From 64b784a834b8a31ca80a6a33a4e0c1059ffa2c22 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 11 Aug 2022 23:53:41 -0700
Subject: [PATCH 01/21] drop tensor, fix up missing imports

---
 .pre-commit-config.yaml |  2 ++
 pyproject.toml          | 12 +++---------
 2 files changed, 5 insertions(+), 9 deletions(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 872031c3af..5cd71c50de 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -65,6 +65,8 @@ repos:
       - id: mypy
         files: src
         args: []
+        additional_dependencies:
+          ['numpy', 'torch', 'jax', 'types-tqdm', 'click', 'types-jsonpatch', 'types-pyyaml', 'types-jsonschema', 'importlib_metadata', 'packaging']
 
 -   repo: https://github.com/nbQA-dev/nbQA
     rev: 1.4.0
diff --git a/pyproject.toml b/pyproject.toml
index 263802fb50..53187fdd8b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -109,23 +109,17 @@ warn_unreachable = true
 [[tool.mypy.overrides]]
 module = [
   'matplotlib.*',
-  'jax.*',
-  'click.*',
-  'click_completion.*',
-  'numpy.*',
   'scipy.*',
-  'jsonpatch.*',
+  'tensorflow.*',
+  'tensorflow_probability.*',
   'uproot.*',
-  'yaml.*',
-  'jsonschema.*',
-  'tqdm.*',
 ]
 ignore_missing_imports = true
 
+
 [[tool.mypy.overrides]]
 module = [
   'pyhf',
-  'pyhf.tensor.*',
   'pyhf.optimize.*',
   'pyhf.contrib.*',
   'pyhf.infer.*',

From 6079e6f920f28865e61fb5f621ba3f8c6089a54f Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 12 Aug 2022 11:06:22 -0700
Subject: [PATCH 02/21] get precommit working

---
 .pre-commit-config.yaml | 2 +-
 pyproject.toml          | 2 ++
 2 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 5cd71c50de..7a216a36ed 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -66,7 +66,7 @@ repos:
         files: src
         args: []
         additional_dependencies:
-          ['numpy', 'torch', 'jax', 'types-tqdm', 'click', 'types-jsonpatch', 'types-pyyaml', 'types-jsonschema', 'importlib_metadata', 'packaging']
+          ['numpy', 'types-tqdm', 'click', 'types-jsonpatch', 'types-pyyaml', 'types-jsonschema', 'importlib_metadata', 'packaging']
 
 -   repo: https://github.com/nbQA-dev/nbQA
     rev: 1.4.0
diff --git a/pyproject.toml b/pyproject.toml
index 53187fdd8b..b108e29be8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -108,10 +108,12 @@ warn_unreachable = true
 
 [[tool.mypy.overrides]]
 module = [
+  'jax.*',
   'matplotlib.*',
   'scipy.*',
   'tensorflow.*',
   'tensorflow_probability.*',
+  'torch.*',
   'uproot.*',
 ]
 ignore_missing_imports = true

From 15c17ca4ccbc3726b4f087ce08308d94f5046867 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Sat, 13 Aug 2022 09:39:16 -0700
Subject: [PATCH 03/21] start typing numpy backend

---
 pyproject.toml | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/pyproject.toml b/pyproject.toml
index b108e29be8..af3d331ad0 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -142,5 +142,11 @@ module = [
   'pyhf.pdf',
   'pyhf.simplemodels',
   'pyhf.probability',
+  'pyhf.tensor.common.*',
+  'pyhf.tensor.manager.*',
+  'pyhf.tensor',
+  'pyhf.tensor.jax_backend.*',
+  'pyhf.tensor.tensorflow_backend.*',
+  'pyhf.tensor.pytorch_backend.*',
 ]
 ignore_errors = true

From 2e05145971e64fab025c076a0aafee94c4a84d7f Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Sat, 13 Aug 2022 09:39:46 -0700
Subject: [PATCH 04/21] first typed up version

---
 src/pyhf/tensor/numpy_backend.py | 150 ++++++++++++++++++++-----------
 1 file changed, 96 insertions(+), 54 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index f97e05d198..4b7cf3b379 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -5,56 +5,74 @@
 from scipy import special
 from scipy.stats import norm, poisson
 
+from typing import TypeVar, Callable, Literal, Sequence, Generic, Tuple, Mapping
+from numpy.typing import (
+    NDArray,
+    NBitBase,
+    ArrayLike,
+)
+
+Shape = Tuple[int, ...]
 
 log = logging.getLogger(__name__)
 
+T = TypeVar("T", bound=NBitBase)
+Tensor = NDArray[np.floating[T]]
+
 
-class _BasicPoisson:
-    def __init__(self, rate):
+class _BasicPoisson(Generic[T]):
+    def __init__(self, rate: Tensor[T]):
         self.rate = rate
 
-    def sample(self, sample_shape):
+    def sample(self, sample_shape: NDArray[np.integer[T]]) -> Tensor[T]:
         return poisson(self.rate).rvs(size=sample_shape + self.rate.shape)
 
-    def log_prob(self, value):
+    def log_prob(self, value: NDArray[np.number[T]]) -> Tensor[T]:
         tensorlib = numpy_backend()
         return tensorlib.poisson_logpdf(value, self.rate)
 
 
-class _BasicNormal:
-    def __init__(self, loc, scale):
+class _BasicNormal(Generic[T]):
+    def __init__(self, loc: NDArray[np.number[T]], scale: NDArray[np.number[T]]):
         self.loc = loc
         self.scale = scale
 
-    def sample(self, sample_shape):
+    def sample(self, sample_shape: NDArray[np.integer[T]]) -> Tensor[T]:
         return norm(self.loc, self.scale).rvs(size=sample_shape + self.loc.shape)
 
-    def log_prob(self, value):
+    def log_prob(self, value: NDArray[np.number[T]]) -> Tensor[T]:
         tensorlib = numpy_backend()
         return tensorlib.normal_logpdf(value, self.loc, self.scale)
 
 
-class numpy_backend:
+class numpy_backend(Generic[T]):
     """NumPy backend for pyhf"""
 
     __slots__ = ['name', 'precision', 'dtypemap', 'default_do_grad']
 
-    def __init__(self, **kwargs):
+    def __init__(self, **kwargs: dict[str, str]):
         self.name = 'numpy'
         self.precision = kwargs.get('precision', '64b')
-        self.dtypemap = {
+        self.dtypemap: Mapping[
+            Literal['float', 'int', 'bool'], np.floating[T] | np.integer[T] | np.bool_
+        ] = {
             'float': np.float64 if self.precision == '64b' else np.float32,
             'int': np.int64 if self.precision == '64b' else np.int32,
             'bool': np.bool_,
         }
         self.default_do_grad = False
 
-    def _setup(self):
+    def _setup(self) -> None:
         """
         Run any global setups for the numpy lib.
         """
 
-    def clip(self, tensor_in, min_value, max_value):
+    def clip(
+        self,
+        tensor_in: Tensor[T],
+        min_value: np.integer[T] | np.floating[T],
+        max_value: np.integer[T] | np.floating[T],
+    ) -> Tensor[T]:
         """
         Clips (limits) the tensor values to be within a specified min and max.
 
@@ -76,7 +94,7 @@ def clip(self, tensor_in, min_value, max_value):
         """
         return np.clip(tensor_in, min_value, max_value)
 
-    def erf(self, tensor_in):
+    def erf(self, tensor_in: Tensor[T]) -> Tensor[T]:
         """
         The error function of complex argument.
 
@@ -96,7 +114,7 @@ def erf(self, tensor_in):
         """
         return special.erf(tensor_in)
 
-    def erfinv(self, tensor_in):
+    def erfinv(self, tensor_in: Tensor[T]) -> Tensor[T]:
         """
         The inverse of the error function of complex argument.
 
