+from dataclasses import dataclass
+from typing import TYPE_CHECKING
+
+import pyarrow as pa
+
+import vgi.log
+
+if TYPE_CHECKING:
+    from vgi.table_function import Output as TableOutput
+    from vgi.table_in_out_function import Output as TableInOutOutput
+
+__all__ = ["OutputComplete"]
+
+
+@dataclass(frozen=True, slots=True)
+class OutputComplete:
+    """Internal: Output with guaranteed non-None batch.
+
+    Used by the framework to normalize generator yields. When the user yields
+    None, Output with None batch, or Message, this class ensures we always
+    have a valid RecordBatch for the protocol.
+
+    Attributes:
+        batch: Always a valid RecordBatch (never None).
+        has_more: If True, generator expects another send() call.
+            Only used by TableInOutGeneratorFunction.
+        log_message: Present when user yielded Message directly.
+
+    """
+
+    batch: pa.RecordBatch
+    has_more: bool = False
+    log_message: vgi.log.Message | None = None
+
+    @classmethod
+    def from_process_result(
+        cls,
+        source: "vgi.log.Message | TableOutput | TableInOutOutput | None",
+        empty_batch: pa.RecordBatch,
+    ) -> "OutputComplete":
+        """Create from user's yield value.
+
+        Args:
+            source: What the user yielded (Output, Message, or None).
+            empty_batch: Empty batch to substitute when needed.
+
+        Returns:
+            Normalized output with guaranteed non-None batch.
+
+        """
+        if source is None:
+            return cls(batch=empty_batch)
+        if isinstance(source, vgi.log.Message):
+            # When yielding a log message, has_more=True so the caller
+            # re-sends the current input after the message is processed
+            return cls(batch=empty_batch, has_more=True, log_message=source)
+        # source is Output (either TableOutput or TableInOutOutput)
+        # TableOutput doesn't have has_more, TableInOutOutput does
+        has_more = getattr(source, "has_more", False)
+        return cls(
+            batch=source.batch if source.batch is not None else empty_batch,
+            has_more=has_more,
+        )
diff --git a/vgi/scalar_function.py b/vgi/scalar_function.py
index cfac8ca..c101d47 100644
--- a/vgi/scalar_function.py
+++ b/vgi/scalar_function.py
@@ -50,6 +50,7 @@ def compute(self, batch: pa.RecordBatch) -> pa.Array:
 import vgi.function
 import vgi.log
 from vgi.exceptions import SchemaValidationError
+from vgi.output_complete import OutputComplete
 from vgi.table_function import Output, ProtocolOutput
 
 __all__ = [
@@ -165,37 +166,6 @@ class ProtocolInput:
     metadata: pa.KeyValueMetadata | None = None
 
 
-@dataclass(frozen=True, slots=True)
-class _ScalarOutputComplete:
-    """Internal: Output with guaranteed non-None batch for scalar functions."""
-
-    batch: pa.RecordBatch
-    log_message: vgi.log.Message | None = None
-
-    @classmethod
-    def from_process_result(
-        cls,
-        source: vgi.log.Message | Output,
-        empty_batch: pa.RecordBatch,
-    ) -> _ScalarOutputComplete:
-        """Create from user's yield value.
-
-        Args:
-            source: What the user yielded (Output or Message).
-            empty_batch: Empty batch to substitute when yielding Message.
-
-        Returns:
-            Normalized output with guaranteed non-None batch.
-
-        """
-        if isinstance(source, vgi.log.Message):
-            return cls(batch=empty_batch, log_message=source)
-        # source is Output
-        return cls(
-            batch=source.batch if source.batch is not None else empty_batch,
-        )
-
-
 class ScalarFunctionGenerator(vgi.function.Function[vgi.function.FunctionInitInput]):
     """Generator-based base class for scalar functions.
 
@@ -299,7 +269,7 @@ def _process_and_validate(
         self,
         generator: ScalarOutputGenerator,
         input_batch: pa.RecordBatch,
-    ) -> _ScalarOutputComplete:
+    ) -> OutputComplete:
         """Process a batch and validate schemas and row count.
 
         Args:
@@ -307,7 +277,7 @@ def _process_and_validate(
             input_batch: The input RecordBatch to process.
 
         Returns:
-            _ScalarOutputComplete with validated output batch.
+            OutputComplete with validated output batch.
 
