diff --git a/ibis/backends/pandas/rewrites.py b/ibis/backends/pandas/rewrites.py
index 87ab218c472b1..d5e1af1e88760 100644
--- a/ibis/backends/pandas/rewrites.py
+++ b/ibis/backends/pandas/rewrites.py
@@ -325,11 +325,11 @@ def rewrite_limit(_, **kwargs):
 
     n = n.as_table().op()
     if isinstance(n, ops.Aggregate):
-        n = rewrite_aggregate.match(n, context={})
+        n = rewrite_aggregate.apply(n)
 
     offset = offset.as_table().op()
     if isinstance(offset, ops.Aggregate):
-        offset = rewrite_aggregate.match(offset, context={})
+        offset = rewrite_aggregate.apply(offset)
 
     return PandasLimit(_.parent, n, offset)
 
diff --git a/ibis/expr/datatypes/core.py b/ibis/expr/datatypes/core.py
index 3efde71630cdc..569e3ad4c0e85 100644
--- a/ibis/expr/datatypes/core.py
+++ b/ibis/expr/datatypes/core.py
@@ -462,7 +462,7 @@ def is_variadic(self) -> bool:
 
 
 @public
-class Unknown(DataType):
+class Unknown(DataType, singleton=True):
     """An unknown type."""
 
     scalar = "UnknownScalar"
@@ -470,7 +470,7 @@ class Unknown(DataType):
 
 
 @public
-class Primitive(DataType):
+class Primitive(DataType, singleton=True):
     """Values with known size."""
 
 
@@ -531,7 +531,7 @@ def nbytes(self) -> int:
 
 
 @public
-class String(Variadic):
+class String(Variadic, singleton=True):
     """A type representing a string.
 
     Notes
@@ -546,7 +546,7 @@ class String(Variadic):
 
 
 @public
-class Binary(Variadic):
+class Binary(Variadic, singleton=True):
     """A type representing a sequence of bytes.
 
     Notes
diff --git a/ibis/expr/datatypes/tests/test_core.py b/ibis/expr/datatypes/tests/test_core.py
index cc48dcbca40f5..c1364509476ad 100644
--- a/ibis/expr/datatypes/tests/test_core.py
+++ b/ibis/expr/datatypes/tests/test_core.py
@@ -432,20 +432,30 @@ def test_struct_equality():
     assert st3 != st2
 
 
-def test_booleqn_equality():
+
+def test_singleton_datatypes():
+    assert dt.null is dt.Null()
+    assert dt.unknown is dt.Unknown()
+    assert dt.boolean is dt.Boolean()
+    assert dt.string is dt.String()
+    assert dt.binary is dt.Binary()
+
+
+def test_singleton_boolean():
     assert dt.Boolean() == dt.boolean
-    assert dt.Boolean() == dt.Boolean()
-    assert dt.Boolean(nullable=True) == dt.boolean
-    assert dt.Boolean(nullable=False) != dt.boolean
-    assert dt.Boolean(nullable=False) == dt.Boolean(nullable=False)
-    assert dt.Boolean(nullable=True) == dt.Boolean(nullable=True)
-    assert dt.Boolean(nullable=True) != dt.Boolean(nullable=False)
-
-
-def test_primite_equality():
-    assert dt.Int64() == dt.int64
-    assert dt.Int64(nullable=False) != dt.int64
-    assert dt.Int64(nullable=False) == dt.Int64(nullable=False)
+    assert dt.Boolean() is dt.boolean
+    assert dt.Boolean() is dt.Boolean()
+    assert dt.Boolean(nullable=True) is dt.boolean
+    assert dt.Boolean(nullable=False) is not dt.boolean
+    assert dt.Boolean(nullable=False) is dt.Boolean(nullable=False)
+    assert dt.Boolean(nullable=True) is dt.Boolean(nullable=True)
+    assert dt.Boolean(nullable=True) is not dt.Boolean(nullable=False)
+
+
+def test_singleton_primitive():
+    assert dt.Int64() is dt.int64
+    assert dt.Int64(nullable=False) is not dt.int64
+    assert dt.Int64(nullable=False) is dt.Int64(nullable=False)
 
 
 def test_array_type_not_equals():
diff --git a/ibis/expr/operations/generic.py b/ibis/expr/operations/generic.py
index a509964a0de30..d461f129fa30c 100644
--- a/ibis/expr/operations/generic.py
+++ b/ibis/expr/operations/generic.py
@@ -175,7 +175,7 @@ def name(self):
 
 
 @public
-class Constant(Scalar):
+class Constant(Scalar, singleton=True):
     """A function that produces a constant."""
 
     shape = ds.scalar
diff --git a/ibis/expr/operations/relations.py b/ibis/expr/operations/relations.py
index 74983a5d0d96f..44e7a20bdc10c 100644
--- a/ibis/expr/operations/relations.py
+++ b/ibis/expr/operations/relations.py
@@ -378,7 +378,7 @@ class Difference(Set):
 class PhysicalTable(Relation):
     """Base class for tables with a name."""
 
-    __slot__ = ("__weakref__",)
+    __slots__ = ("__weakref__",)
 
     name: str
     values = FrozenOrderedDict()