@@ -116,7 +134,7 @@ def erfinv(self, tensor_in):
         """
         return special.erfinv(tensor_in)
 
-    def tile(self, tensor_in, repeats):
+    def tile(self, tensor_in: Tensor[T], repeats: int | Sequence[int]) -> Tensor[T]:
         """
         Repeat tensor data along a specific dimension
 
@@ -138,7 +156,12 @@ def tile(self, tensor_in, repeats):
         """
         return np.tile(tensor_in, repeats)
 
-    def conditional(self, predicate, true_callable, false_callable):
+    def conditional(
+        self,
+        predicate: NDArray[np.bool_],
+        true_callable: Callable[[], Tensor[T]],
+        false_callable: Callable[[], Tensor[T]],
+    ) -> Tensor[T]:
         """
         Runs a callable conditional on the boolean value of the evaluation of a predicate
 
@@ -162,7 +185,7 @@ def conditional(self, predicate, true_callable, false_callable):
         """
         return true_callable() if predicate else false_callable()
 
-    def tolist(self, tensor_in):
+    def tolist(self, tensor_in: ArrayLike) -> list[T]:
         try:
             return tensor_in.tolist()
         except AttributeError:
@@ -170,19 +193,21 @@ def tolist(self, tensor_in):
                 return tensor_in
             raise
 
-    def outer(self, tensor_in_1, tensor_in_2):
+    def outer(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> Tensor[T]:
         return np.outer(tensor_in_1, tensor_in_2)
 
-    def gather(self, tensor, indices):
+    def gather(self, tensor: Tensor[T], indices: NDArray[np.integer[T]]) -> Tensor[T]:
         return tensor[indices]
 
-    def boolean_mask(self, tensor, mask):
+    def boolean_mask(self, tensor: Tensor[T], mask: NDArray[np.bool_]) -> Tensor[T]:
         return tensor[mask]
 
-    def isfinite(self, tensor):
+    def isfinite(self, tensor: Tensor[T]) -> NDArray[np.bool_]:
         return np.isfinite(tensor)
 
-    def astensor(self, tensor_in, dtype='float'):
+    def astensor(
+        self, tensor_in: ArrayLike, dtype: Literal['float'] = 'float'
+    ) -> Tensor[T]:
         """
         Convert to a NumPy array.
 
@@ -213,18 +238,20 @@ def astensor(self, tensor_in, dtype='float'):
 
         return np.asarray(tensor_in, dtype=dtype)
 
-    def sum(self, tensor_in, axis=None):
+    def sum(self, tensor_in: Tensor[T], axis: int | None = None) -> Tensor[T]:
         return np.sum(tensor_in, axis=axis)
 
-    def product(self, tensor_in, axis=None):
+    def product(self, tensor_in: Tensor[T], axis: int | None = None) -> Tensor[T]:
         return np.product(tensor_in, axis=axis)
 
-    def abs(self, tensor):
+    def abs(self, tensor: Tensor[T]) -> Tensor[T]:
         return np.abs(tensor)
 
-    def ones(self, shape, dtype="float"):
+    def ones(
+        self, shape: Shape, dtype_str: Literal["float", "int", "bool"] = "float"
+    ) -> Tensor[T]:
         try:
-            dtype = self.dtypemap[dtype]
+            dtype = self.dtypemap[dtype_str]
         except KeyError:
             log.error(
                 f"Invalid dtype: dtype must be one of {list(self.dtypemap.keys())}.",
@@ -234,9 +261,11 @@ def ones(self, shape, dtype="float"):
 
         return np.ones(shape, dtype=dtype)
 
-    def zeros(self, shape, dtype="float"):
+    def zeros(
+        self, shape: Shape, dtype_str: Literal["float", "int", "bool"] = "float"
+    ) -> Tensor[T]:
         try:
-            dtype = self.dtypemap[dtype]
+            dtype = self.dtypemap[dtype_str]
         except KeyError:
             log.error(
                 f"Invalid dtype: dtype must be one of {list(self.dtypemap.keys())}.",
@@ -246,22 +275,30 @@ def zeros(self, shape, dtype="float"):
 
         return np.zeros(shape, dtype=dtype)
 
-    def power(self, tensor_in_1, tensor_in_2):
+    def power(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> Tensor[T]:
         return np.power(tensor_in_1, tensor_in_2)
 
-    def sqrt(self, tensor_in):
+    def sqrt(self, tensor_in: Tensor[T]) -> Tensor[T]:
         return np.sqrt(tensor_in)
 
-    def divide(self, tensor_in_1, tensor_in_2):
+    def divide(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> Tensor[T]:
         return np.divide(tensor_in_1, tensor_in_2)
 
-    def log(self, tensor_in):
+    def log(self, tensor_in: Tensor[T]) -> Tensor[T]:
         return np.log(tensor_in)
 
-    def exp(self, tensor_in):
+    def exp(self, tensor_in: Tensor[T]) -> Tensor[T]:
         return np.exp(tensor_in)
 
-    def percentile(self, tensor_in, q, axis=None, interpolation="linear"):
+    def percentile(
+        self,
+        tensor_in: Tensor[T],
+        q: Tensor[T],
+        axis: None | Shape = None,
+        interpolation: Literal[
+            "linear", "lower", "higher", "midpoint", "nearest"
+        ] = "linear",
+    ) -> Tensor[T]:
         r"""
         Compute the :math:`q`-th percentile of the tensor along the specified axis.
 
@@ -297,15 +334,18 @@ def percentile(self, tensor_in, q, axis=None, interpolation="linear"):
             NumPy ndarray: The value of the :math:`q`-th percentile of the tensor along the specified axis.
 
         """
-        return np.percentile(tensor_in, q, axis=axis, interpolation=interpolation)
+        # see numpy/numpy#22125
+        return np.percentile(tensor_in, q, axis=axis, interpolation=interpolation)  # type: ignore[call-overload]
 
-    def stack(self, sequence, axis=0):
+    def stack(self, sequence: Sequence[Tensor[T]], axis: int = 0) -> Tensor[T]:
         return np.stack(sequence, axis=axis)
 
-    def where(self, mask, tensor_in_1, tensor_in_2):
+    def where(
+        self, mask: NDArray[np.bool_], tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]
+    ) -> Tensor[T]:
         return np.where(mask, tensor_in_1, tensor_in_2)
 
-    def concatenate(self, sequence, axis=0):
+    def concatenate(self, sequence: Tensor[T], axis: None | int = 0) -> Tensor[T]:
         """
         Join a sequence of arrays along an existing axis.
 
@@ -319,7 +359,7 @@ def concatenate(self, sequence, axis=0):
         """
         return np.concatenate(sequence, axis=axis)
 
-    def simple_broadcast(self, *args):
+    def simple_broadcast(self, *args: Sequence[Tensor[T]]) -> Sequence[Tensor[T]]:
         """
         Broadcast a sequence of 1 dimensional arrays.
 
@@ -341,13 +381,13 @@ def simple_broadcast(self, *args):
         """
         return np.broadcast_arrays(*args)
 
-    def shape(self, tensor):
+    def shape(self, tensor: Tensor[T]) -> Shape:
         return tensor.shape
 
-    def reshape(self, tensor, newshape):
+    def reshape(self, tensor: Tensor[T], newshape: Shape) -> Tensor[T]:
         return np.reshape(tensor, newshape)
 
-    def ravel(self, tensor):
+    def ravel(self, tensor: Tensor[T]) -> Tensor[T]:
         """
         Return a flattened view of the tensor, not a copy.
 
