Static type-checking fix (#34)

* Add support for e.g. jaxtyping.Float[Union[...], ...] in py3.8

Turns out that python3.8, Union lacks the __name__ attribute.  Use repr()
in these cases.

* Fix linter.

* Remove implicit cast to bool in favor of try/except.

.flake8

@@ -1,4 +1,4 @@
 [flake8]
-max-line-length = 120
+max-line-length = 88
 ignore = W291,W293,W503,W504,E123,E126,E203,E402,E701,E731,F722
 per-file-ignores = __init__.py: F401

API.md

@@ -2,60 +2,78 @@
 
 ## Annotating array types
 
-Each array is denoted by a type `dtype[shape]`, such as `f32["batch channels"]`.
+Each array is denoted by a type `dtype[array, shape]`, such as `Float[Array, "batch channels"]`.
 
 ### Shape
 
-The shape should be a string of space-separated symbols, such as "a b c d". Each symbol can be:
-- `int`: fixed-size axis, e.g. `f32["28 28"]`.
-- `str`: variable-size axis, e.g. `f32["channels"]`.
-- `_`: anonymous axis, e.g. `f32["batch channels _ _"]`.
-- `...`: anonymous zero or more axes, e.g. `f32["... c h w"]`
-- `*name`: zero or more variable-size axes, e.g. `f32["*batch c h w"]`
-- Append `#` to a dimension size to indicate that it can be that size *or* equal to one -- i.e. broadcasting is acceptable.
+The shape should be a string of space-separated symbols, such as `"a b c d"`. Each symbol can be either an:
+- `int`: fixed-size axis, e.g. `"28 28"`.
+- `str`: variable-size axis, e.g. `"channels"`.
+- A symbolic expression (without spaces!) in terms of other variable-size axes, e.g. `def remove_last(x: Float[Array, "dim"]) -> Float[Array, "dim-1"]`.
 
-When calling a function, variable-size axes will be matched up across all arguments and checked for consistency. (See [runtime type checking](#runtime-type-checking) below.)
+When calling a function, variable-size axes and symbolic axes will be matched up across all arguments and checked for consistency. (See [runtime type checking](#runtime-type-checking) below.)
+
+In addition some modifiers can be applied:
+- Prepend `*` to a dimension to indicate that it can match multiple axes, e.g. `"*batch c h w"` will match zero or more batch axes.
+- Prepend `#` to a dimension to indicate that it can be that size *or* equal to one -- i.e. broadcasting is acceptable, e.g. `def add(x: Float[Array, "#foo"], y: Float[Array, "#foo"]) -> Float[Array, "#foo"]`.
+- Prepend `_` to a dimension to disable any runtime checking of that dimension (so that it can be used just as documentation). This can also be used as just `_` on its own: e.g. `"b c _ _"`.
+
+When using multiple modifiers, their order does not matter.
+
+As a special case:
+- `...`: anonymous zero or more axes (equivalent to `*_`) e.g. `"... c h w"`
 
 Some notes:
-- To denote a scalar shape use `""`, e.g. `f32[""]`.
-- To denote an arbitrary shape (and only check dtype) use `"..."`, e.g. `f32["..."]`.
-- You cannot have multiple variadic axes, i.e. you can only use `...` or `*name` at most once in each array.
-- An example of broadcasting in one dimension: `add(x: f32["foo#"], y: f32["foo#"]) -> f32["foo#"]`.
-- An example of broadcasting multiple dimensions: `add(x: f32["*foo#"], y: f32["*foo#"]) -> f32["*foo#"]`.
+- To denote a scalar shape use `""`, e.g. `Float[Array, ""]`.
+- To denote an arbitrary shape (and only check dtype) use `"..."`, e.g. `Float[Array, "..."]`.
+- You cannot have more than one use of multiple-axes, i.e. you can only use `...` or `*name` at most once in each array.
+- An example of broadcasting multiple dimensions: `def add(x: Float[Array, "*#foo"], y: Float[Array, "*#foo"]) -> Float[Array, "*#foo"]`.
+- A symbolic expression cannot be evaluated unless all of the axes sizes it refers to have already been processed. In practice this usually means that they should only be used in annotations for the return type, and only use axes declared in the arguments.
 
 ### Dtype
 
 The dtype should be any one of (imported from `jaxtyping`):
-- Any dtype at all: `Array`
-  - Boolean: `b`
-  - Any integer, unsigned integer, floating, or complex: `n` (for <ins>n</ins>umber)
-    - Any floating or complex: `x` (for ine<ins>x</ins>act)
-      - Any floating point: `f`
-        - Floating point: `bf16`, `f16`, `f32`, `f64` (`bf16` is bfloat16)
-      - Any complex: `c`
-        - Complexes: `c64`, `c128`
-    - Any integer or unsigned intger: `t` (for in<ins>t</ins>eger)
-      - Any unsigned integer: `u`
-        - Unsigned integer: `u8`, `u16`, `u32`, `u64`
-      - Any signed integer: `i`
-        - Signed integer: `i8`, `i16`, `i32`, `i64`
+- Any dtype at all: `Shaped`
+  - Boolean: `Bool`
+  - Any integer, unsigned integer, floating, or complex: `Num`
+    - Any floating or complex: `Inexact`
+      - Any floating point: `Float`
+        - Of particular precision: `BFloat16`, `Float16`, `Float32`, `Float64`
+      - Any complex: `Complex`
+        - Of particular precision: `Complex64`, `Complex128`
+    - Any integer or unsigned intger: `Integer`
+      - Any unsigned integer: `UInt`
+        - Of particular precision: `UInt8`, `UInt16`, `UInt32`, `UInt64`
+      - Any signed integer: `Int`
+        - Of particular precision: `Int8`, `Int16`, `Int32`, `Int64`
 
 Unless you really want to force a particular precision, then for most applications you should probably allow any floating-point, any integer, etc. That is, use
 ```python
-from jaxtyping import f
-f["some_shape"]
+from jaxtyping import Array, Float
+Float[Array, "some_shape"]
 ```
 rather than
 ```python
-from jaxtyping import f32
-f32["some_shape"]
+from jaxtyping import Array, Float32
+Float32[Array, "some_shape"]
+```
+
+### Array
+
+The array should typically be a `jaxtyping.Array`, which is an alias for `jax.numpy.ndarray`.
+
+But you can use other types as well. `jaxtyping` has support for JAX, NumPy, TensorFlow, and PyTorch, e.g.:
+```python
+Float[np.ndarray, "..."]
+Float[tf.Tensor, "..."]
+Float[torch.Tensor, "..."]
 ```
 
 ## PyTrees
 
 ### `jaxtyping.PyTree`
 
-Each PyTree is denoted by a type `PyTree[LeafType]`, such as `PyTree[int]` or `PyTree[Union[str, f32["b c"]]]`.
+Each PyTree is denoted by a type `PyTree[LeafType]`, such as `PyTree[int]` or `PyTree[Union[str, Float32[Array, "b c"]]]`.
 
 You can leave off the `[...]`, in which case `PyTree` is simply a suggestively-named alternative to `Any`. ([By definition all types are PyTrees.](https://jax.readthedocs.io/en/latest/pytrees.html))
 
@@ -67,7 +85,7 @@ To enable multi-argument consistency checks (i.e. that shapes match up between a
 
 Regardless of your choice, **this approach synergises beautifully with `jax.jit`!** All shape checks will be performed at trace-time only, and will not impact runtime performance.
 
-### `jaxtyping.jaxtyped`
+### Option 1: `jaxtyping.jaxtyped`
 
 Decorate a function with this to have shapes checked for consistency across multiple arguments.
 
@@ -75,7 +93,7 @@ Example:
 
 ```python
 # Import both the annotation and the `jaxtyped` decorator from `jaxtyping`
-from jaxtyping import f32, jaxtyped
+from jaxtyping import Array, Float32, jaxtyped
 
 # Use your favourite typechecker: usually one of the two lines below.
 from typeguard import typechecked as typechecker
@@ -84,7 +102,9 @@ from beartype import beartype as typechecker
 # Write your function. @jaxtyped must be applied above @typechecker!
 @jaxtyped
 @typechecker
-def batch_outer_product(x: f32["b c1"], y: f32["b c2"]) -> f32["b c1 c2"]:
+def batch_outer_product(x: Float32[Array, "b c1"],
+                        y: Float32[Array, "b c2"]
+                      ) -> Float32[Array, "b c1 c2"]:
     return x[:, :, None] * y[:, None, :]
 ```
 
@@ -102,35 +122,44 @@ this function use the same axes sizes as the function it was called from.
 
 Likewise, this means you can use `isinstance` checks inside a function body
 and have them contribute to the same collection of consistency checks performed
-by a typechecker against its arguments. (Or even forgo a typechecker altogether,
-and just do your own manual `isinstance` checks.)
+by a typechecker against its arguments. (Or even forgo a typechecker that analyses arguments,
+and instead just do your own manual `isinstance` checks.)
 
 Only `isinstance` checks that pass will contribute to the store of axis name-size pairs; those
 that fail will not. As such it is safe to write e.g. `assert not isinstance(x,
-f32["foo"])`.
+Float32[Array, "foo"])`.
 
