diff --git a/pytools/datatable.py b/pytools/datatable.py
index 4dda68f2954daad9d2be7a8c305ac4cee978918f..41c56909cf972ee20291080b5b719aa8586850f6 100644
--- a/pytools/datatable.py
+++ b/pytools/datatable.py
@@ -1,3 +1,5 @@
+from typing import IO, Any, Callable, Iterator, List, Optional, Sequence, Tuple
+
 from pytools import Record
 
 
@@ -9,7 +11,8 @@ An in-memory relational database table
 """
 
 
-class Row(Record):
+# type-ignore-reason: Record is untyped
+class Row(Record):  # type: ignore[misc]
     pass
 
 
@@ -22,7 +25,8 @@ class DataTable:
     .. automethod:: join
     """
 
-    def __init__(self, column_names, column_data=None):
+    def __init__(self, column_names: Sequence[str],
+                 column_data: Optional[List[Any]] = None) -> None:
         """Construct a new table, with the given C{column_names}.
 
         :arg column_names: An indexable of column name strings.
@@ -41,26 +45,26 @@ class DataTable:
         if len(self.column_indices) != len(self.column_names):
             raise RuntimeError("non-unique column names encountered")
 
-    def __bool__(self):
+    def __bool__(self) -> bool:
         return bool(self.data)
 
-    def __len__(self):
+    def __len__(self) -> int:
         return len(self.data)
 
-    def __iter__(self):
+    def __iter__(self) -> Iterator[List[Any]]:
         return self.data.__iter__()
 
-    def __str__(self):
+    def __str__(self) -> str:
         """Return a pretty-printed version of the table."""
 
-        def col_width(i):
+        def col_width(i: int) -> int:
             width = len(self.column_names[i])
             if self:
                 width = max(width, max(len(str(row[i])) for row in self.data))
             return width
         col_widths = [col_width(i) for i in range(len(self.column_names))]
 
-        def format_row(row):
+        def format_row(row: Sequence[str]) -> str:
             return "|".join([str(cell).ljust(col_width)
                       for cell, col_width in zip(row, col_widths)])
 
@@ -69,7 +73,7 @@ class DataTable:
                 [format_row(row) for row in self.data]
         return "\n".join(lines)
 
-    def insert(self, **kwargs):
+    def insert(self, **kwargs: Any) -> None:
         values = [None for i in range(len(self.column_names))]
 
         for key, val in kwargs.items():
@@ -77,16 +81,16 @@ class DataTable:
 
         self.insert_row(tuple(values))
 
-    def insert_row(self, values):
+    def insert_row(self, values: Tuple[Any, ...]) -> None:
         assert isinstance(values, tuple)
         assert len(values) == len(self.column_names)
         self.data.append(values)
 
-    def insert_rows(self, rows):
+    def insert_rows(self, rows: Sequence[Tuple[Any, ...]]) -> None:
         for row in rows:
             self.insert_row(row)
 
-    def filtered(self, **kwargs):
+    def filtered(self, **kwargs: Any) -> "DataTable":
         if not kwargs:
             return self
 
@@ -108,7 +112,7 @@ class DataTable:
 
         return DataTable(self.column_names, result_data)
 
-    def get(self, **kwargs):
+    def get(self, **kwargs: Any) -> Row:
         filtered = self.filtered(**kwargs)
         if not filtered:
             raise RuntimeError("no matching entry for get()")
@@ -117,34 +121,35 @@ class DataTable:
 
         return Row(dict(list(zip(self.column_names, filtered.data[0]))))
 
-    def clear(self):
+    def clear(self) -> None:
         del self.data[:]
 
-    def copy(self):
+    def copy(self) -> "DataTable":
         """Make a copy of the instance, but leave individual rows untouched.
 
         If the rows are modified later, they will also be modified in the copy.
         """
         return DataTable(self.column_names, self.data[:])
 
-    def deep_copy(self):
+    def deep_copy(self) -> "DataTable":
         """Make a copy of the instance down to the row level.
 
