diff --git a/pytato/__init__.py b/pytato/__init__.py
index dcfaf28c87db410713c6d97ba67fa8565baeaf62..f47a61c6c13c0c0f14408c06401e10aecdb917e7 100644
--- a/pytato/__init__.py
+++ b/pytato/__init__.py
@@ -26,7 +26,7 @@ THE SOFTWARE.
 
 from pytato.array import (
         Namespace, Array, DictOfNamedArrays, Tag, UniqueTag,
-        DottedName, Placeholder, make_placeholder,
+        DottedName, Placeholder, make_placeholder, IndexLambda
         )
 
 from pytato.codegen import generate_loopy
@@ -35,6 +35,7 @@ from pytato.program import Target, PyOpenCLTarget
 __all__ = (
         "DottedName", "Namespace", "Array", "DictOfNamedArrays",
         "Tag", "UniqueTag", "Placeholder", "make_placeholder",
+        "IndexLambda",
 
         "generate_loopy",
         "Target", "PyOpenCLTarget",
diff --git a/pytato/array.py b/pytato/array.py
index 737ea463a82bb6f54e629e6368640137237b5699..73cac6fafc3eebbbee13c8c88a7f621a0ba047ce 100644
--- a/pytato/array.py
+++ b/pytato/array.py
@@ -180,7 +180,8 @@ class Namespace(Mapping[str, "Array"]):
         return len(self._symbol_table)
 
     def copy(self) -> Namespace:
-        raise NotImplementedError
+        from pytato.transform import CopyMapper, copy_namespace
+        return copy_namespace(self, CopyMapper(Namespace()))
 
     def assign(self, name: str, value: Array) -> str:
         """Declare a new array.
diff --git a/pytato/transform.py b/pytato/transform.py
index 13546653188a6da64a5f65b1ef3ed68832e115b3..739081a347f413b03c59095c72ef410737e95161 100644
--- a/pytato/transform.py
+++ b/pytato/transform.py
@@ -24,9 +24,9 @@ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 """
 
-from typing import Any, Callable
+from typing import Any, Callable, Dict
 
-from pytato.array import Array
+from pytato.array import Array, IndexLambda, Namespace, Placeholder
 
 __doc__ = """
 .. currentmodule:: pytato.transform
@@ -35,6 +35,8 @@ Transforming Computations
 -------------------------
 
 .. autoclass:: Mapper
+.. autoclass:: CopyMapper
+.. autofunction:: copy_namespace
 
 """
 
@@ -74,7 +76,56 @@ class Mapper:
 
     rec = __call__
 
+
+class CopyMapper(Mapper):
+    namespace: Namespace
+
+    def __init__(self, namespace: Namespace):
+        self.namespace = namespace
+        self.cache: Dict[Array, Array] = {}
+
+    def rec(self, expr: Array) -> Array:  # type: ignore[override]
+        if expr in self.cache:
+            return self.cache[expr]
+        result: Array = super().rec(expr)
+        self.cache[expr] = result
+        return result
+
+    def __call__(self, expr: Array) -> Array:  # type: ignore[override]
+        return self.rec(expr)
+
+    def map_index_lambda(self, expr: IndexLambda) -> Array:
+        bindings = {
+                name: self.rec(subexpr)
+                for name, subexpr in expr.bindings.items()}
+        return IndexLambda(self.namespace,
+                expr=expr.expr,
+                shape=expr.shape,
+                dtype=expr.dtype,
+                bindings=bindings)
+
+    def map_placeholder(self, expr: Placeholder) -> Array:
+        return Placeholder(self.namespace, expr.name, expr.shape, expr.dtype,
+                expr.tags)
+
 # }}}
 
 
+# {{{ mapper frontends
+
+def copy_namespace(namespace: Namespace, copy_mapper: CopyMapper) -> Namespace:
+    """Copy the elements of *namespace* into a new namespace.
+
+    :param namespace: The source namespace
+    :param copy_mapper: A mapper that performs copies into a new namespace
+    :returns: The new namespace
+    """
+    for name, val in namespace.items():
+        mapped_val = copy_mapper(val)
+        if name not in copy_mapper.namespace:
+            copy_mapper.namespace.assign(name, mapped_val)
+    return copy_mapper.namespace
+
+# }}}
+
 # vim: foldmethod=marker
diff --git a/test/test_transform.py b/test/test_transform.py
new file mode 100755
index 0000000000000000000000000000000000000000..cb9f757b25bd37351a67502e62cdf2efc53bb099
--- /dev/null
+++ b/test/test_transform.py
@@ -0,0 +1,57 @@
+#!/usr/bin/env python
+
+__copyright__ = "Copyright (C) 2020 Andreas Kloeckner"
+
+__license__ = """
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+"""
+
+import sys
+
+import numpy as np
+import pyopencl as cl  # noqa
+import pyopencl.array as cl_array  # noqa
+import pyopencl.cltypes as cltypes  # noqa
+import pyopencl.tools as cl_tools  # noqa
+from pyopencl.tools import (  # noqa
+        pytest_generate_tests_for_pyopencl as pytest_generate_tests)
+import pytest  # noqa
+
+import pytato as pt
+
+
+def test_copy_namespace():
+    namespace = pt.Namespace()
+    x = pt.Placeholder(namespace, "x", (5,), np.int)
+    namespace.assign("xsquared", x * x)
+
+    namespace_copy = namespace.copy()
+    assert len(namespace_copy) == 2
+    assert isinstance(namespace_copy["x"], pt.Placeholder)
+    assert isinstance(namespace_copy["xsquared"], pt.IndexLambda)
+
+
+if __name__ == "__main__":
+    if len(sys.argv) > 1:
+        exec(sys.argv[1])
+    else:
+        from pytest import main
+        main([__file__])
+
+# vim: filetype=pyopencl:fdm=marker