@@ -367,7 +407,7 @@ def ravel(self, tensor):
         """
         return np.ravel(tensor)
 
-    def einsum(self, subscripts, *operands):
+    def einsum(self, subscripts: str, *operands: Sequence[Tensor[T]]) -> Tensor[T]:
         """
         Evaluates the Einstein summation convention on the operands.
 
@@ -386,10 +426,10 @@ def einsum(self, subscripts, *operands):
         """
         return np.einsum(subscripts, *operands)
 
-    def poisson_logpdf(self, n, lam):
+    def poisson_logpdf(self, n: Tensor[T], lam: Tensor[T]) -> Tensor[T]:
         return xlogy(n, lam) - lam - gammaln(n + 1.0)
 
-    def poisson(self, n, lam):
+    def poisson(self, n: Tensor[T], lam: Tensor[T]) -> Tensor[T]:
         r"""
         The continuous approximation, using :math:`n! = \Gamma\left(n+1\right)`,
         to the probability mass function of the Poisson distribution evaluated
@@ -433,7 +473,7 @@ def poisson(self, n, lam):
         lam = np.asarray(lam)
         return np.exp(xlogy(n, lam) - lam - gammaln(n + 1.0))
 
-    def normal_logpdf(self, x, mu, sigma):
+    def normal_logpdf(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> Tensor[T]:
         # this is much faster than
         # norm.logpdf(x, loc=mu, scale=sigma)
         # https://codereview.stackexchange.com/questions/69718/fastest-computation-of-n-likelihoods-on-normal-distributions
@@ -446,7 +486,7 @@ def normal_logpdf(self, x, mu, sigma):
     # def normal_logpdf(self, x, mu, sigma):
     #     return norm.logpdf(x, loc=mu, scale=sigma)
 
-    def normal(self, x, mu, sigma):
+    def normal(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> Tensor[T]:
         r"""
         The probability density function of the Normal distribution evaluated
         at :code:`x` given parameters of mean of :code:`mu` and standard deviation
@@ -474,7 +514,9 @@ def normal(self, x, mu, sigma):
         """
         return norm.pdf(x, loc=mu, scale=sigma)
 
-    def normal_cdf(self, x, mu=0, sigma=1):
+    def normal_cdf(
+        self, x: Tensor[T], mu: float | Tensor[T] = 0, sigma: float | Tensor[T] = 1
+    ) -> Tensor[T]:
         """
         The cumulative distribution function for the Normal distribution
 
@@ -498,7 +540,7 @@ def normal_cdf(self, x, mu=0, sigma=1):
         """
         return norm.cdf(x, loc=mu, scale=sigma)
 
-    def poisson_dist(self, rate):
+    def poisson_dist(self, rate: Tensor[T]) -> _BasicPoisson[T]:
         r"""
         The Poisson distribution with rate parameter :code:`rate`.
 
@@ -519,7 +561,7 @@ def poisson_dist(self, rate):
         """
         return _BasicPoisson(rate)
 
-    def normal_dist(self, mu, sigma):
+    def normal_dist(self, mu: Tensor[T], sigma: Tensor[T]) -> _BasicNormal[T]:
         r"""
         The Normal distribution with mean :code:`mu` and standard deviation :code:`sigma`.
 
@@ -543,7 +585,7 @@ def normal_dist(self, mu, sigma):
         """
         return _BasicNormal(mu, sigma)
 
-    def to_numpy(self, tensor_in):
+    def to_numpy(self, tensor_in: Tensor[T]) -> Tensor[T]:
         """
         Return the input tensor as it already is a :class:`numpy.ndarray`.
         This API exists only for ``pyhf.tensorlib`` compatibility.
@@ -571,7 +613,7 @@ def to_numpy(self, tensor_in):
         """
         return tensor_in
 
-    def transpose(self, tensor_in):
+    def transpose(self, tensor_in: Tensor[T]) -> Tensor[T]:
         """
         Transpose the tensor.
 

From a4fb57ae6ba3328f9f7b54e3a97621b4bc2d9bca Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 16 Aug 2022 15:37:38 -0700
Subject: [PATCH 05/21] get numpy_backend typed up?

---
 src/pyhf/tensor/numpy_backend.py | 150 ++++++++++++++++---------------
 src/pyhf/typing.py               |  23 ++++-
 2 files changed, 96 insertions(+), 77 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 4b7cf3b379..6a6709f834 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -5,47 +5,48 @@
 from scipy import special
 from scipy.stats import norm, poisson
 
-from typing import TypeVar, Callable, Literal, Sequence, Generic, Tuple, Mapping
+from pyhf.typing import TensorBackend, Shape, PDF
+
+from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping, cast
 from numpy.typing import (
     NDArray,
     NBitBase,
     ArrayLike,
+    DTypeLike,
 )
 
-Shape = Tuple[int, ...]
+T = TypeVar("T", bound=NBitBase)
+Tensor = NDArray[np.number[T]] | NDArray[np.bool_]
 
 log = logging.getLogger(__name__)
 
-T = TypeVar("T", bound=NBitBase)
-Tensor = NDArray[np.floating[T]]
 
-
-class _BasicPoisson(Generic[T]):
+class _BasicPoisson(PDF):
     def __init__(self, rate: Tensor[T]):
         self.rate = rate
 
-    def sample(self, sample_shape: NDArray[np.integer[T]]) -> Tensor[T]:
-        return poisson(self.rate).rvs(size=sample_shape + self.rate.shape)
+    def sample(self, sample_shape: Shape) -> ArrayLike:
+        return poisson(self.rate).rvs(size=sample_shape + self.rate.shape)  # type: ignore[no-any-return]
 
-    def log_prob(self, value: NDArray[np.number[T]]) -> Tensor[T]:
-        tensorlib = numpy_backend()
+    def log_prob(self, value: NDArray[np.number[T]]) -> ArrayLike:
+        tensorlib: numpy_backend[T] = numpy_backend()
         return tensorlib.poisson_logpdf(value, self.rate)
 
 
-class _BasicNormal(Generic[T]):
-    def __init__(self, loc: NDArray[np.number[T]], scale: NDArray[np.number[T]]):
+class _BasicNormal(PDF):
+    def __init__(self, loc: Tensor[T], scale: Tensor[T]):
         self.loc = loc
         self.scale = scale
 
-    def sample(self, sample_shape: NDArray[np.integer[T]]) -> Tensor[T]:
-        return norm(self.loc, self.scale).rvs(size=sample_shape + self.loc.shape)
+    def sample(self, sample_shape: Shape) -> ArrayLike:
+        return norm(self.loc, self.scale).rvs(size=sample_shape + self.loc.shape)  # type: ignore[no-any-return]
 
-    def log_prob(self, value: NDArray[np.number[T]]) -> Tensor[T]:
-        tensorlib = numpy_backend()
+    def log_prob(self, value: NDArray[np.number[T]]) -> ArrayLike:
+        tensorlib: numpy_backend[T] = numpy_backend()
         return tensorlib.normal_logpdf(value, self.loc, self.scale)
 
 
-class numpy_backend(Generic[T]):
+class numpy_backend(Generic[T], TensorBackend):
     """NumPy backend for pyhf"""
 
     __slots__ = ['name', 'precision', 'dtypemap', 'default_do_grad']
@@ -54,7 +55,8 @@ def __init__(self, **kwargs: dict[str, str]):
         self.name = 'numpy'
         self.precision = kwargs.get('precision', '64b')
         self.dtypemap: Mapping[
-            Literal['float', 'int', 'bool'], np.floating[T] | np.integer[T] | np.bool_
+            Literal['float', 'int', 'bool'],
+            DTypeLike,  # Type[np.floating[T]] | Type[np.integer[T]] | Type[np.bool_],
         ] = {
             'float': np.float64 if self.precision == '64b' else np.float32,
             'int': np.int64 if self.precision == '64b' else np.int32,
@@ -72,7 +74,7 @@ def clip(
         tensor_in: Tensor[T],
         min_value: np.integer[T] | np.floating[T],
         max_value: np.integer[T] | np.floating[T],
-    ) -> Tensor[T]:
+    ) -> ArrayLike:
         """
         Clips (limits) the tensor values to be within a specified min and max.
 