-### `jaxtyping.install_import_hook`
+### Option 2: `jaxtyping.install_import_hook`
 
 It can be a lot of effort to add `@jaxtyped` decorators all over your codebase.
-(Not to mention that double-decorators everywhere are a bit ugly.) The easier
-option is usually to use the import import hook.
+(Not to mention that double-decorators everywhere are a bit ugly.)
 
-Example:
+The easier option is usually to use the import hook.
 
+This can be used via a `with` block; for example:
 ```python
 from jaxtyping import install_import_hook
-# Plus either one of the following:
-install_import_hook("foo", ("typeguard", "typechecked"))  # decorate @jaxtyped and @typeguard.typechecked
-install_import_hook("foo", ("beartype", "beartype"))  # decorate @jaxtyped and @beartype.beartype
-install_import_hook("foo", None)  # decorate only @jaxtyped (if you have manually applied typechecking decorators)
+# Plus any one of the following:
+
+# decorate @jaxtyped and @typeguard.typechecked
+with install_import_hook("foo", ("typeguard", "typechecked")):
+    import foo          # Any module imported inside this `with` block, whose name begins
+    import foo.bar      # with the specified string, will automatically have both `@jaxtyped`
+    import foo.bar.qux  # and the specified typechecker applied to all of their functions.
+
+# decorate @jaxtyped and @beartype.beartype
+with install_import_hook("foo", ("beartype", "beartype")):
+    ...
+    
+# decorate only @jaxtyped (if you want that for some reason)
+with install_import_hook("foo", None):
+    ...
 ```
 
-Any module imported **afterwards**, whose name begins with the specified string, will automatically have both `@jaxtyped` and the specified typechecker applied to all of their functions. (E.g. in the above example `foo`, `foo.bar`, `foo.bar.qux` would all be hook'd).
-
-The import hook may be uninstalled after you've imported all the modules you're interested in:
+If you don't like using the `with` block, the hook can be used without that:
 ```python
-hook = install_import_hook(...)
-...  # perform imports
+hook = install_import_hook(...):
+import ...
 hook.uninstall()
 ```
 
@@ -144,13 +173,13 @@ install_import_hook(["foo", "bar.baz"], ...)
 ```python
 ### entry_point.py
 from jaxtyping import install_import_hook
-install_import_hook("do_stuff", ("typeguard", "typechecked"))
-import do_stuff
+with install_import_hook("do_stuff", ("typeguard", "typechecked")):
+    import do_stuff
 
 ### do_stuff.py
-from jaxtyping import f32
+from jaxtyping import Array, Float32
 
-def g(x: f32["..."]):
+def g(x: Float32[Array, "..."]):
     ...
 ```
 
@@ -159,11 +188,9 @@ def g(x: f32["..."]):
 ```python
 ### __init__.py
 from jaxtyping import install_import_hook
-hook = install_import_hook("my_library_name", ("beartype", "beartype"))
-from .subpackage import foo  # full name is my_library_name.subpackage so will be hook'd
-from .another_subpackage import bar  # full name is my_library_name.another_subpackage so will be hook'd.
-hook.uninstall()
-del hook, install_import_hook, jaxtyping  # keep interface tidy
+with install_import_hook("my_library_name", ("beartype", "beartype")):
+    from .subpackage import foo  # full name is my_library_name.subpackage so will be hook'd
+    from .another_subpackage import bar  # full name is my_library_name.another_subpackage so will be hook'd.
 ```
 
 #### pytest hook
@@ -174,23 +201,29 @@ pytest --jaxtyping-packages=foo,bar.baz,beartype.beartype
 ```
 which will apply the import hook to all modules whose names start with either `foo` or `bar.baz`. The typechecker used in this example is `beartype.beartype`.
 
+## Static type checking
+
+jaxtyping should be compatible with static type checkers (the big three are `mypy`, `pyright`, `pytype`) out of the box.
+
+Due to limitations of static type checkers, only the array type (JAX array vs NumPy array vs PyTorch tensor vs TensorFlow tensor) is checked. Shape and dtype are not checked. [See the FAQ](./FAQ.md) for more details.
+
 ## Abstract base classes
 
 ### `jaxtyping.AbstractDtype`
 
-The base class of all dtypes. This can be used to create your own custom collection of dtypes (analogous to `n`, `x` etc.) For example:
+The base class of all dtypes. This can be used to create your own custom collection of dtypes (analogous to `Float`, `Inexact` etc.) For example:
 ```python
-class u8_or_u16(AbstractDtype):
+class UInt8or16(AbstractDtype):
     dtypes = ["uint8", "uint16"]
 
-u8_or_u16["shape"]
+UInt8or16[Array, "shape"]
 ```
 which is functionally equivalent to
 ```python
-Union[u8["shape"], u16["shape"]]
+Union[UInt8[Array, "shape"], UInt16[Array, "shape"]]
 ```
 
 ### `jaxtyping.AbstractArray`
 
 The base class of all shape-and-dtype-specified arrays, e.g. it's a base class
-for `f32["foo"]`.
+for `Float32[Array, "foo"]`.

FAQ.md

@@ -1,43 +1,48 @@
 # FAQ
 
+## Does jaxtyping work with static type checkers like `mypy`/`pyright`/`pytype`?
+
+There is partial support for these. An annotation of the form `dtype[array, shape]` should be treated as just `array` by a static type checker. Unfortunately full dtype/shape checking is beyond the scope of what static type checking is currently capable of.
+
+(Note that at time of writing, `pytype` has a bug in that `dtype[array, shape]` is sometimes treated as `Any` rather than `array`. `mypy` and `pyright` both work fine.)
+
+## How does jaxtyping interact with `jax.jit`?
+
+jaxtyping and `jax.jit` synergise beautifully.
+
+When calling JAX operations wrapped in a `jax.jit`, then the dtype/shape-checking will happen at trace time. (When JAX traces your function prior to compiling it.) The actual compiled code does not have any dtype/shape-checking, and will therefore still be just as fast as before!
+
 ## `flake8` is throwing an error.
 
 In type annotations, strings are used for two different things. Sometimes they're strings. Sometimes they're "forward references", used to refer to a type that will be defined later.
 
 Some tooling in the Python ecosystem assumes that only the latter is true, and will throw spurious errors if you try to use a string just as a string (like we do).
 
-In the case of `flake8`, at least, this is easily resolved. Multi-dimensional arrays (e.g. `f32["b c"]`) will throw a very unusual error (F722, syntax error in forward annotation), so you can safely just disable this particular error globally. Uni-dimensional arrays (e.g. `f32["x"]`) will throw an error that's actually useful (F821, undefined name), so instead of disabling this globally, you should instead prepend a space to the start of your shape, e.g. `f32[" x"]`. `jaxtyping` will treat this in the same way, whilst `flake8` will now throw an F722 error that you can disable as before.
+In the case of `flake8`, at least, this is easily resolved. Multi-dimensional arrays (e.g. `Float32[Array, "b c"]`) will throw a very unusual error (F722, syntax error in forward annotation), so you can safely just disable this particular error globally. Uni-dimensional arrays (e.g. `Float32[Array, "x"]`) will throw an error that's actually useful (F821, undefined name), so instead of disabling this globally, you should instead prepend a space to the start of your shape, e.g. `Float32[Array, " x"]`. `jaxtyping` will treat this in the same way, whilst `flake8` will now throw an F722 error that you can disable as before.
 
-## What about support for static type checkers, like `mypy`, `pyright`, etc.?
+## Does jaxtyping use [PEP 646](https://www.python.org/dev/peps/pep-0646/) (variadic generics)?
 
-Nope.
+The intention of PEP 646 was to make it possible for static type checkers to perform shape checks of arrays. Unfortunately, this still isn't yet practical, so jaxtyping deliberately does not use this. (Yet?)
 
-Python's static typing ecosystem is a complicated collection of edge cases. Many of them block ML/scientific computing in particular. A few examples:
+The real problem is that Python's static typing ecosystem is a complicated collection of edge cases. Many of them block ML/scientific computing in particular. For example:
 
 1. The static type system is intrinsically not expressive enough to describe operations like concatenation, stacking, or broadcasting.
 
-2. Axes have to be lifted to type-level variables. Meanwhile the approach taken in libraries like `jaxtyping` and [TorchTyping](https://github.com/patrick-kidger/torchtyping) is to use value-level variables for types: because that's what the underlying JAX, PyTorch etc. libraries use! As such, making a static type checker work with these libraries would require either fundamentally rewriting these libraries, or exhaustively maintaining type stubs for them, and would *still* require a `typing.cast` any time you use anything unstubbed (e.g. any third party library, or part of your codebase you haven't typed yet). This is a huge maintenance burden for anyone.
+2. Axes have to be lifted to type-level variables. Meanwhile the approach taken in libraries like `jaxtyping` and [TorchTyping](https://github.com/patrick-kidger/torchtyping) is to use value-level variables for types: because that's what the underlying JAX, PyTorch etc. libraries use! As such, making a static type checker work with these libraries would require either fundamentally rewriting these libraries, or exhaustively maintaining type stubs for them, and would *still* require a `typing.cast` any time you use anything unstubbed (e.g. any third party library, or part of your codebase you haven't typed yet). This is a huge maintenance burden.
 
 3. Static type checkers have a variety of bugs that affect this use case. `mypy` doesn't support `Protocol`s correctly. `pyright` doesn't support genericised subprotocols. etc.
 
-4. Variadic generics exist. Variadic protocols do not. (It's not clear that these have been contemplated.)
+4. Variadic generics exist. Variadic protocols do not. (It's not clear that these were contemplated.)
 
-5. The syntax for static typing is verbose. You have to write things like `Array[Unpack[AnyShape], Literal[3], Height, Width]` instead of `Array["... 3 height width"]`.
+5. The syntax for static typing is a little verbose. You have to write things like `Array[Float32, Unpack[AnyShape], Literal[3], Height, Width]` instead of `Float32[Array, "... 3 height width"]`.
 
-6. [The underlying type system has flaws](https://github.com/patrick-kidger/torchtyping/issues/37#issuecomment-1153294196). [The numeric tower is broken](https://stackoverflow.com/a/69383462); [int is not a number](https://github.com/python/mypy/issues/3186#issuecomment-885718629); [virtual base classes don't work](https://github.com/python/mypy/issues/2922); [complex lies about having comparison operations, so type checkers have to lie about that lie in order to remove them again](https://posita.github.io/numerary/0.4/whytho/); `typing.*` don't work with `isinstance`; co/contra-variance are baked into containers (not specified at use-time); `dict` is variadic despite... not being variadic; bool is a subclass of int (!); ... etc. etc.
-
-## What about [PEP 646](https://www.python.org/dev/peps/pep-0646/) and variadic generics?
-
-[Doesn't change the previous issues, unfortunately.](https://github.com/patrick-kidger/torchtyping/issues/37) All the problems of the previous heading still hold true. They're just also true for types like `AnyDimensionalArray[Batch, Channels, AsManyArgumentsAsWePlease]` as well as types like `TwoDimensionalArray[Batch, Channels]`.
-
-## Is the lack of interaction with static typing a problem?
-
-At least for any software that is mostly just running JAX code, no!
-
-The correct way to use JAX is to put together all your operations, and then put a single `jax.jit` right at the very top. This gives you optimal speed; anything else will be unnecessarily (and substantially) slower.
-
-This means that all the type checking only gets resolved once: at trace time. Afterwards JAX still lowers everything down to the same optimised code.
-
-In some sense, `python myprogram.py` just ends up doing the same as `mypy myprogram.py`. Except instead of throwing away all the work used to parse your code, build the abstract syntax tree, etc. (and requiring you to then run `python myprogram.py` afterwards to actually use it), it can keep it around and just run your code immediately.
-
-TL;DR: `jax.jit` is amazing.
+6. [The underlying type system has flaws](https://github.com/patrick-kidger/torchtyping/issues/37#issuecomment-1153294196).  
+   [The numeric tower is broken](https://stackoverflow.com/a/69383462);  
+   [int is not a number](https://github.com/python/mypy/issues/3186#issuecomment-885718629);  
+   [virtual base classes don't work](https://github.com/python/mypy/issues/2922);  
+   [complex lies about having comparison operations, so type checkers have to lie about that lie in order to remove them again](https://posita.github.io/numerary/0.4/whytho/);  
+   `typing.*` don't work with `isinstance`;  
+   co/contra-variance are baked into containers (not specified at use-time);  
+   `dict` is variadic despite... not being variadic;  
+   bool is a subclass of int (!);  
+   ... etc. etc.

MANIFEST.in

@@ -1,2 +1,2 @@
-include LICENSE
-prune tests
+include jaxtyping/py.typed
+prune test

README.md

@@ -7,15 +7,18 @@ Type annotations **and runtime checking** for:
 
 **For example:**
 ```python
-from jaxtyping import f32, PyTree
+from jaxtyping import Array, Float, PyTree
 
