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# And-Or Shape (aos) Language
Writing data pipelines involves complex data transformations over nested data, e.g., list of dictionaries or dictionary of tensors.
- The *shape* of nested data is not explicit in code and hence not accessible readily to the developer.
- Leads to cognitive burden (guessing shapes), technical debt and inadvertent programming errors.
- Data pipelines are very opaque to examination and comprehension.
---
`aos` is a compact, regex-like language for describing the shapes (schemas) of both homogeneous (tensors) and heterogeneous (dictionaries, tables) data, and combinations, independent of the specific data library.
* Based on an intuitive **regex-like** algebra of data shapes.
* **Infer** `aos` shape from a data instance: `aos.infer.infer_aos`.
* **Validate** data against `aos` shapes anywhere: `aos.checker.instanceof`.
* **Transform** data using `aos` shapes, declaratively: `aos.tfm.do_tfm`.
* Allows writing explicit data shapes, **inline** in code. In Python, use type annotations.
* Write shapes for a variety of data conveniently -- Python native objects (`dict`, `list`, scalars), tensors (`numpy`,` pytorch`, `tf`), `pandas`,`hdf5`,`tiledb`,`xarray`,`struct-tensor`, etc.
### Installation
```pip install aos```
## Shape of Data ?
Consider a few quick examples.
- the shape of scalar data is simply its type, e.g., `int`, ` float`, `str`, ...
- for nested data, eg. list of `int`s: `(int)*`
- for a dictionary of form `{'a': 3, b: 'hi'}` : shape is `(a & int) | (b & str)`.
Now, we can describe the shape of *arbitrary, nested* data with these `&`(and)- `|`(or) expressions. Intuitively, a list is an `or`-structure, a dictionary is an `or` of `and`s, a tensor is an `and`-structure, and so on.
* Why is a `list` an or-structure? Ask: how do we *access* any value `v` in the `list`? Choose **some** index of the list, corresponding to the value `v`.
* Similarly, a `dictionary` is an or-and structure: we pick **one** of the *key*s, together (**and**) with its *value*.
* In contrast, an n-dimensional `tensor` has an `and`-shape: we must choose indices from *all* the dimensions of the tensor to access a scalar value.
* In general, for a data structure, we *ask*: what choices must we make to access a scalar value?
Thinking in terms of `and`-`or` shapes takes a bit of practice initially. Read more about the and-or expressions [here](docs/and-or-thinking.md).
#### More complex `aos` examples
* Lists over shape `s` are denoted as `(s)*`. Shorthand for `(s|..|s)`.
* Dictionary: `(k1 & v1) | (k2 & v2) | ... | (kn & vn)` where `ki` and `vi` is the `i`th key and value.
* Pandas tables: `(n & ( (c1&int)| (c2&str) | ... | (cn&str) )` where `n` is the row dimension (the number of rows) and `c1,...,cn` are column names.
The `aos` expressions are very *compact*. For example, consider a highly nested Python object `X` of type
`Sequence[Tuple[Tuple[str, int], Dict[str, str]]]`
This is both verbose and hard to interpret. Instead, `X`'s `aos` is written compactly as
`((str|int) | (str : str))* `.
> The full data shape may be irrelevant in many cases. To keep it brief, the language supports wildcards: `_` and `...` to allow writing partial shapes.
>
> So, we could write a dictionary's shape as `(k1 & ...)| ... | (kn & ...)`.
## Shape Inference
Unearthing the shape of opaque data instances, e.g., returned from a web request, or passed into a function call, is a major pain.
* Use `aos.infer.infer_aos` to obtain compact shapes of arbitrary data instances.