@@ -92,9 +94,9 @@ def clip(
         Returns:
             NumPy ndarray: A clipped `tensor`
         """
-        return np.clip(tensor_in, min_value, max_value)
+        return cast(Tensor[T], np.clip(tensor_in, min_value, max_value))
 
-    def erf(self, tensor_in: Tensor[T]) -> Tensor[T]:
+    def erf(self, tensor_in: Tensor[T]) -> ArrayLike:
         """
         The error function of complex argument.
 
@@ -112,9 +114,9 @@ def erf(self, tensor_in: Tensor[T]) -> Tensor[T]:
         Returns:
             NumPy ndarray: The values of the error function at the given points.
         """
-        return special.erf(tensor_in)
+        return special.erf(tensor_in)  # type: ignore[no-any-return]
 
-    def erfinv(self, tensor_in: Tensor[T]) -> Tensor[T]:
+    def erfinv(self, tensor_in: Tensor[T]) -> ArrayLike:
         """
         The inverse of the error function of complex argument.
 
@@ -132,9 +134,9 @@ def erfinv(self, tensor_in: Tensor[T]) -> Tensor[T]:
         Returns:
             NumPy ndarray: The values of the inverse of the error function at the given points.
         """
-        return special.erfinv(tensor_in)
+        return special.erfinv(tensor_in)  # type: ignore[no-any-return]
 
-    def tile(self, tensor_in: Tensor[T], repeats: int | Sequence[int]) -> Tensor[T]:
+    def tile(self, tensor_in: Tensor[T], repeats: int | Sequence[int]) -> ArrayLike:
         """
         Repeat tensor data along a specific dimension
 
@@ -154,14 +156,14 @@ def tile(self, tensor_in: Tensor[T], repeats: int | Sequence[int]) -> Tensor[T]:
         Returns:
             NumPy ndarray: The tensor with repeated axes
         """
-        return np.tile(tensor_in, repeats)
+        return cast(Tensor[T], np.tile(tensor_in, repeats))
 
     def conditional(
         self,
         predicate: NDArray[np.bool_],
         true_callable: Callable[[], Tensor[T]],
         false_callable: Callable[[], Tensor[T]],
-    ) -> Tensor[T]:
+    ) -> ArrayLike:
         """
         Runs a callable conditional on the boolean value of the evaluation of a predicate
 
@@ -185,29 +187,29 @@ def conditional(
         """
         return true_callable() if predicate else false_callable()
 
-    def tolist(self, tensor_in: ArrayLike) -> list[T]:
+    def tolist(self, tensor_in: Tensor[T] | list[T]) -> list[T]:
         try:
-            return tensor_in.tolist()
+            return cast(list[T], tensor_in.tolist())  # type: ignore[union-attr]
         except AttributeError:
             if isinstance(tensor_in, list):
                 return tensor_in
             raise
 
-    def outer(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> Tensor[T]:
-        return np.outer(tensor_in_1, tensor_in_2)
+    def outer(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> ArrayLike:
+        return np.outer(tensor_in_1, tensor_in_2)  # type: ignore[arg-type]
 
-    def gather(self, tensor: Tensor[T], indices: NDArray[np.integer[T]]) -> Tensor[T]:
-        return tensor[indices]
+    def gather(self, tensor: Tensor[T], indices: NDArray[np.integer[T]]) -> ArrayLike:
+        return tensor[indices]  # type: ignore[no-any-return]
 
-    def boolean_mask(self, tensor: Tensor[T], mask: NDArray[np.bool_]) -> Tensor[T]:
-        return tensor[mask]
+    def boolean_mask(self, tensor: Tensor[T], mask: NDArray[np.bool_]) -> ArrayLike:
+        return tensor[mask]  # type: ignore[no-any-return]
 
     def isfinite(self, tensor: Tensor[T]) -> NDArray[np.bool_]:
         return np.isfinite(tensor)
 
     def astensor(
-        self, tensor_in: ArrayLike, dtype: Literal['float'] = 'float'
-    ) -> Tensor[T]:
+        self, tensor_in: ArrayLike, dtype_str: Literal['float'] = 'float'
+    ) -> ArrayLike:
         """
         Convert to a NumPy array.
 
@@ -229,7 +231,7 @@ def astensor(
             `numpy.ndarray`: A multi-dimensional, fixed-size homogeneous array.
         """
         try:
-            dtype = self.dtypemap[dtype]
+            dtype = self.dtypemap[dtype_str]
         except KeyError:
             log.error(
                 'Invalid dtype: dtype must be float, int, or bool.', exc_info=True
@@ -238,18 +240,18 @@ def astensor(
 
         return np.asarray(tensor_in, dtype=dtype)
 
-    def sum(self, tensor_in: Tensor[T], axis: int | None = None) -> Tensor[T]:
+    def sum(self, tensor_in: Tensor[T], axis: int | None = None) -> ArrayLike:
         return np.sum(tensor_in, axis=axis)
 
-    def product(self, tensor_in: Tensor[T], axis: int | None = None) -> Tensor[T]:
-        return np.product(tensor_in, axis=axis)
+    def product(self, tensor_in: Tensor[T], axis: Shape | None = None) -> ArrayLike:
+        return np.product(tensor_in, axis=axis)  # type: ignore[arg-type]
 
-    def abs(self, tensor: Tensor[T]) -> Tensor[T]:
+    def abs(self, tensor: Tensor[T]) -> ArrayLike:
         return np.abs(tensor)
 
     def ones(
         self, shape: Shape, dtype_str: Literal["float", "int", "bool"] = "float"
-    ) -> Tensor[T]:
+    ) -> ArrayLike:
         try:
             dtype = self.dtypemap[dtype_str]
         except KeyError:
@@ -263,7 +265,7 @@ def ones(
 
     def zeros(
         self, shape: Shape, dtype_str: Literal["float", "int", "bool"] = "float"
-    ) -> Tensor[T]:
+    ) -> ArrayLike:
         try:
             dtype = self.dtypemap[dtype_str]
         except KeyError:
@@ -275,19 +277,19 @@ def zeros(
 
         return np.zeros(shape, dtype=dtype)
 
-    def power(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> Tensor[T]:
+    def power(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> ArrayLike:
         return np.power(tensor_in_1, tensor_in_2)
 
-    def sqrt(self, tensor_in: Tensor[T]) -> Tensor[T]:
+    def sqrt(self, tensor_in: Tensor[T]) -> ArrayLike:
         return np.sqrt(tensor_in)
 
-    def divide(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> Tensor[T]:
+    def divide(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> ArrayLike:
         return np.divide(tensor_in_1, tensor_in_2)
 
-    def log(self, tensor_in: Tensor[T]) -> Tensor[T]:
+    def log(self, tensor_in: Tensor[T]) -> ArrayLike:
         return np.log(tensor_in)
 
-    def exp(self, tensor_in: Tensor[T]) -> Tensor[T]:
+    def exp(self, tensor_in: Tensor[T]) -> ArrayLike:
         return np.exp(tensor_in)
 
     def percentile(
@@ -298,7 +300,7 @@ def percentile(
         interpolation: Literal[
             "linear", "lower", "higher", "midpoint", "nearest"
         ] = "linear",
-    ) -> Tensor[T]:
+    ) -> ArrayLike:
         r"""
         Compute the :math:`q`-th percentile of the tensor along the specified axis.
 