-def matrix_multiply(x: f32["dim1 dim2"], y: f32["dim2 dim3"]) -> f32["dim1 dim3"]:
+# Accepts floating-point 2D arrays with matching dimensions
+def matrix_multiply(x: Float[Array, "dim1 dim2"],
+                    y: Float[Array, "dim2 dim3"]
+                  ) -> Float[Array, "dim1 dim3"]:
     ...
 
 def accepts_pytree_of_ints(x: PyTree[int]):
     ...
 
-def accepts_pytree_of_arrays(x: PyTree[f32["batch c1 c2"]]):
+def accepts_pytree_of_arrays(x: PyTree[Float[Array, "batch c1 c2"]]):
     ...
 ```
 
@@ -49,7 +52,7 @@ SymPy<->JAX conversion; train symbolic expressions via gradient descent: [sympy2
 
 Shape annotations + runtime type checking is inspired by [TorchTyping](https://github.com/patrick-kidger/torchtyping).
 
-The concise syntax is inspired by [etils.array_types](https://github.com/google/etils/tree/main/etils/array_types).
+The concise syntax is partially inspired by [etils.array_types](https://github.com/google/etils/tree/main/etils/array_types).
 
 ### Disclaimer
 

jaxtyping/__init__.py

@@ -17,38 +17,54 @@
 # IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 # CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 
+import typing
+
+
+if typing.TYPE_CHECKING:
+    # type checkers don't know which branch below will be executed
+    from jax.numpy import ndarray as Array
+else:
+    if getattr(typing, "GENERATING_DOCUMENTATION", False):
+
+        class Array:
+            pass
+
+        Array.__module__ = "builtins"
+    else:
+        from jax.numpy import ndarray as Array
+
 from .array_types import (
     AbstractArray,
     AbstractDtype,
-    Array,
-    b,
-    bf16,
-    c,
-    c64,
-    c128,
-    f,
-    f16,
-    f32,
-    f64,
+    BFloat16,
+    Bool,
+    Complex,
+    Complex64,
+    Complex128,
+    Float,
+    Float16,
+    Float32,
+    Float64,
     get_array_name_format,
-    i,
-    i8,
-    i16,
-    i32,
-    i64,
-    n,
+    Inexact,
+    Int,
+    Int8,
+    Int16,
+    Int32,
+    Int64,
+    Integer,
+    Num,
     set_array_name_format,
-    t,
-    u,
-    u8,
-    u16,
-    u32,
-    u64,
-    x,
+    Shaped,
+    UInt,
+    UInt8,
+    UInt16,
+    UInt32,
+    UInt64,
 )
 from .decorator import jaxtyped
 from .import_hook import install_import_hook
 from .pytree_type import PyTree
 
 
-__version__ = "0.0.2"
+__version__ = "0.2.6"

jaxtyping/array_types.py

@@ -17,11 +17,13 @@
 # IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 # CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 
+import enum
 import functools as ft
-from typing import Any, Dict, List, NoReturn, Optional, Tuple, Union
+import typing
+from typing import Any, Dict, List, NoReturn, Optional, Tuple, TYPE_CHECKING, Union
 from typing_extensions import Literal
 
-import jax.numpy as jnp
+import numpy as np
 
 from .decorator import storage
 
@@ -40,10 +42,17 @@ def set_array_name_format(value):
 
 _any_dtype = object()
 
+
 _anonymous_dim = object()
 _anonymous_variadic_dim = object()
 
 
+class _DimType(enum.Enum):
+    named = enum.auto()
+    fixed = enum.auto()
+    symbolic = enum.auto()
+
+
 class _NamedDim:
     def __init__(self, name, broadcastable):
         self.name = name
@@ -62,21 +71,28 @@ class _FixedDim:
         self.broadcastable = broadcastable
 
 
+class _SymbolicDim:
+    def __init__(self, expr, broadcastable):
+        self.expr = expr
+        self.broadcastable = broadcastable
+
+
 _AbstractDimOrVariadicDim = Union[
     Literal[_anonymous_dim],
     Literal[_anonymous_variadic_dim],
     _NamedDim,
     _NamedVariadicDim,
     _FixedDim,
+    _SymbolicDim,
 ]
-_AbstractDim = Union[Literal[_anonymous_dim], _NamedDim, _FixedDim]
+_AbstractDim = Union[Literal[_anonymous_dim], _NamedDim, _FixedDim, _SymbolicDim]
 
 
 def _check_dims(
     cls_dims: List[_AbstractDim],
     obj_shape: Tuple[int],
-    memo: Dict[str, Union[int, Tuple[int]]],
-):
+    single_memo: Dict[str, int],
+) -> bool:
     assert len(cls_dims) == len(obj_shape)
     for cls_dim, obj_size in zip(cls_dims, obj_shape):
         if cls_dim is _anonymous_dim:
@@ -86,12 +102,24 @@ def _check_dims(
         elif type(cls_dim) is _FixedDim:
             if cls_dim.size != obj_size:
                 return False
+        elif type(cls_dim) is _SymbolicDim:
+            try:
+                eval_size = eval(cls_dim.expr, single_memo)
+            except NameError as e:
+                raise NameError(
+                    f"Cannot process symbolic dimension '{cls_dim.expr}' as some "
+                    "dimension names have not been processed. In practice you should "
+                    "usually only use symbolic dimensions in annotations for return "
+                    "types, referring only to dimensions annotated for arguments."
+                ) from e
+            if eval_size != obj_size:
+                return False
         else:
             assert type(cls_dim) is _NamedDim
             try:
-                cls_size = memo[cls_dim.name]
+                cls_size = single_memo[cls_dim.name]
             except KeyError:
-                memo[cls_dim.name] = obj_size
+                single_memo[cls_dim.name] = obj_size
             else:
                 if cls_size != obj_size:
                     return False
@@ -100,36 +128,67 @@ def _check_dims(
 
 class _MetaAbstractArray(type):
     def __instancecheck__(cls, obj):
-        if not isinstance(obj, jnp.ndarray):
+        if not isinstance(obj, cls.array_type):
             return False
 
-        if cls.dtypes is not _any_dtype and obj.dtype not in cls.dtypes:
+        if hasattr(obj.dtype, "type") and hasattr(obj.dtype.type, "__name__"):
+            # JAX, numpy
+            dtype = obj.dtype.type.__name__
+        elif hasattr(obj.dtype, "as_numpy_dtype"):
+            # TensorFlow
+            dtype = obj.dtype.as_numpy_dtype.__name__
+        else:
+            # PyTorch
+            repr_dtype = repr(obj.dtype).split(".")
+            if len(repr_dtype) == 2 and repr_dtype[0] == "torch":
+                dtype = repr_dtype[1]
+            else:
+                raise RuntimeError(
+                    "Unrecognised array/tensor type to extract dtype from"
+                )
+
+        if cls.dtypes is not _any_dtype and dtype not in cls.dtypes:
             return False
 
-        if len(storage.memo_stack) == 0:
+        no_temp_memo = hasattr(storage, "memo_stack") and len(storage.memo_stack) != 0
+
+        if no_temp_memo:
+            single_memo, variadic_memo, variadic_broadcast_memo = storage.memo_stack[-1]
+            # Make a copy so we don't mutate the original memo during the shape check.
+            single_memo = single_memo.copy()
+            variadic_memo = variadic_memo.copy()
+            variadic_broadcast_memo = variadic_broadcast_memo.copy()
+        else:
             # `isinstance` happening outside any @jaxtyped decorators, e.g. at the
             # global scope. In this case just create a temporary memo, since we're not
             # going to be comparing against any stored values anyway.
-            memo = {}
-            temp_memo = True
-        else:
-            # Make a copy so we don't mutate the original memo during the shape check.
-            memo = storage.memo_stack[-1].copy()
-            temp_memo = False
+            single_memo = {}
+            variadic_memo = {}
+            variadic_broadcast_memo = {}
 
-        if cls._check_shape(obj, memo):
+        if cls._check_shape(obj, single_memo, variadic_memo, variadic_broadcast_memo):
             # We update the memo every time we successfully pass a shape check
-            if not temp_memo:
-                storage.memo_stack[-1] = memo
+            if no_temp_memo:
+                storage.memo_stack[-1] = (
+                    single_memo,
+                    variadic_memo,
+                    variadic_broadcast_memo,
+                )
             return True
         else:
             return False
 
-    def _check_shape(cls, obj, memo):
+    def _check_shape(
+        cls,
+        obj,
+        single_memo: Dict[str, int],
+        variadic_memo: Dict[str, Tuple[int, ...]],
+        variadic_broadcast_memo: Dict[str, List[Tuple[int, ...]]],
+    ):
         if cls.index_variadic is None:
             if obj.ndim != len(cls.dims):
