diff --git a/pytato/array.py b/pytato/array.py
index 6e3bf69757173d8545a22aff88d5ed822be4ff27..1391103fb33823cffd9f9f897f10e4d803788b01 100644
--- a/pytato/array.py
+++ b/pytato/array.py
@@ -91,7 +91,7 @@ import pytato.scalar_expr as scalar_expr
 
 from dataclasses import dataclass
 from pytools import is_single_valued
-from typing import Optional, Dict, Any, Mapping, Iterator, Tuple, Union
+from typing import Optional, Dict, Any, Mapping, Iterator, Tuple, Union, FrozenSet
 
 
 # {{{ dotted name
@@ -240,7 +240,7 @@ class UniqueTag(Tag):
     """
 
 
-TagsType = Dict[DottedName, Tag]
+TagsType = FrozenSet[Tag]
 
 # }}}
 
@@ -356,8 +356,7 @@ class Array:
 
     .. attribute:: tags
 
-        A :class:`dict` mapping :class:`DottedName` instances
-        to instances of the :class:`Tag` interface.
+        A :class:`tuple` of :class:`Tag` instances.
 
         Motivation: `RDF
         <https://en.wikipedia.org/wiki/Resource_Description_Framework>`__
@@ -377,7 +376,7 @@ class Array:
     def __init__(self, namespace: Namespace,
                  tags: Optional[TagsType] = None):
         if tags is None:
-            tags = {}
+            tags = frozenset()
 
         self.namespace = namespace
         self.tags = tags
@@ -404,11 +403,17 @@ class Array:
         tags of this type are already present, an error
         is raised.
         """
-        raise NotImplementedError
-        return self.copy()
+        return self.copy(tags=self.tags | frozenset([tag]))
 
-    def without_tag(self, dotted_name: DottedName) -> Array:
-        raise NotImplementedError
+    def without_tag(self, tag: Tag, verify_existence: bool = True) -> Array:
+        new_tags = tuple(
+                t for t in self.tags
+                if t != tag)
+
+        if verify_existence and len(new_tags) == len(self.tags):
+            raise ValueError(f"tag '{tag}' was not present")
+
+        return self.copy(tags=new_tags)
 
     # TODO:
     # - codegen interface
@@ -536,7 +541,7 @@ class IndexLambda(Array):
             self, namespace: Namespace, expr: prim.Expression,
             shape: ShapeType, dtype: np.dtype,
             bindings: Optional[Dict[str, Array]] = None,
-            tags: Optional[Dict[DottedName, Tag]] = None):
+            tags: Optional[TagsType] = None):
 
         if bindings is None:
             bindings = {}