@@ -335,17 +337,17 @@ def percentile(
 
         """
         # see numpy/numpy#22125
-        return np.percentile(tensor_in, q, axis=axis, interpolation=interpolation)  # type: ignore[call-overload]
+        return np.percentile(tensor_in, q, axis=axis, interpolation=interpolation)  # type: ignore[call-overload,no-any-return]
 
-    def stack(self, sequence: Sequence[Tensor[T]], axis: int = 0) -> Tensor[T]:
+    def stack(self, sequence: Sequence[Tensor[T]], axis: int = 0) -> ArrayLike:
         return np.stack(sequence, axis=axis)
 
     def where(
         self, mask: NDArray[np.bool_], tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]
-    ) -> Tensor[T]:
+    ) -> ArrayLike:
         return np.where(mask, tensor_in_1, tensor_in_2)
 
-    def concatenate(self, sequence: Tensor[T], axis: None | int = 0) -> Tensor[T]:
+    def concatenate(self, sequence: Tensor[T], axis: None | int = 0) -> ArrayLike:
         """
         Join a sequence of arrays along an existing axis.
 
@@ -384,10 +386,10 @@ def simple_broadcast(self, *args: Sequence[Tensor[T]]) -> Sequence[Tensor[T]]:
     def shape(self, tensor: Tensor[T]) -> Shape:
         return tensor.shape
 
-    def reshape(self, tensor: Tensor[T], newshape: Shape) -> Tensor[T]:
+    def reshape(self, tensor: Tensor[T], newshape: Shape) -> ArrayLike:
         return np.reshape(tensor, newshape)
 
-    def ravel(self, tensor: Tensor[T]) -> Tensor[T]:
+    def ravel(self, tensor: Tensor[T]) -> ArrayLike:
         """
         Return a flattened view of the tensor, not a copy.
 
@@ -407,7 +409,7 @@ def ravel(self, tensor: Tensor[T]) -> Tensor[T]:
         """
         return np.ravel(tensor)
 
-    def einsum(self, subscripts: str, *operands: Sequence[Tensor[T]]) -> Tensor[T]:
+    def einsum(self, subscripts: str, *operands: Sequence[Tensor[T]]) -> ArrayLike:
         """
         Evaluates the Einstein summation convention on the operands.
 
@@ -424,12 +426,12 @@ def einsum(self, subscripts: str, *operands: Sequence[Tensor[T]]) -> Tensor[T]:
         Returns:
             tensor: the calculation based on the Einstein summation convention
         """
-        return np.einsum(subscripts, *operands)
+        return np.einsum(subscripts, *operands)  # type: ignore[arg-type,no-any-return]
 
-    def poisson_logpdf(self, n: Tensor[T], lam: Tensor[T]) -> Tensor[T]:
-        return xlogy(n, lam) - lam - gammaln(n + 1.0)
+    def poisson_logpdf(self, n: Tensor[T], lam: Tensor[T]) -> ArrayLike:
+        return cast(ArrayLike, xlogy(n, lam) - lam - gammaln(n + 1.0))
 
-    def poisson(self, n: Tensor[T], lam: Tensor[T]) -> Tensor[T]:
+    def poisson(self, n: Tensor[T], lam: Tensor[T]) -> ArrayLike:
         r"""
         The continuous approximation, using :math:`n! = \Gamma\left(n+1\right)`,
         to the probability mass function of the Poisson distribution evaluated
@@ -469,11 +471,11 @@ def poisson(self, n: Tensor[T], lam: Tensor[T]) -> Tensor[T]:
         Returns:
             NumPy float: Value of the continuous approximation to Poisson(n|lam)
         """
-        n = np.asarray(n)
-        lam = np.asarray(lam)
-        return np.exp(xlogy(n, lam) - lam - gammaln(n + 1.0))
+        _n = np.asarray(n)
+        _lam = np.asarray(lam)
+        return np.exp(xlogy(_n, _lam) - _lam - gammaln(_n + 1.0))  # type: ignore[no-any-return,operator]
 
-    def normal_logpdf(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> Tensor[T]:
+    def normal_logpdf(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> ArrayLike:
         # this is much faster than
         # norm.logpdf(x, loc=mu, scale=sigma)
         # https://codereview.stackexchange.com/questions/69718/fastest-computation-of-n-likelihoods-on-normal-distributions
@@ -481,12 +483,12 @@ def normal_logpdf(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> Tensor
         root2pi = np.sqrt(2 * np.pi)
         prefactor = -np.log(sigma * root2pi)
         summand = -np.square(np.divide((x - mu), (root2 * sigma)))
-        return prefactor + summand
+        return prefactor + summand  # type: ignore[no-any-return]
 
     # def normal_logpdf(self, x, mu, sigma):
     #     return norm.logpdf(x, loc=mu, scale=sigma)
 
-    def normal(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> Tensor[T]:
+    def normal(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> ArrayLike:
         r"""
         The probability density function of the Normal distribution evaluated
         at :code:`x` given parameters of mean of :code:`mu` and standard deviation
@@ -512,11 +514,11 @@ def normal(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> Tensor[T]:
         Returns:
             NumPy float: Value of Normal(x|mu, sigma)
         """
-        return norm.pdf(x, loc=mu, scale=sigma)
+        return norm.pdf(x, loc=mu, scale=sigma)  # type: ignore[no-any-return]
 
     def normal_cdf(
         self, x: Tensor[T], mu: float | Tensor[T] = 0, sigma: float | Tensor[T] = 1
-    ) -> Tensor[T]:
+    ) -> ArrayLike:
         """
         The cumulative distribution function for the Normal distribution
 
@@ -538,9 +540,9 @@ def normal_cdf(
         Returns:
             NumPy float: The CDF
         """
-        return norm.cdf(x, loc=mu, scale=sigma)
+        return norm.cdf(x, loc=mu, scale=sigma)  # type: ignore[no-any-return]
 
-    def poisson_dist(self, rate: Tensor[T]) -> _BasicPoisson[T]:
+    def poisson_dist(self, rate: Tensor[T]) -> PDF:
         r"""
         The Poisson distribution with rate parameter :code:`rate`.
 
@@ -561,7 +563,7 @@ def poisson_dist(self, rate: Tensor[T]) -> _BasicPoisson[T]:
         """
         return _BasicPoisson(rate)
 
-    def normal_dist(self, mu: Tensor[T], sigma: Tensor[T]) -> _BasicNormal[T]:
+    def normal_dist(self, mu: Tensor[T], sigma: Tensor[T]) -> PDF:
         r"""
         The Normal distribution with mean :code:`mu` and standard deviation :code:`sigma`.
 
