diff --git a/transforge/bag.py b/transforge/bag.py
new file mode 100644
index 0000000..4b4fdcb
--- /dev/null
+++ b/transforge/bag.py
@@ -0,0 +1,76 @@
+from __future__ import annotations
+
+from transforge.type import Type
+from typing import Iterator, Iterable
+from collections.abc import MutableSet
+
+class TypeUnion(MutableSet[Type]):
+
+    def __init__(self, xs: Iterable[Type] = ()) -> None:
+        self.data: set[Type] = set()
+        for x in xs:
+            self.add(x)
+
+    def __contains__(self, value: object) -> bool:
+        return value in self.data
+
+    def __iter__(self) -> Iterator[Type]:
+        return iter(self.data)
+
+    def __len__(self) -> int:
+        return len(self.data)
+
+    def __repr__(self) -> str:
+        return repr(self.data)
+
+    def is_subtype(self, other: Type | "TypeUnion") -> bool:
+        if isinstance(other, Type):
+            return bool(self) and all(x.is_subtype(other) for x in self.data)
+        else:
+            assert isinstance(other, TypeUnion)
+            return bool(self) and all(all(x.is_subtype(y) for x in self.data) 
+                for y in other.data)
+
+    def add(self, new: Type) -> None:
+        to_remove = set()
+        for t in self.data:
+            if new.is_subtype(t):
+                to_remove.add(t)
+            elif t.is_subtype(new):
+                return
+        self.data -= to_remove
+        self.data.add(new)
+
+    def discard(self, item: Type) -> None:
+        self.data.discard(item)
+
+
+# TODO: sort on type depth, so that the most specific types are checked first
+class Bag(object):
+    """A bag of types is a conjunction of disjunctions (cq intersection of 
+    unions) of concrete types. A bag is unordered and contains no duplicates, 
+    nor even supertypes of types that are already in the bag. That is, if you 
+    have a type A with subtypes B and C, then adding A, and either B or C will 
+    result in a bag containing only either B or C."""
+
+    def __init__(self) -> None:
+        self.content: list[TypeUnion] = []
+
+    def add(self, *new_types: Type):
+        """Add a type to the bag. If multiple types are given, the union of 
+        these types is added."""
+
+        # Any disjuncts that are covered already by other types in the bag can 
+        # be dropped
+        new = TypeUnion(nt for nt in new_types
+            if any(t.is_subtype(nt) for t in self.content))
+
+        if not new:
+            return
+
+        # Conversely, any types in the bag that are obsoleted by the new type 
+        # can also be removed
+        self.content = [c for c in self.content
+            if not new.is_subtype(c)]
+
+        self.content.append(new)
diff --git a/transforge/query.py b/transforge/query.py
index 7a95d0c..d33e8ce 100644
--- a/transforge/query.py
+++ b/transforge/query.py
@@ -19,6 +19,7 @@
 from transforge.lang import Language
 from transforge.graph import (
     TransformationGraph, CyclicTransformationGraphError)
+from transforge.bag import Bag
 
 
 def union(prefix: str, subjects: Iterable[Node]) -> Iterator[str]:
@@ -232,30 +233,21 @@ def sparql(*elems: str | Iterable[str]) -> str:
         return result
 
     def types(self) -> Iterator[str]:
-        """
-        Conditions for matching on the bag of types used in a query.
-        """
-
-        # Only the types that *definitely* occur
-        types: set[URIRef] = set()
-        for type_choice in self.type.values():
-            if len(type_choice) == 1:
-                assert isinstance(type_choice[0], URIRef)
-                types.add(type_choice[0])
-
-        for type in types:
-            yield f"?workflow :contains/rdfs:subClassOf* {type.n3()}."
-            # yield f"{next(self.generator).n3()} {next(self.generator).n3()}
-            # {type.n3()}."
-
-        # Also include union types. TODO this is temporary until #79 is
-        # resolved; see also:
-        # https://github.com/quangis/transformation-algebra/issues/77#issuecomment-1215064807
-        for type_choice in self.type.values():
-            if len([t for t in type_choice if t not in types]) >= 2:
-                yield from union(
-                    f"{next(self.generator).n3()} {next(self.generator).n3()}",
-                    type_choice)
+        """Conditions for matching on the bag of types used in a query."""
+        # See also issues 79 and 77
+
+        bag = Bag()
+        for tus in self.type.values():
+            bag.add(*(self.lang.parse_type_uri(tu) for tu in tus))
+
+        for ts in bag.content:
+            if len(ts) == 1:
+                yield (
+                    f"?workflow :contains/rdfs:subClassOf* "
+                    f"{self.lang.uri(next(iter(ts))).n3()}.")
+            elif len(ts) > 1:
+                yield from union("?workflow :contains/rdfs:subClassOf* ", 
+                    (self.lang.uri(t) for t in ts))
 
     def operators(self) -> Iterator[str]:
         """