diff --git a/decent_array/_constants.py b/decent_array/_constants.py
index a05e32b..a53514d 100644
--- a/decent_array/_constants.py
+++ b/decent_array/_constants.py
@@ -2,9 +2,24 @@
 
 import math
 
-_CONSTANTS = ["e", "inf", "nan", "pi"]
+_CONSTANTS = {
+    "e": math.e,
+    "inf": math.inf,
+    "nan": math.nan,
+    "pi": math.pi,
+}
 
-e = math.e
-inf = math.inf
-nan = math.nan
-pi = math.pi
+e = _CONSTANTS["e"]
+inf = _CONSTANTS["inf"]
+nan = _CONSTANTS["nan"]
+pi = _CONSTANTS["pi"]
+
+
+def _reset() -> None:
+    """Set/reset constants to the Python math defaults."""
+    global e, inf, nan, pi  # noqa: PLW0603
+
+    e = _CONSTANTS["e"]
+    inf = _CONSTANTS["inf"]
+    nan = _CONSTANTS["nan"]
+    pi = _CONSTANTS["pi"]
diff --git a/decent_array/interoperability/_backend_manager.py b/decent_array/interoperability/_backend_manager.py
index c897fea..658f5aa 100644
--- a/decent_array/interoperability/_backend_manager.py
+++ b/decent_array/interoperability/_backend_manager.py
@@ -131,6 +131,17 @@ def reset_backends() -> None:
     for listener in _BACKEND_LISTENERS:
         listener(None)
 
+    # clear dtypes bindings
+    for dt in dtypes._ALL_DTYPES:  # noqa: SLF001
+        dt._available = False  # noqa: SLF001
+        dt._backend_dtype = None  # noqa: SLF001
+
+    dtypes._AVAILABLE_DTYPES.clear()  # noqa: SLF001
+    dtypes._BACKEND_DTYPE_TO_DTYPE.clear()  # noqa: SLF001
+
+    # clear constants bindings, restoring to Python math defaults
+    constants._reset()  # noqa: SLF001
+
 
 def default_device() -> Devices:
     """
@@ -219,6 +230,14 @@ def _bind_dtypes(backend: Backend | None) -> None:
         dt._available = backend_dt is not None  # noqa: SLF001
         dt._backend_dtype = backend_dt  # noqa: SLF001
 
+    # refresh caches of available dtypes and reverse mapping
+    dtypes._AVAILABLE_DTYPES.clear()  # noqa: SLF001
+    dtypes._AVAILABLE_DTYPES.update(dt for dt in dtypes._ALL_DTYPES if dt.available)  # noqa: SLF001
+
+    dtypes._BACKEND_DTYPE_TO_DTYPE.clear()  # noqa: SLF001
+    for dt in dtypes._AVAILABLE_DTYPES:  # noqa: SLF001
+        dtypes._BACKEND_DTYPE_TO_DTYPE[dt.backend_dtype] = dt  # noqa: SLF001
+
 
 def _bind_constants(backend: Backend | None) -> None:
     """Bind constants to the corresponding backend constants."""
@@ -226,6 +245,5 @@ def _bind_constants(backend: Backend | None) -> None:
         return
     for name in constants._CONSTANTS:  # noqa: SLF001
         backend_c = getattr(backend, name, None)
-        if backend_c is None:
-            return
-        setattr(constants, name, backend_c)
+        if backend_c is not None:
+            setattr(constants, name, backend_c)
diff --git a/decent_array/types/_dtypes.py b/decent_array/types/_dtypes.py
index f8dec4c..63334c8 100644
--- a/decent_array/types/_dtypes.py
+++ b/decent_array/types/_dtypes.py
@@ -74,7 +74,7 @@ def __eq__(self, other: object) -> bool:
         """Check equivalence by ``name`` attributes."""
         if not isinstance(other, dtype):
             return NotImplemented
-        return self.name == other.name and self.available and other.available
+        return self.name == other.name
 
     def __hash__(self) -> int:
         """Hash of the dtype."""
@@ -131,12 +131,9 @@ def __hash__(self) -> int:
 _ALL_DTYPES = _BOOL_DTYPES | _NUMERIC_DTYPES | _MISCELLANEOUS_DTYPES
 
 
-_AVAILABLE_DTYPES = {dt for dt in _ALL_DTYPES if dt.available}
-
-
+# caches for available dtypes and reverse mapping; these are populated during set_backend
+_AVAILABLE_DTYPES: set[dtype] = set()
 _BACKEND_DTYPE_TO_DTYPE: dict[Any, dtype] = {}
-for dt in _AVAILABLE_DTYPES:
-    _BACKEND_DTYPE_TO_DTYPE[dt._backend_dtype] = dt  # noqa: SLF001
 