@@ -585,7 +587,7 @@ def normal_dist(self, mu: Tensor[T], sigma: Tensor[T]) -> _BasicNormal[T]:
         """
         return _BasicNormal(mu, sigma)
 
-    def to_numpy(self, tensor_in: Tensor[T]) -> Tensor[T]:
+    def to_numpy(self, tensor_in: Tensor[T]) -> ArrayLike:
         """
         Return the input tensor as it already is a :class:`numpy.ndarray`.
         This API exists only for ``pyhf.tensorlib`` compatibility.
@@ -613,7 +615,7 @@ def to_numpy(self, tensor_in: Tensor[T]) -> Tensor[T]:
         """
         return tensor_in
 
-    def transpose(self, tensor_in: Tensor[T]) -> Tensor[T]:
+    def transpose(self, tensor_in: Tensor[T]) -> ArrayLike:
         """
         Transpose the tensor.
 
diff --git a/src/pyhf/typing.py b/src/pyhf/typing.py
index 50a6237199..9cd17f2265 100644
--- a/src/pyhf/typing.py
+++ b/src/pyhf/typing.py
@@ -1,11 +1,12 @@
 import os
 import sys
-from typing import MutableSequence, Sequence, Union
+from typing import MutableSequence, Sequence, Union, Tuple, SupportsIndex, Any
+
 
 if sys.version_info >= (3, 8):
-    from typing import Literal, TypedDict
+    from typing import Literal, TypedDict, Protocol
 else:
-    from typing_extensions import Literal, TypedDict
+    from typing_extensions import Literal, TypedDict, Protocol
 
 __all__ = (
     "PathOrStr",
@@ -27,9 +28,13 @@
     "Workspace",
 )
 
+
 # TODO: Switch to os.PathLike[str] once Python 3.8 support dropped
 PathOrStr = Union[str, "os.PathLike[str]"]
 
+Shape = Tuple[int, ...]
+ShapeLike = Union[SupportsIndex, Sequence[SupportsIndex]]
+
 
 class ParameterBase(TypedDict, total=False):
     auxdata: Sequence[float]
@@ -132,3 +137,15 @@ class Workspace(TypedDict):
     measurements: Sequence[Measurement]
     channels: Sequence[Channel]
     observations: Sequence[Observation]
+
+
+class TensorBackend(Protocol):
+    ...
+
+
+class PDF(Protocol):
+    def sample(self, sample_shape: Shape) -> Any:
+        ...
+
+    def log_prob(self, value: Any) -> Any:
+        ...

From 8dea9fbf1d71cfd569fe0c29caab5289617149e1 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 16 Aug 2022 15:43:03 -0700
Subject: [PATCH 06/21] pass

---
 src/pyhf/readxml.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/pyhf/readxml.py b/src/pyhf/readxml.py
index f46620cb90..212ff6a01e 100644
--- a/src/pyhf/readxml.py
+++ b/src/pyhf/readxml.py
@@ -438,7 +438,7 @@ def parse(
     mounts = mounts or []
     toplvl = ET.parse(configfile)
     inputs = tqdm.tqdm(
-        [x.text for x in toplvl.findall('Input')],
+        [x.text for x in toplvl.findall('Input') if x.text],
         unit='channel',
         disable=not (track_progress),
     )

From 8ce8d5e95a143344fd98003b2ed6db2a3ac5d034 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 16 Aug 2022 15:48:54 -0700
Subject: [PATCH 07/21] drop cast for now

---
 src/pyhf/tensor/numpy_backend.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 6a6709f834..2473bdab18 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -7,7 +7,7 @@
 
 from pyhf.typing import TensorBackend, Shape, PDF
 
-from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping, cast
+from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping
 from numpy.typing import (
     NDArray,
     NBitBase,
@@ -94,7 +94,7 @@ def clip(
         Returns:
             NumPy ndarray: A clipped `tensor`
         """
-        return cast(Tensor[T], np.clip(tensor_in, min_value, max_value))
+        return np.clip(tensor_in, min_value, max_value)
 
     def erf(self, tensor_in: Tensor[T]) -> ArrayLike:
         """
@@ -156,7 +156,7 @@ def tile(self, tensor_in: Tensor[T], repeats: int | Sequence[int]) -> ArrayLike:
         Returns:
             NumPy ndarray: The tensor with repeated axes
         """
-        return cast(Tensor[T], np.tile(tensor_in, repeats))
+        return np.tile(tensor_in, repeats)
 
     def conditional(
         self,
@@ -189,7 +189,7 @@ def conditional(
 
     def tolist(self, tensor_in: Tensor[T] | list[T]) -> list[T]:
         try:
-            return cast(list[T], tensor_in.tolist())  # type: ignore[union-attr]
+            return tensor_in.tolist()  # type: ignore[union-attr,no-any-return]
         except AttributeError:
             if isinstance(tensor_in, list):
                 return tensor_in
@@ -429,7 +429,7 @@ def einsum(self, subscripts: str, *operands: Sequence[Tensor[T]]) -> ArrayLike:
         return np.einsum(subscripts, *operands)  # type: ignore[arg-type,no-any-return]
 
     def poisson_logpdf(self, n: Tensor[T], lam: Tensor[T]) -> ArrayLike:
-        return cast(ArrayLike, xlogy(n, lam) - lam - gammaln(n + 1.0))
+        return xlogy(n, lam) - lam - gammaln(n + 1.0)  # type: ignore[no-any-return]
 
     def poisson(self, n: Tensor[T], lam: Tensor[T]) -> ArrayLike:
         r"""

From 314441cfcbd7f2fef774a9caecd8d790dabeff9f Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 16 Aug 2022 16:12:44 -0700
Subject: [PATCH 08/21] fix up

---
 src/pyhf/tensor/numpy_backend.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 2473bdab18..4529c5a7e6 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -5,7 +5,7 @@
 from scipy import special
 from scipy.stats import norm, poisson
 
-from pyhf.typing import TensorBackend, Shape, PDF
+from pyhf.typing import TensorBackend, Shape
 
 from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping
 from numpy.typing import (
@@ -21,7 +21,7 @@
 log = logging.getLogger(__name__)
 
 
-class _BasicPoisson(PDF):
+class _BasicPoisson:
     def __init__(self, rate: Tensor[T]):
         self.rate = rate
 
@@ -33,7 +33,7 @@ def log_prob(self, value: NDArray[np.number[T]]) -> ArrayLike:
         return tensorlib.poisson_logpdf(value, self.rate)
 
 
-class _BasicNormal(PDF):
+class _BasicNormal:
     def __init__(self, loc: Tensor[T], scale: Tensor[T]):
         self.loc = loc
         self.scale = scale
@@ -542,7 +542,7 @@ def normal_cdf(
         """
         return norm.cdf(x, loc=mu, scale=sigma)  # type: ignore[no-any-return]
 
-    def poisson_dist(self, rate: Tensor[T]) -> PDF:
+    def poisson_dist(self, rate: Tensor[T]) -> _BasicPoisson:
         r"""
         The Poisson distribution with rate parameter :code:`rate`.
 
@@ -563,7 +563,7 @@ def poisson_dist(self, rate: Tensor[T]) -> PDF:
         """
         return _BasicPoisson(rate)
 
-    def normal_dist(self, mu: Tensor[T], sigma: Tensor[T]) -> PDF:
+    def normal_dist(self, mu: Tensor[T], sigma: Tensor[T]) -> _BasicNormal:
         r"""
         The Normal distribution with mean :code:`mu` and standard deviation :code:`sigma`.
 

From d7934edc1acf12789152aba2b7d71dfa950f612f Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 16 Aug 2022 16:24:43 -0700
Subject: [PATCH 09/21] more

---
 src/pyhf/tensor/numpy_backend.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 4529c5a7e6..3b7dec18a9 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -7,7 +7,7 @@
 
 from pyhf.typing import TensorBackend, Shape
 
-from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping
+from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping, Union
 from numpy.typing import (
     NDArray,
     NBitBase,
@@ -16,7 +16,7 @@
 )
 
 T = TypeVar("T", bound=NBitBase)
-Tensor = NDArray[np.number[T]] | NDArray[np.bool_]
+Tensor = Union[NDArray[np.number[T]], NDArray[np.bool_]]
 
 log = logging.getLogger(__name__)
 

From 536d2cd35878f4aaf431ffbf3b9ea0efb620cc7c Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 23 Aug 2022 11:50:28 -0700
Subject: [PATCH 10/21] drop TensorBackend as its protocol

---
 src/pyhf/tensor/numpy_backend.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 3b7dec18a9..c0fa805392 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -5,7 +5,7 @@
 from scipy import special
 from scipy.stats import norm, poisson
 