* From command line, run `aos-infer <filename.json>`
```python
from aos.infer import infer_aos
def test_infer():
d = {
"checked": False,
"dimensions": { "width": 5, "height": 10},
"id": 1,
"name": "A green door",
"price": 12.5,
"tags": ["home","green"]
}
infer_aos(d)
# ((checked & bool)
# | (dimensions & ((width & int) | (height & int)))
# | (id & int) | (name & str) | (price & float) | (tags & (str *)))
dlist = []
for i in range(100):
d['id'] = i
dlist.append(d.copy())
infer_aos(dlist)
# ((checked & bool)
# | (dimensions & ((width & int) | (height & int)))
# | (id & int) | (name & str) | (price & float) | (tags & (str *)))*
```
## Shape/Schema Validation
Using `aos.checker.instanceof`, we can
* write `aos` assertions to validate data shapes (schemas).
* validate data structure partially using placeholders: `_` matches a scalar, `...` matches an arbitrary object (sub-tree).
* works with python objects, pandas, numpy, ..., extensible to other data types (libraries).
```python
from aos.checker import instanceof
def test_pyobj():
d = {'city': 'New York', 'country': 'USA'}
t1 = ('Google', 2001)
t2 = (t1, d)
instanceof(t2, '(str | int) | (str & str)') #valid
instanceof(t2, '... | (str & _)') #valid
instanceof(t2, '(_ | _) | (str & int)') #error
tlist = [('a', 1), ('b', 2)]
instanceof(tlist, '(str | int)*') #valid
def test_pandas():
d = {'id': 'CS2_056', 'cost': 2, 'name': 'Tap'}
df = pd.DataFrame([d.items()], columns=list(d.keys()) )
instanceof(df, '1 & (id | cost | name)')
def test_numpy():
#arr = np.array()
arr = np.array([[1,2,3],[4,5,6]])
instanceof(arr, '2 & 3')
def test_pytorch():
#arr = np.array()
arr = torch.tensor([[1,2,3],[4,5,6]])
instanceof(arr, '2 & 3')
```
## Transformations with AOS
Because `aos` expressions can both *match* and *specify* heterogeneous data shapes, we can write `aos` **rules** to **transform** data.
The rules are written as `lhs -> rhs`, where both `lhs` and `rhs` are `aos` expressions:
* `lhs` *matches* a part (sub-tree) of the input data instance *I*.
* `query` variables in the `lhs` *capture* (bind with) parts of *I*.
* `rhs` specifies the expected shape (aos) of the output data instance *O*.
To write rules, ask: which *parts* of *I*, do we need to construct *O* ?
```python
from aos.tfm import do_tfm
def tfm_example():
# input data
I = {'items': [{'k': 1}, {'k': 2}, {'k': 3}],
'names': ['A', 'B', 'C']}
# specify transformation (left aos -> right aos)
# using `query` variables `k` and `v`
# here `k` binds with each of the keys in the list and
# `v` binds with the corresponding value
# the `lhs` automatically ignores parts of I, which are irrelevant to O
tfm = 'items & (k & v)* -> values & (v)*'
O = do_tfm(I, tfm)
print(O) # {'values': [1, 2, 3]}
```
The above example illustrates a simple JSON transformation using `aos` rules. Rules can be more complex, e.g., include *conditions*, *function* application on query variables. They work not only with JSON data, but also apply to heterogeneous nested objects.
See more examples [here](tests/test_tfm_json.py) and [here](tests/test_tfm_spark_json.py).
## And-Or Shape Dimensions
The above examples of use strings or type names (`str`) or integer values (`2`,`3`) in shape expressions. A more principled approach is to first declare **dimension names** and define shape over these names.
Data is defined over two kinds of dimensions:
* **Continuous**. A range of values, e.g., a numpy array of shape (5, 200) is defined over two continuous dimensions, say `n` and `d`, where `n` ranges over values `0-4` and `d` ranges over `0-199`.
* **Categorical**. A set of names, e.g., a dictionary `{'a': 4, 'b': 5}` is defined over *keys* (dim names) `['a', 'b']`. One can also view each key, e.g., `a` or `b` , as a **Singleton** dimension.
**Programmatic API**. The library provides an API to declare both type of dimensions and `aos` expressions over these dimensions, e.g., declare `n` and `d` as two continuous dimensions and then define shape `n & d`.
## Status
*The library is under active development. More documentation coming soon..*