[Python-ideas] Add 'composable' decorator to functools (with @ matrix multiplication)

[Ivan Levkivskyi]

Dear all,

The matrix multiplication operator @ is going to be introduced in Python
3.5 and I am thinking about the following idea:

The semantics of matrix multiplication is the composition of the
corresponding linear transformations.
A linear transformation is a particular example of a more general concept -
functions.
The latter are frequently composed with ("wrap") each other. For example:

plot(real(sqrt(data)))

However, it is not very readable in case of many wrapping layers.
Therefore, it could be useful to employ
the matrix multiplication operator @ for indication of function
composition. This could be done by such (simplified) decorator:

class composable:

    def __init__(self, func):
        self.func = func

    def __call__(self, arg):
        return self.func(arg)

    def __matmul__(self, other):
        def composition(*args, **kwargs):
            return self.func(other(*args, **kwargs))
        return composable(composition)

I think using such decorator with functions that are going to be deeply
wrapped
could improve readability.
You could compare (note that only the outermost function should be
decorated):

plot(sorted(sqrt(real(data_array)))) vs. (plot @ sorted @ sqrt @ real)
(data_array)

I think the latter is more readable, also compare

def sunique(lst):
    return sorted(list(set(lst)))

vs.

sunique = sorted @ list @ set

Apart from readability, there are following pros of the proposed decorator:

1. Similar semantics as for matrix multiplication.
2. Same symbol for composition as for decorators.
3. The symbol @ resembles mathematical notation for function composition: ∘

I think it could be a good idea to add such a decorator to the stdlib
functools module.
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