-from pyhf.typing import TensorBackend, Shape
+from pyhf.typing import Shape
 
 from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping, Union
 from numpy.typing import (
@@ -46,7 +46,7 @@ def log_prob(self, value: NDArray[np.number[T]]) -> ArrayLike:
         return tensorlib.normal_logpdf(value, self.loc, self.scale)
 
 
-class numpy_backend(Generic[T], TensorBackend):
+class numpy_backend(Generic[T]):
     """NumPy backend for pyhf"""
 
     __slots__ = ['name', 'precision', 'dtypemap', 'default_do_grad']

From 41dc1a8fdf3ba32d05534c6c25a913fa784b569f Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 23 Aug 2022 12:07:26 -0700
Subject: [PATCH 11/21] fix up

---
 src/pyhf/tensor/numpy_backend.py | 26 ++++++++++++++++----------
 1 file changed, 16 insertions(+), 10 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index c0fa805392..7bf0bb2e0e 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -1,4 +1,5 @@
 """NumPy Tensor Library Module."""
+from __future__ import annotations
 import numpy as np
 import logging
 from scipy.special import gammaln, xlogy
@@ -7,6 +8,7 @@
 
 from pyhf.typing import Shape
 
+import sys
 from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping, Union
 from numpy.typing import (
     NDArray,
@@ -16,7 +18,11 @@
 )
 
 T = TypeVar("T", bound=NBitBase)
-Tensor = Union[NDArray[np.number[T]], NDArray[np.bool_]]
+
+if sys.version_info >= (3, 9):
+    Tensor = Union[NDArray[np.number[T]], NDArray[np.bool_]]
+else:
+    Tensor = NDArray
 
 log = logging.getLogger(__name__)
 
@@ -208,7 +214,7 @@ def isfinite(self, tensor: Tensor[T]) -> NDArray[np.bool_]:
         return np.isfinite(tensor)
 
     def astensor(
-        self, tensor_in: ArrayLike, dtype_str: Literal['float'] = 'float'
+        self, tensor_in: ArrayLike, dtype: Literal['float'] = 'float'
     ) -> ArrayLike:
         """
         Convert to a NumPy array.
@@ -231,14 +237,14 @@ def astensor(
             `numpy.ndarray`: A multi-dimensional, fixed-size homogeneous array.
         """
         try:
-            dtype = self.dtypemap[dtype_str]
+            dtype_obj = self.dtypemap[dtype]
         except KeyError:
             log.error(
                 'Invalid dtype: dtype must be float, int, or bool.', exc_info=True
             )
             raise
 
-        return np.asarray(tensor_in, dtype=dtype)
+        return np.asarray(tensor_in, dtype=dtype_obj)
 
     def sum(self, tensor_in: Tensor[T], axis: int | None = None) -> ArrayLike:
         return np.sum(tensor_in, axis=axis)
@@ -250,10 +256,10 @@ def abs(self, tensor: Tensor[T]) -> ArrayLike:
         return np.abs(tensor)
 
     def ones(
-        self, shape: Shape, dtype_str: Literal["float", "int", "bool"] = "float"
+        self, shape: Shape, dtype: Literal["float", "int", "bool"] = "float"
     ) -> ArrayLike:
         try:
-            dtype = self.dtypemap[dtype_str]
+            dtype_obj = self.dtypemap[dtype]
         except KeyError:
             log.error(
                 f"Invalid dtype: dtype must be one of {list(self.dtypemap.keys())}.",
@@ -261,13 +267,13 @@ def ones(
             )
             raise
 
-        return np.ones(shape, dtype=dtype)
+        return np.ones(shape, dtype=dtype_obj)
 
     def zeros(
-        self, shape: Shape, dtype_str: Literal["float", "int", "bool"] = "float"
+        self, shape: Shape, dtype: Literal["float", "int", "bool"] = "float"
     ) -> ArrayLike:
         try:
-            dtype = self.dtypemap[dtype_str]
+            dtype_obj = self.dtypemap[dtype]
         except KeyError:
             log.error(
                 f"Invalid dtype: dtype must be one of {list(self.dtypemap.keys())}.",
@@ -275,7 +281,7 @@ def zeros(
             )
             raise
 
-        return np.zeros(shape, dtype=dtype)
+        return np.zeros(shape, dtype=dtype_obj)
 
     def power(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> ArrayLike:
         return np.power(tensor_in_1, tensor_in_2)

From 50fcc4a58503e3fcf7109df18ed6489e91cc6c85 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 23 Aug 2022 12:11:16 -0700
Subject: [PATCH 12/21] sigh

---
 src/pyhf/typing.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/pyhf/typing.py b/src/pyhf/typing.py
index 9cd17f2265..bf9c7f134c 100644
--- a/src/pyhf/typing.py
+++ b/src/pyhf/typing.py
@@ -1,12 +1,12 @@
 import os
 import sys
-from typing import MutableSequence, Sequence, Union, Tuple, SupportsIndex, Any
+from typing import MutableSequence, Sequence, Union, Tuple, Any
 
 
 if sys.version_info >= (3, 8):
-    from typing import Literal, TypedDict, Protocol
+    from typing import Literal, TypedDict, Protocol, SupportsIndex
 else:
-    from typing_extensions import Literal, TypedDict, Protocol
+    from typing_extensions import Literal, TypedDict, Protocol, SupportsIndex
 
 __all__ = (
     "PathOrStr",

From d1a84d78a03d0b2b0bc52b7b01183ce399e31bab Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 23 Aug 2022 12:20:02 -0700
Subject: [PATCH 13/21] run pre-commit with 3.7 and 3.10

---
 .pre-commit-config.yaml | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 7a216a36ed..f995831229 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -62,11 +62,16 @@ repos:
 -   repo: https://github.com/pre-commit/mirrors-mypy
     rev: v0.971
     hooks:
-      - id: mypy
+      - &mypy
+        id: mypy
+        name: mypy with Python 3.7
         files: src
-        args: []
         additional_dependencies:
           ['numpy', 'types-tqdm', 'click', 'types-jsonpatch', 'types-pyyaml', 'types-jsonschema', 'importlib_metadata', 'packaging']
+        args: ["--python-version=3.7"]
+      - <<: *mypy
+        name: mypy with Python 3.10
+        args: ["--python-version=3.10"]
 
 -   repo: https://github.com/nbQA-dev/nbQA
     rev: 1.4.0

From 7d4691b5068ccf3274547ae8e4bc6e1205113162 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 23 Aug 2022 12:24:49 -0700
Subject: [PATCH 14/21] get it working in 3.7

---
 src/pyhf/tensor/numpy_backend.py | 9 ++++-----
 src/pyhf/typing.py               | 1 +
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 7bf0bb2e0e..795e50b3f3 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -6,10 +6,9 @@
 from scipy import special
 from scipy.stats import norm, poisson
 
-from pyhf.typing import Shape
+from pyhf.typing import Shape, Literal
 
-import sys
-from typing import TypeVar, Callable, Literal, Sequence, Generic, Mapping, Union
+from typing import TypeVar, Callable, Sequence, Generic, Mapping, Union, TYPE_CHECKING
 from numpy.typing import (
     NDArray,
     NBitBase,
@@ -19,10 +18,10 @@
 
 T = TypeVar("T", bound=NBitBase)
 
-if sys.version_info >= (3, 9):
+if TYPE_CHECKING:
     Tensor = Union[NDArray[np.number[T]], NDArray[np.bool_]]
 else:
-    Tensor = NDArray
+    Tensor = Generic
 
 log = logging.getLogger(__name__)
 
diff --git a/src/pyhf/typing.py b/src/pyhf/typing.py
index bf9c7f134c..fc1934bb40 100644
--- a/src/pyhf/typing.py
+++ b/src/pyhf/typing.py
@@ -26,6 +26,7 @@
     "Channel",
     "Observation",
     "Workspace",
+    "Literal",
 )
 