         Raises:
             SchemaValidationError: If input or output batch schema doesn't match.
@@ -315,7 +285,7 @@ def _process_and_validate(
 
         """
         self._validate_input_schema(input_batch)
-        result: _ScalarOutputComplete = _ScalarOutputComplete.from_process_result(
+        result: OutputComplete = OutputComplete.from_process_result(
             generator.send(input_batch),
             self.empty_output_batch,
         )
@@ -330,22 +300,22 @@ def _process_with_exception_handling(
         self,
         generator: ScalarOutputGenerator,
         input_batch: pa.RecordBatch,
-    ) -> _ScalarOutputComplete:
+    ) -> OutputComplete:
         """Process a batch with exception handling.
 
         Wraps _process_and_validate to catch exceptions and convert them
-        to _ScalarOutputComplete with an error log message.
+        to OutputComplete with an error log message.
         """
         try:
             return self._process_and_validate(generator, input_batch)
         except Exception as e:
-            return _ScalarOutputComplete(
+            return OutputComplete(
                 batch=self.empty_output_batch,
                 log_message=vgi.log.Message.from_exception(e),
             )
 
     @final
-    def _should_terminate(self, result: _ScalarOutputComplete) -> bool:
+    def _should_terminate(self, result: OutputComplete) -> bool:
         """Check if processing should terminate due to an exception."""
         return (
             result.log_message is not None
diff --git a/vgi/table_function.py b/vgi/table_function.py
index 9073439..c742726 100644
--- a/vgi/table_function.py
+++ b/vgi/table_function.py
@@ -31,6 +31,7 @@
 import vgi.function
 import vgi.ipc_utils
 import vgi.log
+from vgi.output_complete import OutputComplete
 
 __all__ = [
     "TableCardinality",
@@ -133,47 +134,6 @@ class Output:
 OutputGenerator = Generator[vgi.log.Message | Output, None, None]
 
 
-@dataclass(frozen=True, slots=True)
-class _OutputComplete:
-    """Internal: Output with guaranteed non-None batch.
-
-    Used by the framework to normalize generator yields. When the user yields
-    None, Output with None batch, or Message, this class ensures we always
-    have a valid RecordBatch for the protocol.
-
-    Attributes:
-        batch: Always a valid RecordBatch (never None).
-        log_message: Present when user yielded Message directly.
-
-    """
-
-    batch: pa.RecordBatch
-    log_message: vgi.log.Message | None = None
-
-    @classmethod
-    def from_process_result(
-        cls,
-        source: vgi.log.Message | Output,
-        empty_batch: pa.RecordBatch,
-    ) -> "_OutputComplete":
-        """Create from user's yield value.
-
-        Args:
-            source: What the user yielded (Output or Message).
-            empty_batch: Empty batch to substitute when needed.
-
-        Returns:
-            Normalized output with guaranteed non-None batch.
-
-        """
-        if isinstance(source, vgi.log.Message):
-            return cls(batch=empty_batch, log_message=source)
-        # source is Output
-        return cls(
-            batch=source.batch if source.batch is not None else empty_batch,
-        )
-
-
 @dataclass(frozen=True, slots=True)
 class ProtocolOutput:
     """Output yielded by the generator after each send().
@@ -210,7 +170,7 @@ def metadata(
         )
 
     @classmethod
-    def from_process_result(cls, process_result: "_OutputComplete") -> "ProtocolOutput":
+    def from_process_result(cls, process_result: "OutputComplete") -> "ProtocolOutput":
         """Create a ProtocolOutput from an Output and status.
 
         Args:
@@ -384,7 +344,7 @@ def process(self) -> OutputGenerator:
     """
 
     @final
-    def _process_and_validate(self, generator: OutputGenerator) -> _OutputComplete:
+    def _process_and_validate(self, generator: OutputGenerator) -> OutputComplete:
         """Process a batch and validate the output schema.
 
         Converts the result of the generator to OutputComplete, and
@@ -400,7 +360,7 @@ def _process_and_validate(self, generator: OutputGenerator) -> _OutputComplete:
             SchemaValidationError: If output batch schema doesn't match.
 
         """
-        result: _OutputComplete = _OutputComplete.from_process_result(
+        result: OutputComplete = OutputComplete.from_process_result(
             generator.send(None),
             self.empty_output_batch,
         )
@@ -411,7 +371,7 @@ def _process_and_validate(self, generator: OutputGenerator) -> _OutputComplete:
     def _process_with_exception_handling(
         self,
         generator: OutputGenerator,
-    ) -> _OutputComplete:
+    ) -> OutputComplete:
         """Process a batch with exception handling.
 