                 return False
-            return _check_dims(cls.dims, obj.shape, memo)
+            return _check_dims(cls.dims, obj.shape, single_memo)
         else:
             if obj.ndim < len(cls.dims) - 1:
                 return False
@@ -137,38 +196,47 @@ class _MetaAbstractArray(type):
             j = -(len(cls.dims) - i - 1)
             if j == 0:
                 j = None
-            if not _check_dims(cls.dims[:i], obj.shape[:i], memo):
+            if not _check_dims(cls.dims[:i], obj.shape[:i], single_memo):
                 return False
-            if j is not None and not _check_dims(cls.dims[j:], obj.shape[j:], memo):
+            if j is not None and not _check_dims(
+                cls.dims[j:], obj.shape[j:], single_memo
+            ):
                 return False
             variadic_dim = cls.dims[i]
-            if variadic_dim is not _anonymous_variadic_dim:
+            if variadic_dim is _anonymous_variadic_dim:
+                return True
+            else:
+                assert type(variadic_dim) is _NamedVariadicDim
                 variadic_name = variadic_dim.name
                 try:
-                    variadic_shape = memo[variadic_name]
+                    if variadic_dim.broadcastable:
+                        variadic_shapes = variadic_broadcast_memo[variadic_name]
+                    else:
+                        variadic_shape = variadic_memo[variadic_name]
                 except KeyError:
-                    memo[variadic_name] = obj.shape[i:j]
+                    if variadic_dim.broadcastable:
+                        variadic_broadcast_memo[variadic_name] = [obj.shape[i:j]]
+                    else:
+                        variadic_memo[variadic_name] = obj.shape[i:j]
+                    return True
                 else:
                     if variadic_dim.broadcastable:
-                        new_variadic_shape = []
-                        obj_shape = obj.shape[i:j]
-                        if len(variadic_shape) != len(obj_shape):
-                            return False
-                        for old_size, new_size in zip(variadic_shape, obj_shape):
-                            if old_size == 1:
-                                new_variadic_shape.append(new_size)
-                            else:
-                                if new_size != 1 and old_size != new_size:
-                                    return False
-                                new_variadic_shape.append(old_size)
-                        memo[variadic_name] = tuple(new_variadic_shape)
+                        new_shape = obj.shape[i:j]
+                        for existing_shape in variadic_shapes:
+                            try:
+                                np.broadcast_shapes(new_shape, existing_shape)
+                            except ValueError:
+                                return False
+                        variadic_shapes.append(new_shape)
+                        return True
                     else:
                         return variadic_shape == obj.shape[i:j]
-            return True
+            assert False
 
 
 class AbstractArray(metaclass=_MetaAbstractArray):
-    dtypes: List[jnp.dtype]
+    array_type: Any
+    dtypes: List[str]
     dims: List[_AbstractDimOrVariadicDim]
     index_variadic: Optional[int]
 
@@ -176,16 +244,24 @@ class AbstractArray(metaclass=_MetaAbstractArray):
 class _MetaAbstractDtype(type):
     def __instancecheck__(cls, obj: Any) -> NoReturn:
         raise RuntimeError(
-            f"Do not use `isinstance(x, jaxtyping.{cls.__name__}`. If you want to "
+            f"Do not use `isinstance(x, jaxtyping.{cls.__name__})`. If you want to "
             "check just the dtype of an array, then use "
-            f'`jaxtyping.{cls.__name__}["..."]`.'
+            f'`jaxtyping.{cls.__name__}[jnp.ndarray, "..."]`.'
         )
 
     @ft.lru_cache(maxsize=None)
-    def __getitem__(cls, dim_str: str) -> _MetaAbstractArray:
+    def __getitem__(cls, item: Tuple[Any, str]) -> _MetaAbstractArray:
+        if not isinstance(item, tuple) or len(item) != 2:
+            raise ValueError(
+                "As of jaxtyping v0.2.0, type annotations must now include an explicit "
+                "array type. For example `jaxtyping.Float32[jnp.ndarray, 'foo bar']`."
+            )
+        array_type, dim_str = item
+        del item
         if not isinstance(dim_str, str):
             raise ValueError(
-                "Shape specification must be a string. Axes should be separated with spaces."
+                "Shape specification must be a string. Axes should be separated with "
+                "spaces."
             )
         dims = []
         index_variadic = None
@@ -195,121 +271,250 @@ class _MetaAbstractDtype(type):
                 raise ValueError(
                     "Dimensions should be separated with spaces, not commas"
                 )
-            broadcastable = False
             if elem.endswith("#"):
-                broadcastable = True
-                elem = elem[:-1]
-            try:
-                elem = int(elem)
-            except ValueError:
-                if elem == "_":
-                    elem = _anonymous_dim
-                elif elem == "...":
-                    if index_variadic is not None:
-                        raise ValueError("Cannot have multiple variadic dimensions")
-                    index_variadic = index
-                    elem = _anonymous_variadic_dim
-                elif elem[0] == "*":
-                    if index_variadic is not None:
-                        raise ValueError("Cannot have multiple variadic dimensions")
-                    index_variadic = index
-                    elem = _NamedVariadicDim(elem[1:], broadcastable)
-                else:
-                    elem = _NamedDim(elem, broadcastable)
+                raise ValueError(
+                    "As of jaxtyping v0.1.0, broadcastable dimensions are now denoted "
+                    "with a # at the start, rather than at the end"
+                )
+
+            if "..." in elem:
+                if elem != "...":
+                    raise ValueError(
+                        "Anonymous multiple dimension '...' must be used on its own; "
+                        f"got {elem}"
+                    )
+                broadcastable = False
+                variadic = True
+                anonymous = True
+                dim_type = _DimType.named
             else:
+                broadcastable = False
+                variadic = False
+                anonymous = False
+                while True:
+                    if len(elem) == 0:
+                        # This branch needed as just `_` is valid
+                        break
+                    first_char = elem[0]
+                    if first_char == "#":
+                        if broadcastable:
+                            raise ValueError(
+                                "Do not use # twice to denote broadcastability, e.g. "
+                                "`##foo` is not allowed"
+                            )
+                        broadcastable = True
+                        elem = elem[1:]
+                    elif first_char == "*":
+                        if variadic:
+                            raise ValueError(
+                                "Do not use * twice to denote accepting multiple "
+                                "dimensions, e.g. `**foo` is not allowed"
+                            )
+                        variadic = True
+                        elem = elem[1:]
+                    elif first_char == "_":
+                        if anonymous:
+                            raise ValueError(
+                                "Do not use _ twice to denote anonymity, e.g. `__foo` "
+                                "is not allowed"
+                            )
+                        anonymous = True
+                        elem = elem[1:]
+                    else:
+                        break
+                try:
+                    elem = int(elem)
+                except ValueError:
+                    if len(elem) == 0 or elem.isidentifier():
+                        dim_type = _DimType.named
+                    else:
+                        dim_type = _DimType.symbolic
+                else:
+                    dim_type = _DimType.fixed
+
+            if variadic:
+                if index_variadic is not None:
+                    raise ValueError(
+                        "Cannot use multiple-dimension specifiers (`*name` or `...`) "
+                        "more than once"
+                    )
+                index_variadic = index
+
+            if dim_type is _DimType.fixed:
+                if variadic:
+                    raise ValueError(
+                        "Cannot have a fixed axis bind to multiple dimensions, e.g. "
+                        "`*4` is not allowed"
+                    )
+                if anonymous:
+                    raise ValueError(
+                        "Cannot have a fixed axis be anonymous, e.g. `_4` is not "
+                        "allowed"
+                    )
                 elem = _FixedDim(elem, broadcastable)
+            elif dim_type is _DimType.named:
+                if anonymous:
+                    if broadcastable:
+                        raise ValueError(
+                            "Cannot have a dimension be both anonymous and "
+                            "broadcastable, e.g. `#_` is not allowed"
+                        )
+                    if variadic:
+                        elem = _anonymous_variadic_dim
+                    else:
+                        elem = _anonymous_dim
+                else:
+                    if variadic:
+                        elem = _NamedVariadicDim(elem, broadcastable)
+                    else:
+                        elem = _NamedDim(elem, broadcastable)
+            else:
+                assert dim_type is _DimType.symbolic
+                if anonymous:
+                    raise ValueError(
+                        "Cannot have a symbolic dimension be anonymous, e.g. "
+                        "`_foo+bar` is not allowed"
+                    )
+                if variadic:
+                    raise ValueError(
+                        "Cannot have symbolic multiple-dimensions, e.g. "
+                        "`*foo+bar` is not allowed"
+                    )
+                elem = compile(elem, "<string>", "eval")
+                elem = _SymbolicDim(elem, broadcastable)
             dims.append(elem)
         if _array_name_format == "dtype_and_shape":
-            name = f"{cls.__name__}['{dim_str}']"
+            # In python 3.8, e.g., typing.Union lacks `__name__`.
+            try:
+                type_str = array_type.__name__
+            except AttributeError:
+                type_str = repr(array_type)
+            name = f"{cls.__name__}[{type_str}, '{dim_str}']"
         elif _array_name_format == "array":
-            name = "Array"
+            name = array_type.__name__
         else:
             raise ValueError(f"array_name_format {_array_name_format} not recognised")
-        return _MetaAbstractArray(
+        out = _MetaAbstractArray(
             name,
             (AbstractArray,),
-            dict(dtypes=cls.dtypes, dims=dims, index_variadic=index_variadic),
+            dict(
+                array_type=array_type,
+                dtypes=cls.dtypes,
+                dims=dims,
+                index_variadic=index_variadic,
+            ),
         )
+        if getattr(typing, "GENERATING_DOCUMENTATION", False):
+            out.__module__ = "builtins"
+        else:
+            out.__module__ = "jaxtyping"
+        return out
 
 
 class AbstractDtype(metaclass=_MetaAbstractDtype):
-    dtypes: Union[str, List[str], Literal[_any_dtype]]
+    dtypes: Union[Literal[_any_dtype], List[str]]
 
     def __init__(self, *args, **kwargs):
         raise RuntimeError(
             "AbstractDtype cannot be instantiated. Perhaps you wrote e.g. "
-            '`f32("shape")` when you mean `f32["shape"]`?'
+            '`Float32("shape")` when you mean `Float32[jnp.ndarray, "shape"]`?'
         )
 
     def __init_subclass__(cls, **kwargs):
         super().__init_subclass__(**kwargs)
 
-        dtypes = cls.dtypes
-        if dtypes is not _any_dtype:
-            if not isinstance(dtypes, list):
-                dtypes = [dtypes]
-            dtypes = [jnp.dtype(d) for d in dtypes]
+        dtypes: Union[Literal[_any_dtype], str, List[str]] = cls.dtypes
+        if isinstance(dtypes, str):
+            dtypes = [dtypes]
         cls.dtypes = dtypes
 
 
-_bool = "bool"
-_uint8 = "uint8"
-_uint16 = "uint16"
-_uint32 = "uint32"
-_uint64 = "uint64"
-_int8 = "int8"
-_int16 = "int16"
-_int32 = "int32"
-_int64 = "int64"
-_bfloat16 = "bfloat16"
-_float16 = "float16"
-_float32 = "float32"
-_float64 = "float64"
-_complex64 = "complex64"
-_complex128 = "complex128"
+if TYPE_CHECKING:
+    # Note that `from typing_extensions import Annotated; ... = Annotated`
+    # does not work with static type checkers. `Annotated` is a typeform rather
+    # than a type, meaning it cannot be assigned.
+    from typing_extensions import Annotated as BFloat16
+    from typing_extensions import Annotated as Bool
+    from typing_extensions import Annotated as Complex
+    from typing_extensions import Annotated as Complex64
+    from typing_extensions import Annotated as Complex128
+    from typing_extensions import Annotated as Float
+    from typing_extensions import Annotated as Float16
+    from typing_extensions import Annotated as Float32
+    from typing_extensions import Annotated as Float64
+    from typing_extensions import Annotated as Inexact
+    from typing_extensions import Annotated as Int
+    from typing_extensions import Annotated as Int8
+    from typing_extensions import Annotated as Int16
+    from typing_extensions import Annotated as Int32
+    from typing_extensions import Annotated as Int64
+    from typing_extensions import Annotated as Integer
+    from typing_extensions import Annotated as Num
+    from typing_extensions import Annotated as Shaped
+    from typing_extensions import Annotated as UInt
+    from typing_extensions import Annotated as UInt8
+    from typing_extensions import Annotated as UInt16
+    from typing_extensions import Annotated as UInt32
+    from typing_extensions import Annotated as UInt64
+else:
+    _bool = "bool_"
+    _uint8 = "uint8"
+    _uint16 = "uint16"
+    _uint32 = "uint32"
+    _uint64 = "uint64"
+    _int8 = "int8"
+    _int16 = "int16"
+    _int32 = "int32"
+    _int64 = "int64"
+    _bfloat16 = "bfloat16"
+    _float16 = "float16"
+    _float32 = "float32"
+    _float64 = "float64"
+    _complex64 = "complex64"
+    _complex128 = "complex128"
 
+    def _make_dtype(_dtypes, name):
+        class _Cls(AbstractDtype):
+            dtypes = _dtypes
 
-def _make_dtype(_dtypes, name):
-    class _Cls(AbstractDtype):
-        dtypes = _dtypes
+        _Cls.__name__ = name
+        _Cls.__qualname__ = name
+        if getattr(typing, "GENERATING_DOCUMENTATION", False):
+            _Cls.__module__ = "builtins"
+        else:
+            _Cls.__module__ = "jaxtyping"
+        return _Cls
 
-    _Cls.__name__ = name
-    _Cls.__qualname__ = name
-    return _Cls
+    UInt8 = _make_dtype(_uint8, "UInt8")
+    UInt16 = _make_dtype(_uint16, "UInt16")
+    UInt32 = _make_dtype(_uint32, "UInt32")
+    UInt64 = _make_dtype(_uint64, "UInt64")
+    Int8 = _make_dtype(_int8, "Int8")
+    Int16 = _make_dtype(_int16, "Int16")
+    Int32 = _make_dtype(_int32, "Int32")
+    Int64 = _make_dtype(_int64, "Int64")
+    BFloat16 = _make_dtype(_bfloat16, "BFloat16")
+    Float16 = _make_dtype(_float16, "Float16")
+    Float32 = _make_dtype(_float32, "Float32")
+    Float64 = _make_dtype(_float64, "Float64")
+    Complex64 = _make_dtype(_complex64, "Complex64")
+    Complex128 = _make_dtype(_complex128, "Complex128")
 
+    uints = [_uint8, _uint16, _uint32, _uint64]
+    ints = [_int8, _int16, _int32, _int64]
+    floats = [_bfloat16, _float16, _float32, _float64]
+    complexes = [_complex64, _complex128]
 
-b = _make_dtype(_bool, "b")
-u8 = _make_dtype(_uint8, "u8")
-u16 = _make_dtype(_uint16, "u16")
-u32 = _make_dtype(_uint32, "u32")
-u64 = _make_dtype(_uint64, "u64")
-i8 = _make_dtype(_int8, "i8")
-i16 = _make_dtype(_int16, "i16")
-i32 = _make_dtype(_int32, "i32")
-i64 = _make_dtype(_int64, "i64")
-bf16 = _make_dtype(_bfloat16, "bf16")
-f16 = _make_dtype(_float16, "f16")
-f32 = _make_dtype(_float32, "f32")
-f64 = _make_dtype(_float64, "f64")
-c64 = _make_dtype(_complex64, "c64")
-c128 = _make_dtype(_complex128, "c128")
+    # We match NumPy's type hierarachy in what types to provide. See the diagram at
+    # https://numpy.org/doc/stable/reference/arrays.scalars.html#scalars
 
-uints = [_uint8, _uint16, _uint32, _uint64]
-ints = [_int8, _int16, _int32, _int64]
-floats = [_bfloat16, _float16, _float32, _float64]
-complexes = [_complex64, _complex128]
+    Bool = _make_dtype(_bool, "Bool")
+    UInt = _make_dtype(uints, "UInt")
+    Int = _make_dtype(ints, "Int")
+    Integer = _make_dtype(uints + ints, "Integer")
+    Float = _make_dtype(floats, "Float")
+    Complex = _make_dtype(complexes, "Complex")
+    Inexact = _make_dtype(floats + complexes, "Inexact")
+    Num = _make_dtype(uints + ints + floats + complexes, "Num")
 
-# We match NumPy's type hierarachy in what types to provide. See the diagram at
-# https://numpy.org/doc/stable/reference/arrays.scalars.html#scalars
-#
-# No attempt is made to match up against their character codes: all of the below are
-# abstract base classes without NumPy chararacter codes.
-
-u = _make_dtype(uints, "u")
-i = _make_dtype(ints, "i")
-t = _make_dtype(uints + ints, "t")  # integer
-f = _make_dtype(floats, "f")
-c = _make_dtype(complexes, "c")
-x = _make_dtype(floats + complexes, "x")  # inexact
-n = _make_dtype(uints + ints + floats + complexes, "n")  # number
-Array = _make_dtype(_any_dtype, "Array")
+    Shaped = _make_dtype(_any_dtype, "Shaped")

jaxtyping/decorator.py

@@ -22,17 +22,26 @@ import threading
 
 
 storage = threading.local()
-storage.memo_stack = []
+
+
+class _Jaxtyped:
+    def __init__(self, fn):
+        self.fn = fn
+
+    def __get__(self, instance, owner):
+        return ft.wraps(self.fn)(_Jaxtyped(self.fn.__get__(instance, owner)))
+
+    def __call__(self, *args, **kwargs):
+        try:
+            memo_stack = storage.memo_stack
+        except AttributeError:
+            memo_stack = storage.memo_stack = []
+        memo_stack.append(({}, {}, {}))
+        try:
+            return self.fn(*args, **kwargs)
+        finally:
+            memo_stack.pop()
 
 
 def jaxtyped(fn):
-    @ft.wraps(fn)
-    def wrapper(*args, **kwargs):
-        memo = {}
-        storage.memo_stack.append(memo)
-        try:
-            return fn(*args, **kwargs)
-        finally:
-            storage.memo_stack.pop()
-
-    return wrapper
+    return ft.wraps(fn)(_Jaxtyped(fn))

jaxtyping/import_hook.py

@@ -31,19 +31,20 @@
 #
 # Permission is hereby granted, free of charge, to any person obtaining a copy of this
 # software and associated documentation files (the "Software"), to deal in the Software
-# without restriction, including without limitation the rights to use, copy, modify, merge,
-# publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons
-# to whom the Software is furnished to do so, subject to the following conditions:
+# without restriction, including without limitation the rights to use, copy, modify,
+# merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
+# permit persons to whom the Software is furnished to do so, subject to the following
+# conditions:
 #
-# The above copyright notice and this permission notice shall be included in all copies or
-# substantial portions of the Software.
+# The above copyright notice and this permission notice shall be included in all copies
+# or substantial portions of the Software.
 #
 # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
-# INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
-# PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE
-# FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
-# OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
-# DEALINGS IN THE SOFTWARE.
+# INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
+# PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
+# CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE
+# OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 #
 # ---------
 
@@ -148,7 +149,8 @@ class _JaxtypingLoader(SourceFileLoader):
         )
 
     def exec_module(self, module):
-        # Use a custom optimization marker – the import lock should make this monkey patch safe
+        # Use a custom optimization marker - the import lock should make this monkey
+        # patch safe
         with patch(
             "importlib._bootstrap_external.cache_from_source",
             _optimized_cache_from_source,
@@ -216,7 +218,8 @@ class ImportHookManager:
 def install_import_hook(
     modules: Iterable[str], typechecker: Optional[Tuple[str, str]]
 ) -> ImportHookManager:
-    """Automatically apply `@jaxtyped`, and optionally a type checker, to all classes and functions.
+    """Automatically apply `@jaxtyped`, and optionally a type checker, to all classes
+    and functions.
 
     It will only be applied to modules loaded **after** this hook has been installed.
 

jaxtyping/py.typed

@@ -0,0 +1 @@
+

jaxtyping/pytree_type.py

@@ -18,7 +18,9 @@
 # CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 
 import functools as ft
-from typing import Generic, TypeVar
+import typing
+from typing import Generic, TYPE_CHECKING, TypeVar
+from typing_extensions import Protocol
 
 import jax
 import typeguard
@@ -33,6 +35,7 @@ class _FakePyTree(Generic[_T]):
 
 _FakePyTree.__name__ = "PyTree"
 _FakePyTree.__qualname__ = "PyTree"
+_FakePyTree.__module__ = "builtins"
 # Can't do type("PyTree", (Generic[_T],), {}) because dynamic subclassing of typeforms
 # isn't allowed.
 # Can't do types.new_class("PyTree", (Generic[_T],), {}) because that has __module__
@@ -49,7 +52,12 @@ class _MetaPyTree(type):
     @ft.lru_cache(maxsize=None)
     def __getitem__(cls, item):
         name = str(_FakePyTree[item])
-        return _MetaSubscriptPyTree(name, (), {"leaftype": item})
+        out = _MetaSubscriptPyTree(name, (), {"leaftype": item})
+        if getattr(typing, "GENERATING_DOCUMENTATION", False):
+            out.__module__ = "builtins"
+        else:
+            out.__module__ = "jaxtyping"
+        return out
 
 
 class _MetaSubscriptPyTree(type):
@@ -79,7 +87,18 @@ class _MetaSubscriptPyTree(type):
         return all(map(is_leaftype, leaves))
 
 
-PyTree = _MetaPyTree("PyTree", (), {})
+if TYPE_CHECKING:
+    # Work around pytype bug #1288
+    # pytype: skip-file
+    class PyTree(Protocol[_T]):
+        pass
+
+else:
+    PyTree = _MetaPyTree("PyTree", (), {})
+    if getattr(typing, "GENERATING_DOCUMENTATION", False):
+        PyTree.__module__ = "builtins"
+    else:
+        PyTree.__module__ = "jaxtyping"
 # Can't do `class PyTree(Generic[_T]): ...` because we need to override the
-# instancecheck for PyTree[foo], but we subclassing
+# instancecheck for PyTree[foo], but subclassing
 # `type(Generic[int])`, i.e. `typing._GenericAlias` is disallowed.

setup.py

@@ -28,7 +28,8 @@ _here = pathlib.Path(__file__).resolve().parent
 
 name = "jaxtyping"
 
-# for simplicity we actually store the version in the __version__ attribute in the source
+# for simplicity we actually store the version in the __version__ attribute in the
+# source
 with open(_here / name / "__init__.py") as f:
     meta_match = re.search(r"^__version__ = ['\"]([^'\"]*)['\"]", f.read(), re.M)
     if meta_match:
@@ -40,7 +41,10 @@ author = "Patrick Kidger"
 
 author_email = "contact@kidger.site"
 
-description = "Type annotations and runtime checking for shape and dtype of JAX arrays, and PyTrees."
+description = (
+    "Type annotations and runtime checking for shape and dtype of JAX "
+    "arrays, and PyTrees."
+)
 
 with open(_here / "README.md", "r") as f:
     readme = f.read()
@@ -63,7 +67,12 @@ python_requires = "~=3.7"
 
 # We use typeguard internally (in a fairly minimal way), but it's not required that
 # end users make the same choice.
-install_requires = ["jax>=0.3.4", "typeguard>=2.13.3", "typing_extensions>=4.2.0"]
+install_requires = [
+    "jax>=0.3.4",
+    "numpy>=1.20.0",
+    "typeguard>=2.13.3",
+    "typing_extensions>=4.2.0",
+]
 
 entry_points = dict(pytest11=["jaxtyping = jaxtyping.pytest_plugin"])
 
@@ -85,4 +94,5 @@ setuptools.setup(
     install_requires=install_requires,
     entry_points=entry_points,
     packages=[name],
+    include_package_data=True,
 )

test/conftest.py

@@ -19,13 +19,24 @@
 
 import random
 
-import beartype
 import jax.random as jr
 import pytest
 import typeguard
 
 
-@pytest.fixture(params=[typeguard.typechecked, beartype.beartype])
+try:
+    import beartype
+except ImportError:
+
+    def skip(*args, **kwargs):
+        pytest.skip("Beartype not installed")
+
+    typecheck_params = [typeguard.typechecked, skip]
+else:
+    typecheck_params = [typeguard.typechecked, beartype.beartype]
+
+
+@pytest.fixture(params=typecheck_params)
 def typecheck(request):
     return request.param
 
@@ -37,6 +48,3 @@ def getkey():
         return jr.PRNGKey(random.randint(0, 2**31 - 1))
 
     return _getkey
-
-
-ParamException = (TypeError, beartype.roar.BeartypeCallHintParamViolation)

test/helpers.py

@@ -17,12 +17,17 @@
 # IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 # CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 
-import beartype
 import equinox as eqx
 
 
-ParamError = (TypeError, beartype.roar.BeartypeCallHintParamViolation)
-ReturnError = (TypeError, beartype.roar.BeartypeCallHintReturnViolation)
+try:
+    import beartype
+except ImportError:
+    ParamError = TypeError
+    ReturnError = TypeError
+else:
+    ParamError = (TypeError, beartype.roar.BeartypeCallHintParamViolation)
+    ReturnError = (TypeError, beartype.roar.BeartypeCallHintReturnViolation)
 
 
 @eqx.filter_jit

test/import_hook_tester_beartype.py

@@ -19,12 +19,13 @@
 
 import jax.numpy as jnp
 import pytest
-from helpers import ParamError
 
-from jaxtyping import f32
+from jaxtyping import Float32
+
+from .helpers import ParamError
 
 
-def g(x: f32[" b"]):
+def g(x: Float32[jnp.ndarray, " b"]):
     pass
 
 

test/import_hook_tester_broken_checker.py

@@ -19,12 +19,13 @@
 
 import jax.numpy as jnp
 import pytest
-from helpers import ParamError
 
-from jaxtyping import f32
+from jaxtyping import Float32
+
+from .helpers import ParamError
 
 
-def g(x: f32[" b"]):
+def g(x: Float32[jnp.ndarray, " b"]):
     pass
 
 

test/import_hook_tester_transitive/another_file.py

@@ -19,12 +19,13 @@
 
 import jax.numpy as jnp
 import pytest
-from helpers import ParamError
 
-from jaxtyping import f32
+from jaxtyping import Float32
+
+from ..helpers import ParamError
 
 
-def g(x: f32[" b"]):
+def g(x: Float32[jnp.ndarray, " b"]):
     pass
 
 

test/import_hook_tester_typeguard.py

@@ -19,12 +19,13 @@
 
 import jax.numpy as jnp
 import pytest
-from helpers import ParamError
 
-from jaxtyping import f32
+from jaxtyping import Float32
+
+from .helpers import ParamError
 
 
-def g(x: f32[" b"]):
+def g(x: Float32[jnp.ndarray, " b"]):
     pass
 
 

test/test_array.py

@@ -20,31 +20,64 @@
 import jax.numpy as jnp
 import jax.random as jr
 import pytest
-from helpers import ParamError, ReturnError
 
-from jaxtyping import Array, f, f32, jaxtyped
+from jaxtyping import AbstractDtype, Array, Float, Float32, jaxtyped, Shaped
+
+from .helpers import ParamError, ReturnError
 
 
 def test_basic(typecheck):
     @jaxtyped
     @typecheck
-    def g(x: Array["..."]):
+    def g(x: Shaped[Array, "..."]):
         pass
 
     g(jnp.array(1.0))
 
 
+def test_dtypes():
+    from jaxtyping import (  # noqa: F401
+        Array,
+        BFloat16,
+        Bool,
+        Complex,
+        Complex64,
+        Complex128,
+        Float,
+        Float16,
+        Float32,
+        Float64,
+        Inexact,
+        Int,
+        Int8,
+        Int16,
+        Int32,
+        Int64,
+        Num,
+        Shaped,
+        UInt,
+        UInt8,
+        UInt16,
+        UInt32,
+        UInt64,
+    )
+
+    for key, val in locals().items():
+        if issubclass(val, AbstractDtype):
+            assert key == val.__name__
+
+
 def test_return(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f["b c"]) -> f["c b"]:
+    def g(x: Float[Array, "b c"]) -> Float[Array, "c b"]:
         return jnp.transpose(x)
 
     g(jr.normal(getkey(), (3, 4)))
 
     @jaxtyped
     @typecheck
-    def h(x: f["b c"]) -> f["b c"]:
+    def h(x: Float[Array, "b c"]) -> Float[Array, "b c"]:
         return jnp.transpose(x)
 
     with pytest.raises(ReturnError):
@@ -54,7 +87,7 @@ def test_return(typecheck, getkey):
 def test_two_args(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: Array["b c"], y: Array["c d"]):
+    def g(x: Shaped[Array, "b c"], y: Shaped[Array, "c d"]):
         return x @ y
 
     g(jr.normal(getkey(), (3, 4)), jr.normal(getkey(), (4, 5)))
@@ -63,7 +96,7 @@ def test_two_args(typecheck, getkey):
 
     @jaxtyped
     @typecheck
-    def h(x: Array["b c"], y: Array["c d"]) -> Array["b d"]:
+    def h(x: Shaped[Array, "b c"], y: Shaped[Array, "c d"]) -> Shaped[Array, "b d"]:
         return x @ y
 
     h(jr.normal(getkey(), (3, 4)), jr.normal(getkey(), (4, 5)))
@@ -74,7 +107,7 @@ def test_two_args(typecheck, getkey):
 def test_any_dtype(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: Array["a b"]) -> Array["a b"]:
+    def g(x: Shaped[Array, "a b"]) -> Shaped[Array, "a b"]:
         return x
 
     g(jr.normal(getkey(), (3, 4)))
@@ -91,12 +124,12 @@ def test_any_dtype(typecheck, getkey):
 def test_nested_jaxtyped(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["b c"], transpose: bool) -> f32["c b"]:
+    def g(x: Float32[Array, "b c"], transpose: bool) -> Float32[Array, "c b"]:
         return h(x, transpose)
 
     @jaxtyped
     @typecheck
-    def h(x: f32["c b"], transpose: bool) -> f32["b c"]:
+    def h(x: Float32[Array, "c b"], transpose: bool) -> Float32[Array, "b c"]:
         if transpose:
             return jnp.transpose(x)
         else:
@@ -112,11 +145,11 @@ def test_nested_jaxtyped(typecheck, getkey):
 def test_nested_nojaxtyped(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["b c"]):
+    def g(x: Float32[Array, "b c"]):
         return h(x)
 
     @typecheck
-    def h(x: f32["c b"]):
+    def h(x: Float32[Array, "c b"]):
         return x
 
     with pytest.raises(ParamError):
@@ -126,14 +159,14 @@ def test_nested_nojaxtyped(typecheck, getkey):
 def test_isinstance(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["b c"]) -> f32[" z"]:
+    def g(x: Float32[Array, "b c"]) -> Float32[Array, " z"]:
         y = jnp.transpose(x)
-        assert isinstance(y, f32["c b"])
+        assert isinstance(y, Float32[Array, "c b"])
         assert not isinstance(
-            y, f32["b z"]
+            y, Float32[Array, "b z"]
         )  # z left unbound as b!=c (unless x symmetric, which it isn't)
         out = jr.normal(getkey(), (500,))
-        assert isinstance(out, f32["z"])  # z now bound
+        assert isinstance(out, Float32[Array, "z"])  # z now bound
         return out
 
     g(jr.normal(getkey(), (2, 3)))
@@ -142,7 +175,9 @@ def test_isinstance(typecheck, getkey):
 def test_fixed(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["4 5 foo"], y: f32[" foo"]) -> f32["4 5"]:
+    def g(
+        x: Float32[Array, "4 5 foo"], y: Float32[Array, " foo"]
+    ) -> Float32[Array, "4 5"]:
         return x @ y
 
     a = jr.normal(getkey(), (4, 5, 2))
@@ -157,7 +192,7 @@ def test_fixed(typecheck, getkey):
 def test_anonymous(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["foo _"], y: f32[" _"]):
+    def g(x: Float32[Array, "foo _"], y: Float32[Array, " _"]):
         pass
 
     a = jr.normal(getkey(), (3, 4))
@@ -168,7 +203,11 @@ def test_anonymous(typecheck, getkey):
 def test_named_variadic(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["*batch foo"], y: f32[" *batch"], z: f32[" foo"]):
+    def g(
+        x: Float32[Array, "*batch foo"],
+        y: Float32[Array, " *batch"],
+        z: Float32[Array, " foo"],
+    ):
         pass
 
     c = jr.normal(getkey(), (5,))
@@ -188,7 +227,7 @@ def test_named_variadic(typecheck, getkey):
 
     @jaxtyped
     @typecheck
-    def h(x: f32[" foo *batch"], y: f32[" foo *batch bar"]):
+    def h(x: Float32[Array, " foo *batch"], y: Float32[Array, " foo *batch bar"]):
         pass
 
     a = jr.normal(getkey(), (4,))
@@ -204,7 +243,7 @@ def test_named_variadic(typecheck, getkey):