         The copy's rows may be modified independently from the original.
         """
         return DataTable(self.column_names, [row[:] for row in self.data])
 
-    def sort(self, columns, reverse=False):
+    def sort(self, columns: Sequence[str], reverse: bool = False) -> None:
         col_indices = [self.column_indices[col] for col in columns]
 
-        def mykey(row):
+        def mykey(row: Sequence[Any]) -> Tuple[Any, ...]:
             return tuple(
                     row[col_index]
                     for col_index in col_indices)
 
         self.data.sort(reverse=reverse, key=mykey)
 
-    def aggregated(self, groupby, agg_column, aggregate_func):
+    def aggregated(self, groupby: Sequence[str], agg_column: str,
+                   aggregate_func: Callable[[Sequence[Any]], Any]) -> "DataTable":
         gb_indices = [self.column_indices[col] for col in groupby]
         agg_index = self.column_indices[agg_column]
 
@@ -153,8 +158,8 @@ class DataTable:
         result_data = []
 
         # to pacify pyflakes:
-        last_values = None
-        agg_values = None
+        last_values: Tuple[Any, ...] = ()
+        agg_values: List[Row] = []
 
         for row in self.data:
             this_values = tuple(row[i] for i in gb_indices)
@@ -175,8 +180,9 @@ class DataTable:
                 [self.column_names[i] for i in gb_indices] + [agg_column],
                 result_data)
 
-    def join(self, column, other_column, other_table, outer=False):
-        """Return a tabled joining this and the C{other_table} on C{column}.
+    def join(self, column: str, other_column: str, other_table: "DataTable",
+             outer: bool = False) -> "DataTable":
+        """Return a table joining this and the C{other_table} on C{column}.
 
         The new table has the following columns:
         - C{column}, titled the same as in this table.
@@ -187,7 +193,7 @@ class DataTable:
         by which they are joined.
         """  # pylint:disable=too-many-locals,too-many-branches
 
-        def without(indexable, idx):
+        def without(indexable: Tuple[str, ...], idx: int) -> Tuple[str, ...]:
             return indexable[:idx] + indexable[idx+1:]
 
         this_key_idx = self.column_indices[column]
@@ -196,9 +202,9 @@ class DataTable:
         this_iter = self.data.__iter__()
         other_iter = other_table.data.__iter__()
 
-        result_columns = [self.column_names[this_key_idx]] + \
-                without(self.column_names, this_key_idx) + \
-                without(other_table.column_names, other_key_idx)
+        result_columns = tuple(self.column_names[this_key_idx]) + \
+                without(tuple(self.column_names), this_key_idx) + \
+                without(tuple(other_table.column_names), other_key_idx)
 
         result_data = []
 
@@ -266,17 +272,17 @@ class DataTable:
 
         return DataTable(result_columns, result_data)
 
-    def restricted(self, columns):
+    def restricted(self, columns: Sequence[str]) -> "DataTable":
         col_indices = [self.column_indices[col] for col in columns]
 
         return DataTable(columns,
                 [[row[i] for i in col_indices] for row in self.data])
 
-    def column_data(self, column):
+    def column_data(self, column: str) -> List[Tuple[Any, ...]]:
         col_index = self.column_indices[column]
         return [row[col_index] for row in self.data]
 
-    def write_csv(self, filelike, **kwargs):
+    def write_csv(self, filelike: IO[Any], **kwargs: Any) -> None:
         from csv import writer
         csvwriter = writer(filelike, **kwargs)
         csvwriter.writerow(self.column_names)
diff --git a/run-mypy.sh b/run-mypy.sh
index 2d08e14414a52b33baa7c16a4576cd6e68b7e001..39055a8cd2fd878fb36c1d05f51e90b26083cc12 100755
--- a/run-mypy.sh
+++ b/run-mypy.sh
@@ -1,3 +1,7 @@
 #! /bin/bash
 
+set -ex
+
 mypy --show-error-codes pytools
+
+mypy --strict --follow-imports=skip pytools/datatable.py