         Wraps _process_and_validate to catch exceptions and convert them
@@ -425,13 +385,13 @@ def _process_with_exception_handling(
         except StopIteration:
             raise
         except Exception as e:
-            return _OutputComplete(
+            return OutputComplete(
                 batch=self.empty_output_batch,
                 log_message=vgi.log.Message.from_exception(e),
             )
 
     @final
-    def _should_terminate(self, result: _OutputComplete) -> bool:
+    def _should_terminate(self, result: OutputComplete) -> bool:
         """Check if processing should terminate due to an exception."""
         return (
             result.log_message is not None
diff --git a/vgi/table_in_out_function.py b/vgi/table_in_out_function.py
index 879ca5d..a3d8378 100644
--- a/vgi/table_in_out_function.py
+++ b/vgi/table_in_out_function.py
@@ -78,6 +78,7 @@ def process(self, batch: pa.RecordBatch) -> OutputGenerator:
 import vgi.ipc_utils
 import vgi.log
 import vgi.table_function
+from vgi.output_complete import OutputComplete
 
 __all__ = [
     "ProtocolInput",
@@ -181,7 +182,7 @@ def metadata(
 
     @classmethod
     def from_process_result(
-        cls, process_result: "_OutputComplete", in_finalize_phase: bool
+        cls, process_result: "OutputComplete", in_finalize_phase: bool
     ) -> "ProtocolOutput":
         """Create a ProtocolOutput from an Output and status.
 
@@ -353,52 +354,6 @@ def wrapper(self: T, first_batch: pa.RecordBatch) -> OutputGenerator:
     return wrapper
 
 
-@dataclass(frozen=True, slots=True)
-class _OutputComplete:
-    """Internal: Output with guaranteed non-None batch.
-
-    Used by the framework to normalize generator yields. When the user yields
-    None, Output with None batch, or Message, this class ensures we always
-    have a valid RecordBatch for the protocol.
-
-    Attributes:
-        batch: Always a valid RecordBatch (never None).
-        has_more: If True, generator expects another send() call.
-        log_message: Present when user yielded Message directly.
-
-    """
-
-    batch: pa.RecordBatch
-    has_more: bool = False
-    log_message: vgi.log.Message | None = None
-
-    @classmethod
-    def from_process_result(
-        cls,
-        source: vgi.log.Message | Output | None,
-        empty_batch: pa.RecordBatch,
-    ) -> "_OutputComplete":
-        """Create from user's yield value.
-
-        Args:
-            source: What the user yielded (Output, Message, or None).
-            empty_batch: Empty batch to substitute when needed.
-
-        Returns:
-            Normalized output with guaranteed non-None batch.
-
-        """
-        if source is None:
-            return cls(batch=empty_batch)
-        if isinstance(source, vgi.log.Message):
-            return cls(batch=empty_batch, has_more=True, log_message=source)
-        # source is Output
-        return cls(
-            batch=source.batch if source.batch is not None else empty_batch,
-            has_more=source.has_more,
-        )
-
-
 class TableInOutGeneratorFunction(vgi.table_function.TableFunctionBase):
     """Base class for streaming table functions that transform Arrow RecordBatches.
 
@@ -588,7 +543,7 @@ def _process_and_validate(
         self,
         generator: OutputGenerator,
         batch: pa.RecordBatch | None,
-    ) -> _OutputComplete:
+    ) -> OutputComplete:
         """Process a batch and validate both input and output schemas.
 
         Validates the input batch schema, sends it to the generator, converts
@@ -607,7 +562,7 @@ def _process_and_validate(
         """
         if batch is not None:
             self._validate_input_schema(batch)
-        result: _OutputComplete = _OutputComplete.from_process_result(
+        result: OutputComplete = OutputComplete.from_process_result(
             generator.send(batch),
             self.empty_output_batch,
         )
@@ -619,7 +574,7 @@ def _process_with_exception_handling(
         self,
         generator: OutputGenerator,
         batch: pa.RecordBatch | None,
-    ) -> _OutputComplete:
+    ) -> OutputComplete:
         """Process a batch with exception handling.
 
         Wraps _process_and_validate to catch exceptions and convert them
@@ -628,13 +583,13 @@ def _process_with_exception_handling(
         try:
             return self._process_and_validate(generator, batch)
         except Exception as e:
-            return _OutputComplete(
+            return OutputComplete(
                 batch=self.empty_output_batch,
                 log_message=vgi.log.Message.from_exception(e),
             )
 
     @final
-    def _should_terminate(self, result: _OutputComplete) -> bool:
+    def _should_terminate(self, result: OutputComplete) -> bool:
         """Check if processing should terminate due to an exception."""
         return (
             result.log_message is not None