 def test_anonymous_variadic(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["... foo"], y: f32[" foo"]):
+    def g(x: Float32[Array, "... foo"], y: Float32[Array, " foo"]):
         pass
 
     a1 = jr.normal(getkey(), (5,))
@@ -226,7 +265,7 @@ def test_anonymous_variadic(typecheck, getkey):
 def test_broadcast_fixed(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32["4#"]):
+    def g(x: Float32[Array, "#4"]):
         pass
 
     g(jr.normal(getkey(), (4,)))
@@ -239,7 +278,7 @@ def test_broadcast_fixed(typecheck, getkey):
 def test_broadcast_named(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32[" foo#"], y: f32[" foo#"]):
+    def g(x: Float32[Array, " #foo"], y: Float32[Array, " #foo"]):
         pass
 
     a = jr.normal(getkey(), (3,))
@@ -263,7 +302,7 @@ def test_broadcast_named(typecheck, getkey):
 def test_broadcast_variadic_named(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: f32[" *foo#"], y: f32[" *foo#"]):
+    def g(x: Float32[Array, " *#foo"], y: Float32[Array, " *#foo"]):
         pass
 
     a = jr.normal(getkey(), (3,))
@@ -282,12 +321,11 @@ def test_broadcast_variadic_named(typecheck, getkey):
     g(b, b)
     g(c, c)
     g(d, d)
+    g(b, c)
     with pytest.raises(ParamError):
         g(a, b)
     with pytest.raises(ParamError):
         g(a, c)
-    with pytest.raises(ParamError):
-        g(b, c)
     with pytest.raises(ParamError):
         g(a, b)
     with pytest.raises(ParamError):
@@ -295,26 +333,20 @@ def test_broadcast_variadic_named(typecheck, getkey):
 
     g(a, j)
     g(b, j)
-    with pytest.raises(ParamError):
-        g(c, j)
-    with pytest.raises(ParamError):
-        g(d, j)
-    with pytest.raises(ParamError):
-        g(b, k)
+    g(c, j)
+    g(d, j)
+    g(b, k)
     g(c, k)
     with pytest.raises(ParamError):
         g(d, k)
     with pytest.raises(ParamError):
         g(c, l)
     g(d, l)
-    with pytest.raises(ParamError):
-        g(a, m)
+    g(a, m)
     g(c, m)
     g(d, m)
-    with pytest.raises(ParamError):
-        g(a, n)
-    with pytest.raises(ParamError):
-        g(b, n)
+    g(a, n)
+    g(b, n)
     with pytest.raises(ParamError):
         g(c, n)
     with pytest.raises(ParamError):
@@ -326,6 +358,54 @@ def test_broadcast_variadic_named(typecheck, getkey):
         g(o, a)
 
 
-def test_no_commas(typecheck, getkey):
+def test_no_commas():
     with pytest.raises(ValueError):
-        f32["foo, bar"]
+        Float32[Array, "foo, bar"]
+
+
+def test_symbolic(typecheck, getkey):
+    @jaxtyped
+    @typecheck
+    def make_slice(x: Float32[Array, " dim"]) -> Float32[Array, " dim-1"]:
+        return x[1:]
+
+    @jaxtyped
+    @typecheck
+    def cat(x: Float32[Array, " dim"]) -> Float32[Array, " 2*dim"]:
+        return jnp.concatenate([x, x])
+
+    @jaxtyped
+    @typecheck
+    def bad_make_slice(x: Float32[Array, " dim"]) -> Float32[Array, " dim-1"]:
+        return x
+
+    @jaxtyped
+    @typecheck
+    def bad_cat(x: Float32[Array, " dim"]) -> Float32[Array, " 2*dim"]:
+        return jnp.concatenate([x, x, x])
+
+    x = jr.normal(getkey(), (5,))
+    assert make_slice(x).shape == (4,)
+    assert cat(x).shape == (10,)
+
+    y = jr.normal(getkey(), (3, 4))
+    with pytest.raises(ParamError):
+        make_slice(y)
+    with pytest.raises(ParamError):
+        cat(y)
+
+    with pytest.raises(ReturnError):
+        bad_make_slice(x)
+    with pytest.raises(ReturnError):
+        bad_cat(x)
+
+
+def test_incomplete_symbolic(typecheck, getkey):
+    @jaxtyped
+    @typecheck
+    def foo(x: Float32[Array, " 2*dim"]):
+        pass
+
+    x = jr.normal(getkey(), (4,))
+    with pytest.raises(NameError):
+        foo(x)

test/test_decorator.py

@@ -0,0 +1,13 @@
+from jaxtyping import jaxtyped
+
+
+class M:
+    @jaxtyped
+    @classmethod
+    def f(cls):
+        return 3
+
+
+# Check that the @jaxtyped decorator doesn't blat the __get__ of @classmethod
+def test_decorator():
+    assert M.f() == 3

test/test_import_hook.py

@@ -24,33 +24,40 @@ from jaxtyping import install_import_hook
 
 def test_import_hook_typeguard():
     hook = install_import_hook(
-        "import_hook_tester_typeguard", ("typeguard", "typechecked")
+        "test.import_hook_tester_typeguard", ("typeguard", "typechecked")
     )
-    import import_hook_tester_typeguard  # noqa: F401
+    from . import import_hook_tester_typeguard  # noqa: F401
 
     hook.uninstall()
 
 
 def test_import_hook_beartype():
-    hook = install_import_hook("import_hook_tester_beartype", ("beartype", "beartype"))
-    import import_hook_tester_beartype  # noqa: F401
+    try:
+        import beartype  # noqa: F401
+    except ImportError:
+        pytest.skip("Beartype not installed")
+    else:
+        hook = install_import_hook(
+            "test.import_hook_tester_beartype", ("beartype", "beartype")
+        )
+        from . import import_hook_tester_beartype  # noqa: F401
 
-    hook.uninstall()
+        hook.uninstall()
 
 
 def test_import_hook_transitive():
     hook = install_import_hook(
-        "import_hook_tester_transitive", ("typeguard", "typechecked")
+        "test.import_hook_tester_transitive", ("typeguard", "typechecked")
     )
-    import import_hook_tester_transitive  # noqa: F401
+    from . import import_hook_tester_transitive  # noqa: F401
 
     hook.uninstall()
 
 
 def test_import_hook_broken_checker():
     hook = install_import_hook(
-        "import_hook_tester_broken_checker", ("jaxtyping", "does_not_exist")
+        "test.import_hook_tester_broken_checker", ("jaxtyping", "does_not_exist")
     )
     with pytest.raises(AttributeError):
-        import import_hook_tester_broken_checker  # noqa: F401
+        from . import import_hook_tester_broken_checker  # noqa: F401
     hook.uninstall()

test/test_pytree.py

@@ -24,9 +24,10 @@ import jax
 import jax.numpy as jnp
 import jax.random as jr
 import pytest
-from helpers import make_mlp, ParamError
 
-from jaxtyping import f, jaxtyped, PyTree
+from jaxtyping import Float, jaxtyped, PyTree
+
+from .helpers import make_mlp, ParamError
 
 
 def test_direct(typecheck):
@@ -94,7 +95,7 @@ def test_nested_pytrees(getkey, typecheck):
 def test_pytree_array(typecheck):
     @jaxtyped
     @typecheck
-    def g(x: PyTree[f["..."]]):
+    def g(x: PyTree[Float[jnp.ndarray, "..."]]):
         pass
 
     g(jnp.array(1.0))
@@ -108,7 +109,7 @@ def test_pytree_array(typecheck):
 def test_pytree_shaped_array(typecheck, getkey):
     @jaxtyped
     @typecheck
-    def g(x: PyTree[f["b c"]]):
+    def g(x: PyTree[Float[jnp.ndarray, "b c"]]):
         pass
 
     g(jnp.array([[1.0]]))

test/test_threading.py

@@ -0,0 +1,66 @@
+# Copyright (c) 2022 Google LLC
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy of
+# this software and associated documentation files (the "Software"), to deal in
+# the Software without restriction, including without limitation the rights to
+# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+# the Software, and to permit persons to whom the Software is furnished to do so,
+# subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
+# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
+# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+import threading
+
+import jax.numpy as jnp
+from typeguard import typechecked
+
+from jaxtyping import Array, Float, jaxtyped
+
+
+class _ErrorableThread(threading.Thread):
+    def run(self):
+        try:
+            super().run()
+        except Exception as e:
+            self.exc = e
+        finally:
+            del self._target, self._args, self._kwargs
+
+    def join(self, timeout=None):
+        super().join(timeout)
+        if hasattr(self, "exc"):
+            raise self.exc
+
+
+def test_threading_jaxtyped():
+    @jaxtyped
+    @typechecked
+    def add(x: Float[Array, "a b"], y: Float[Array, "a b"]) -> Float[Array, "a b"]:
+        return x + y
+
+    def run():
+        a = jnp.array([[1.0, 2.0]])
+        b = jnp.array([[2.0, 3.0]])
+        add(a, b)
+
+    thread = _ErrorableThread(target=run)
+    thread.start()
+    thread.join()
+
+
+def test_threading_nojaxtyped():
+    def run():
+        a = jnp.array([[1.0, 2.0]])
+        assert isinstance(a, Float[Array, "..."])
+
+    thread = _ErrorableThread(target=run)
+    thread.start()
+    thread.join()