 

From 38b7893c10d93a18804505b47dcda718ab2dde8f Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 12 Aug 2022 02:30:53 -0400
Subject: [PATCH 15/21] test: Ignore TYPE_CHECKING for coverage (#1937)

* Add .coveragerc file with configuration to ignore TYPE_CHECKING.
  - ref: https://coverage.readthedocs.io/en/6.4.3/excluding.html#advanced-exclusion
---
 .coveragerc | 3 +++
 1 file changed, 3 insertions(+)
 create mode 100644 .coveragerc

diff --git a/.coveragerc b/.coveragerc
new file mode 100644
index 0000000000..0856c037f2
--- /dev/null
+++ b/.coveragerc
@@ -0,0 +1,3 @@
+[report]
+exclude_lines =
+    if TYPE_CHECKING:

From c936365fe385ec6dc1ba49830e2445da7838262e Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 23 Aug 2022 12:41:05 -0700
Subject: [PATCH 16/21] skip the typing.py file

---
 .coveragerc | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/.coveragerc b/.coveragerc
index 0856c037f2..6662eda9e1 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -1,3 +1,5 @@
 [report]
 exclude_lines =
     if TYPE_CHECKING:
+omit =
+    src/pyhf/typing.py

From 0916c4f65e4d1296fd3f0fcf4b018b1de60f5bae Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Tue, 23 Aug 2022 13:04:00 -0700
Subject: [PATCH 17/21] tell codecov to ignore typing.py

---
 codecov.yml | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/codecov.yml b/codecov.yml
index 914f860929..61da747a9d 100644
--- a/codecov.yml
+++ b/codecov.yml
@@ -3,3 +3,6 @@ coverage:
     project:
       default:
         threshold: 0.2%
+
+ignore:
+  - "**/typing.py"

From b222f857941d045976b43a8eb34eff3b68ae46b1 Mon Sep 17 00:00:00 2001
From: Matthew Feickert <matthew.feickert@cern.ch>
Date: Fri, 26 Aug 2022 02:10:03 -0500
Subject: [PATCH 18/21] Add comment that the Pythons type checked are extrema

---
 .pre-commit-config.yaml | 1 +
 pyproject.toml          | 1 -
 2 files changed, 1 insertion(+), 1 deletion(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index f995831229..67e9854ef3 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -61,6 +61,7 @@ repos:
 
 -   repo: https://github.com/pre-commit/mirrors-mypy
     rev: v0.971
+    # check the oldest and newest supported Pythons
     hooks:
       - &mypy
         id: mypy
diff --git a/pyproject.toml b/pyproject.toml
index af3d331ad0..2708c44b7f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -118,7 +118,6 @@ module = [
 ]
 ignore_missing_imports = true
 
-
 [[tool.mypy.overrides]]
 module = [
   'pyhf',

From 41cd3afd06ede919165385a8687e9eefa513e262 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 26 Aug 2022 07:12:20 -0400
Subject: [PATCH 19/21] Apply suggestions from code review

Co-authored-by: Matthew Feickert <matthew.feickert@cern.ch>
---
 src/pyhf/tensor/numpy_backend.py | 18 +++++++-----------
 src/pyhf/typing.py               |  7 +++----
 2 files changed, 10 insertions(+), 15 deletions(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 795e50b3f3..9ad28dc879 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -1,20 +1,16 @@
 """NumPy Tensor Library Module."""
 from __future__ import annotations
-import numpy as np
+
 import logging
-from scipy.special import gammaln, xlogy
+from typing import TYPE_CHECKING, Callable, Generic, Mapping, Sequence, TypeVar, Union
+
+import numpy as np
+from numpy.typing import ArrayLike, DTypeLike, NBitBase, NDArray
 from scipy import special
+from scipy.special import gammaln, xlogy
 from scipy.stats import norm, poisson
 
-from pyhf.typing import Shape, Literal
-
-from typing import TypeVar, Callable, Sequence, Generic, Mapping, Union, TYPE_CHECKING
-from numpy.typing import (
-    NDArray,
-    NBitBase,
-    ArrayLike,
-    DTypeLike,
-)
+from pyhf.typing import Literal, Shape
 
 T = TypeVar("T", bound=NBitBase)
 
diff --git a/src/pyhf/typing.py b/src/pyhf/typing.py
index fc1934bb40..ffa10d8d58 100644
--- a/src/pyhf/typing.py
+++ b/src/pyhf/typing.py
@@ -1,12 +1,11 @@
 import os
 import sys
-from typing import MutableSequence, Sequence, Union, Tuple, Any
-
+from typing import Any, MutableSequence, Sequence, Tuple, Union
 
 if sys.version_info >= (3, 8):
-    from typing import Literal, TypedDict, Protocol, SupportsIndex
+    from typing import Literal, Protocol, SupportsIndex, TypedDict
 else:
-    from typing_extensions import Literal, TypedDict, Protocol, SupportsIndex
+    from typing_extensions import Literal, Protocol, SupportsIndex, TypedDict
 
 __all__ = (
     "PathOrStr",

From 50985c9491f22e6cc6981c617b63f518d3598fd2 Mon Sep 17 00:00:00 2001
From: Matthew Feickert <matthew.feickert@cern.ch>
Date: Fri, 26 Aug 2022 10:11:33 -0500
Subject: [PATCH 20/21] use full url

---
 src/pyhf/tensor/numpy_backend.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index 9ad28dc879..c54b1e411d 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -337,7 +337,7 @@ def percentile(
             NumPy ndarray: The value of the :math:`q`-th percentile of the tensor along the specified axis.
 
         """
-        # see numpy/numpy#22125
+        # see https://github.com/numpy/numpy/issues/22125
         return np.percentile(tensor_in, q, axis=axis, interpolation=interpolation)  # type: ignore[call-overload,no-any-return]
 
     def stack(self, sequence: Sequence[Tensor[T]], axis: int = 0) -> ArrayLike:

From 1f66041ba30b8b3ee714156d225e29341fc71f32 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 26 Aug 2022 08:31:47 -0700
Subject: [PATCH 21/21] drop TYPE_CHECKING

---
 .coveragerc                      | 2 --
 src/pyhf/tensor/numpy_backend.py | 7 ++-----
 2 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/.coveragerc b/.coveragerc
index 6662eda9e1..4b634a8785 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -1,5 +1,3 @@
 [report]
-exclude_lines =
-    if TYPE_CHECKING:
 omit =
     src/pyhf/typing.py
diff --git a/src/pyhf/tensor/numpy_backend.py b/src/pyhf/tensor/numpy_backend.py
index c54b1e411d..1e623d0147 100644
--- a/src/pyhf/tensor/numpy_backend.py
+++ b/src/pyhf/tensor/numpy_backend.py
@@ -2,7 +2,7 @@
 from __future__ import annotations
 
 import logging
-from typing import TYPE_CHECKING, Callable, Generic, Mapping, Sequence, TypeVar, Union
+from typing import Callable, Generic, Mapping, Sequence, TypeVar, Union
 
 import numpy as np
 from numpy.typing import ArrayLike, DTypeLike, NBitBase, NDArray
@@ -14,10 +14,7 @@
 
 T = TypeVar("T", bound=NBitBase)
 
-if TYPE_CHECKING:
-    Tensor = Union[NDArray[np.number[T]], NDArray[np.bool_]]
-else:
-    Tensor = Generic
+Tensor = Union["NDArray[np.number[T]]", "NDArray[np.bool_]"]
 
 log = logging.getLogger(__name__)