diff --git a/src/resolvelib/resolvers.pyi b/src/resolvelib/resolvers.pyi
index 0eb5b21..528a1a2 100644
--- a/src/resolvelib/resolvers.pyi
+++ b/src/resolvelib/resolvers.pyi
@@ -55,6 +55,18 @@ class ResolutionImpossible(ResolutionError, Generic[RT, CT]):
 class ResolutionTooDeep(ResolutionError):
     round_count: int
 
+# This should be a NamedTuple, but Python 3.6 has a bug that prevents it.
+# https://stackoverflow.com/a/50531189/1376863
+class State(tuple, Generic[RT, CT, KT]):
+    mapping: Mapping[KT, CT]
+    criteria: Mapping[KT, Criterion[RT, CT, KT]]
+    backtrack_causes: Collection[RequirementInformation[RT, CT]]
+
+class Resolution(Generic[RT, CT, KT]):
+    def resolve(
+        self, requirements: Iterable[RT], max_rounds: int
+    ) -> State[RT, CT, KT]: ...
+
 class Result(Generic[RT, CT, KT]):
     mapping: Mapping[KT, CT]
     graph: DirectedGraph[Optional[KT]]
diff --git a/tests/test_resolvers.py b/tests/test_resolvers.py
index 01159e9..176108f 100644
--- a/tests/test_resolvers.py
+++ b/tests/test_resolvers.py
@@ -21,11 +21,11 @@
     ResolutionImpossible,
     Resolver,
 )
-from resolvelib.resolvers import Resolution  # type: ignore
 from resolvelib.resolvers import (
     Criterion,
     RequirementInformation,
     RequirementsConflicted,
+    Resolution,
 )
 
 
@@ -187,7 +187,7 @@ def test_pin_conflict_with_self(monkeypatch, reporter):
         ],
     }  # type: Mapping[str, Sequence[Candidate]]
 
-    class Provider(AbstractProvider):  # AbstractProvider[int, Candidate, str]
+    class Provider(AbstractProvider):  # AbstractProvider[str, Candidate, str]
         def identify(self, requirement_or_candidate):
             # type: (Union[str, Candidate]) -> str
             result = (
@@ -230,7 +230,9 @@ def is_satisfied_by(self, requirement, candidate):
 
     # patch Resolution._get_updated_criteria to collect rejected states
     rejected_criteria = []  # type: List[Criterion]
-    get_updated_criteria_orig = Resolution._get_updated_criteria
+    get_updated_criteria_orig = (
+        Resolution._get_updated_criteria  # type: ignore[attr-defined]
+    )
 
     def get_updated_criteria_patch(self, candidate):
         try: