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+# Quick Start Guide
+
+`hypothesis-torch` is a package of `hypothesis` strategies for various Pytorch structures (including tensors and modules).
+
+## What is `hypothesis` and property-based testing?
+In short, property-based testing is a testing methodology where the developer defined properties a unit of code should have, and the testing framework generates arbitrary inputs (following the developer's guidelines) to test the code against these properties. This is in contrast to example-based testing, where the developer provides specific inputs and expected outputs. This is exceptionally useful for (but by no means limited to!) [NP-class problems](https://en.wikipedia.org/wiki/NP_(complexity)) where solving is difficult, but checking a solution is easy. 
+
+[Hypothesis](https://hypothesis.readthedocs.io/en/latest/) is a powerful property-based testing library for Python. It
+lacks built-in support for Pytorch tensors and modules, so this library provides strategies for generating them.
+
+The [`hypothesis` quick start guide](https://hypothesis.readthedocs.io/en/latest/quickstart.html) is a great place to start if you're new to property-based testing.
+
+## Installation
+`hypothesis-torch` can be installed via pip:
+```bash
+pip install hypothesis-torch
+```
+
+Optionally, you can also install the `huggingface` extra to also install the `transformers` library:
+```bash
+pip install hypothesis-torch[huggingface]
+```
+
+Strategies for generating Hugging Face transformer models are provided in the `hypothesis_torch.huggingface` module. If 
+and only if `transformers` is installed when `hypothesis-torch` is imported, these strategies will be available from
+the root `hypothesis_torch` module.
+
+## An example with tensors
+
+Suppose we have written a function that takes two PyTorch tensors, and [projects](https://en.wikipedia.org/wiki/Vector_projection) the second one onto the first one (treating all tensors as vectors).
+
+We consequently want to define our function to have the following properties (which constitute one definition of a vector projection):
+    1. The projection (output tensor) should all be parallel to the first input tensor.
+    2. The second input tensor subtracted by the projection should be orthogonal to the first input tensor.
+
+We might use these properties to define a test for our function. We can use `hypothesis-torch` to generate random tensors to test our function against these properties.
+
+In the sample below, the two tensors will be in single precision (`torch.float32`) and have a shape of `(1, 2, 3)`, but these values could be changed to any valid values for the `dtype`, `shape`.
+
+```python
+import torch
+import hypothesis_torch
+from hypothesis import given
+from hypothesis import strategies as st
+
+def project(tensor1: torch.Tensor, tensor2: torch.Tensor) -> torch.Tensor:
+    """Project tensor2 onto tensor1."""
+    return tensor2.dot(tensor1) / tensor1.dot(tensor1) * tensor1
+
+@given(
+    tensor1=hypothesis_torch.tensor_strategy(
+        dtype=torch.float32,
+        shape=(1,2,3),
+    ), 
+    tensor2=hypothesis_torch.tensor_strategy(
+        dtype=torch.float32,
+        shape=(1,2,3),
+    ),
+)
+def test_projection(tensor1: torch.Tensor, tensor2: torch.Tensor):
+    projection = project(tensor1, tensor2)
+    # Property 1
+    # The projection (output tensor) should all be parallel to the first input tensor.
+    # Two vectors are parallel if and only if their cosine similarity is 1.
+    assert torch.allclose(torch.nn.functional.cosine_similarity(projection, tensor1), torch.tensor(1.0))
+    
+    # Property 2
+    # The second input tensor subtracted by the projection should be orthogonal to the first input tensor.
+    # Two vectors are orthogonal if and only if their dot product is 0.
+    difference = tensor2 - projection
+    assert torch.allclose(difference.dot(tensor1), torch.tensor(0.0))
+```
+
+Our test does not require any knowledge of the implementation of `project`, nor does it require any specific examples of input tensors. 
+Instead, it generates random tensors and tests the function against the properties we defined. `hypothesis` will use the `tensor_strategy`
+to attempt to find a counterexample to our properties. If it finds one, it will shrink the input tensors to the smallest possible example 
+that violates the properties.
+
+Very quickly, however, `hypothesis` will inform us that our function fails (will raise an division by zero error) for the example `torch.Tensor([[[0,0,0],[0,0,0]]])`. 
+This should be expected, however, because the projection of any vector onto the zero vector is undefined. In this case, we should add a hypothesis assume to ensure that the first tensor is not the zero tensor.
+
+```python
+import torch
+import hypothesis_torch
+from hypothesis import given, assume
+from hypothesis import strategies as st
+
+def project(tensor1: torch.Tensor, tensor2: torch.Tensor) -> torch.Tensor:
+    """Project tensor2 onto tensor1."""
+    return tensor2.dot(tensor1) / tensor1.dot(tensor1) * tensor1
+
+@given(
+    tensor1=hypothesis_torch.tensor_strategy(
+        dtype=torch.float32,
+        shape=(1,2,3),
+    ), 
+    tensor2=hypothesis_torch.tensor_strategy(
+        dtype=torch.float32,
+        shape=(1,2,3),
+    ),
+)
+def test_projection(tensor1: torch.Tensor, tensor2: torch.Tensor):
+
+    # Assume that the first tensor is not the zero tensor, because the projection of any vector onto the zero vector is undefined.
+    # We have to use a small epsilon value because the values are floats and we can still have numerical instability close to 0 vectors.
+    assume(tensor1.norm().item() > 1e-6)
+    
+    projection = project(tensor1, tensor2)
+    # Property 1
+    # The projection (output tensor) should all be parallel to the first input tensor.
+    # Two vectors are parallel if and only if their cosine similarity is 1.
+    assert torch.allclose(torch.nn.functional.cosine_similarity(projection, tensor1), torch.tensor(1.0))
+    
+    # Property 2
+    # The second input tensor subtracted by the projection should be orthogonal to the first input tensor.
+    # Two vectors are orthogonal if and only if their dot product is 0.
+    difference = tensor2 - projection
+    assert torch.allclose(difference.dot(tensor1), torch.tensor(0.0))
+```