Clean up aesara.graph.optdb docstrings and signatures

tests/graph/test_optdb.py

 import pytest
 
-from aesara.graph.optdb import OptimizationDatabase, opt
+from aesara.graph import opt
+from aesara.graph.optdb import (
+    EquilibriumDB,
+    LocalGroupDB,
+    OptimizationDatabase,
+    ProxyDB,
+    SequenceDB,
+)
 
 
-class TestDB:
-    def test_name_clashes(self):
-        class Opt(opt.GlobalOptimizer):  # inheritance buys __hash__
-            name = "blah"
+class TestOpt(opt.GlobalOptimizer):
+    name = "blah"
+
+    def apply(self, fgraph):
+        pass
 
-            def apply(self, fgraph):
-                pass
 
+class TestDB:
+    def test_register(self):
         db = OptimizationDatabase()
-        db.register("a", Opt())
+        db.register("a", TestOpt())
 
-        db.register("b", Opt())
+        db.register("b", TestOpt())
 
-        db.register("c", Opt(), "z", "asdf")
+        db.register("c", TestOpt(), "z", "asdf")
 
         assert "a" in db
         assert "b" in db
         assert "c" in db
 
-        with pytest.raises(ValueError, match=r"The name.*"):
-            db.register("c", Opt())  # name taken
+        with pytest.raises(ValueError, match=r"The tag.*"):
+            db.register("c", TestOpt())  # name taken
 
-        with pytest.raises(ValueError, match=r"The name.*"):
-            db.register("z", Opt())  # name collides with tag
+        with pytest.raises(ValueError, match=r"The tag.*"):
+            db.register("z", TestOpt())  # name collides with tag
 
         with pytest.raises(ValueError, match=r"The tag.*"):
-            db.register("u", Opt(), "b")  # name new but tag collides with name
+            db.register("u", TestOpt(), "b")  # name new but tag collides with name
+
+        with pytest.raises(TypeError, match=r".* is not a valid.*"):
+            db.register("d", 1)
+
+    def test_EquilibriumDB(self):
+        eq_db = EquilibriumDB()
+
+        with pytest.raises(ValueError, match=r"`final_opt` and.*"):
+            eq_db.register("d", TestOpt(), final_opt=True, cleanup=True)
+
+    def test_SequenceDB(self):
+        seq_db = SequenceDB(failure_callback=None)
+
+        res = seq_db.query("+a")
+
+        assert isinstance(res, opt.SeqOptimizer)
+        assert res.data == []
+
+        seq_db.register("b", TestOpt(), 1)
+
+        from io import StringIO
+
+        out_file = StringIO()
+        seq_db.print_summary(stream=out_file)
+
+        res = out_file.getvalue()
+
+        assert str(id(seq_db)) in res
+        assert "names {'b'}" in res
+
+        with pytest.raises(TypeError, match=r"`position` must be.*"):
+            seq_db.register("c", TestOpt(), object())
+
+    def test_LocalGroupDB(self):
+        lg_db = LocalGroupDB()
+
+        lg_db.register("a", TestOpt(), 1)
+
+        assert "a" in lg_db.__position__
+
+        with pytest.raises(TypeError, match=r"`position` must be.*"):
+            lg_db.register("b", TestOpt(), position=object())
+
+    def test_ProxyDB(self):
+        with pytest.raises(TypeError, match=r"`db` must be.*"):
+            ProxyDB(object())