paragraph 1.2.1

A computation graph micro-framework providing seamless lazy and concurrent evaluation.

A pure Python micro-framework supporting seamless lazy and concurrent evaluation of computation graphs.

Introduction

Paragraph adds the functional programming paradigm to Python in a minimal fashion. One additional class, Variable, and a function decorator, op, is all it takes to turn regular Python code into a computation graph, i.e. a computer representation of a system of equations:

>>> import paragraph as pg
>>> import operator
>>> x, y = pg.Variable("x"), pg.Variable("y")
>>> add = pg.op(operator.add)
>>> s = add.op(x, y)

The few lines above fully instantiate a computation graph, here in its simplest form with just one equation relating x, y and s via the function add. Given values for the input variables x and y, the value of s is resolved as follows:

>>> pg.evaluate([s], {x: 5, y: 10})
[15]

Key features

The main benefits of using paragraph stem from the following features of pg.session.evaluate:

Lazy evaluation

Irrespective of the size of the computation graph, only the operations required to evaluate the output variables are executed. Consider the following extension of the above graph:

>>> z = pg.Variable("z")
>>> t = add.op(y, z)

Then the statement:

>>> pg.evaluate([t], {y: 10, z: 50})
[60]

just ignores the variables s and x altogether, since they do not contribute to the evaluation of t. In particular, the operation add(x, y) is not executed.

Eager currying

Invoking an op with invariable arguments (that is, arguments that are not of type Variable) just returns an invariable value: evaluation is eager whenever possible. If invariable arguments are provided for a subset of the input variables, the computation graph can be simplified using solve, which returns a new variable:

>>> u_x = pg.solve([u], {y: 10, z: 50})[0]

Here, u_x is a different variable from u: it now depends on a single input variable (x), and it knows nothing about a variable y or z, instead storing a reference to the value of their sum t, i.e. 60.

Thus, pg.session.solve acts much as functools.partial, except it simplifies the system of equations where possible by executing dependent operations whose arguments are invariable.

Graph composition

Assume a variable y depends on a number of input variables x_1,…, x_p, and another variable v on u_1,…,``u_q`` (not necessarily different), and v should be identified to x_p. The following statement:

>>> y_v = pg.solve([y], args={x_p: v})[0]

returns a new variable y_v that depends on x_1,…, x_{p-1} as well as on u_1,…, u_q, as if the two computation graphs defining y and v had been pieced together.

Note that the respective input variables may overlap, with the restriction that v should not depend on x_p as that would result in a circular dependency. Also, additional arguments may be added to args in the statement above to set further values of the input variables x_1,…, x_{p-1}. However, values cannot be set for u_1,…, u_q here, since they are not dependencies of y, but of y_v.

Transparent multithreading

Invoking evaluate or solve with an instance of concurrent.ThreadPoolExecutor will allow independent blocks of the computation graph to run in separate threads:

>>> with ThreadPoolExecutor as ex:
...     res = pg.evaluate([z_t], {t: 5}, ex)

This is particularly beneficial if large subsets of the graph are independent.

Constraints

Side-effects

The features listed above come at some price, essentially because the order in which operations are actually executed generally differs from the order of their invocations. For paragraph to guarantee that a variable always evaluates to the same value given the same inputs, as in a system of mathematical equations, it is paramount that operations remain free of side-effects, i.e. they never mutate an object they received as an argument, or store as an attribute. The state sequence of the object would be, by definition, out of the control of the programmer.

There is close to nothing paragraph can do to prevent such a thing happening. When in doubt, make sure to operate on a copy of the argument.

Typing

Variables do not carry any information regarding the type of the value they represent, which precludes binding a method of the underlying value to an instance of Variable: such instructions can appear only within the code of an op. Since binary operators are implemented using special methods in Python, this also precludes such statements as:

>>> s = x + y

for this would be resolved by the Python interpreter into s = x.__add__(y), then s = y.__radd__(x), yet none of these methods is defined by Variable.

For more information please consult the documentation.