 
 _ALIASES = {
diff --git a/pyproject.toml b/pyproject.toml
index 937c05c..738be87 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [project]
 name = "decent-array"
-version = "0.2.3"
+version = "0.2.4"
 authors = [{name = "Simon Granström"}, {name = "Nicola Bastianello"}]
 maintainers = [{name = "Team Decent"}]
 description = "A library of array operations and linear algebra primitives for interoperability across ML frameworks."
diff --git a/tests/test_backend_manager.py b/tests/test_backend_manager.py
index 8e890c6..98e153c 100644
--- a/tests/test_backend_manager.py
+++ b/tests/test_backend_manager.py
@@ -98,8 +98,15 @@ def test_set_backend_instantiates_dtypes() -> None:
     dt2 = float32  # global dtype bound during set_dtype
     dt3 = dtype("float32")  # backend is set, so this is bound to backend dtype
 
-    assert dt1 != dt2  # dtypes are not equal if not avaiable, and dt1 is not available
-    assert dt2 == dt3  # available because bound to backend, and equal
+    # check availability status
+    assert not dt1.available
+    assert dt2.available
+    assert dt3.available
+
+    # equality check the name attribute, so all these should be true (irrespective of availability)
+    assert dt1 == dt2
+    assert dt1 == dt3
+    assert dt2 == dt3
 
     dt4 = dtype("int16")
     assert dt3 != dt4
diff --git a/tests/test_bindings.py b/tests/test_bindings.py
new file mode 100644
index 0000000..4c13e7c
--- /dev/null
+++ b/tests/test_bindings.py
@@ -0,0 +1,92 @@
+"""Tests for dtype initialization and backend binding."""
+
+from __future__ import annotations
+
+import math
+import pytest
+
+from decent_array.interoperability import _backend_manager
+from decent_array.interoperability._backend_manager import reset_backends
+from decent_array.types import _dtypes
+import decent_array._constants as constants
+
+
+@pytest.fixture(autouse=True)
+def reset_backend_state():
+    """Reset backend state before and after each test."""
+    reset_backends()
+    yield
+    reset_backends()
+
+
+def test_all_dtypes_are_bound_to_backend(backend: tuple) -> None:
+    """Every dtype is bound to the corresponding backend attribute."""
+    backend_instance = _backend_manager._BACKEND_INSTANCE
+
+    assert backend_instance is not None
+
+    for name in _dtypes._SUPPORTED:
+        dt = getattr(_dtypes, name)
+        expected_backend_dtype = getattr(backend_instance, name, None)
+
+        assert dt.backend_dtype is expected_backend_dtype
+        assert dt.available is (expected_backend_dtype is not None)
+
+
+def test_available_dtypes_cache_is_correct(backend: tuple) -> None:
+    expected = {
+        dt for dt in _dtypes._ALL_DTYPES if dt.available
+    }
+
+    assert _dtypes._AVAILABLE_DTYPES == expected
+
+
+def test_dtypes_returns_only_available_dtypes(backend: tuple) -> None:
+    available = _dtypes.dtypes()
+
+    assert available
+    assert all(dt.available for dt in available.values())
+    assert set(available.values()) == _dtypes._AVAILABLE_DTYPES
+
+
+def test_backend_dtype_mapping_is_correct(backend: tuple) -> None:
+    expected = {
+        dt.backend_dtype: dt
+        for dt in _dtypes._AVAILABLE_DTYPES
+    }
+
+    assert _dtypes._BACKEND_DTYPE_TO_DTYPE == expected
+
+    for dt in _dtypes._AVAILABLE_DTYPES:
+        assert (
+            _dtypes._BACKEND_DTYPE_TO_DTYPE[dt.backend_dtype]
+            is dt
+        )
+
+
+def test_reset_clears_dtype_bindings(backend: tuple) -> None:
+    """Resetting backends clears dtype bindings and caches."""
+    assert _backend_manager._BACKEND_INSTANCE is not None
+    assert _dtypes._AVAILABLE_DTYPES
+
+    reset_backends()
+
+    assert _backend_manager._BACKEND_INSTANCE is None
+    assert not _dtypes._AVAILABLE_DTYPES
+    assert not _dtypes._BACKEND_DTYPE_TO_DTYPE
+
+    for dt in _dtypes._ALL_DTYPES:
+        assert dt.available is False
+        assert dt.backend_dtype is None
+
+
+def test_reset_restores_default_constants(backend: tuple) -> None:
+    """Resetting the backend restores Python math defaults."""
+    assert _backend_manager._BACKEND_INSTANCE is not None
+
+    reset_backends()
+
+    assert constants.e == math.e
+    assert constants.inf == math.inf
+    assert math.isnan(constants.nan)
+    assert constants.pi == math.pi