matchpy 0.3

A pattern matching library.

A pattern matching libary for python.

Work in progress

Overview

This package implements pattern matching in python. It is similar to the implementation in Mathematica. A detailed example of how you can use matchpy can be found in the documentation.

In addition to the basic matching algorithm, there are data structures that can be used for more efficient many-to-one matching like the ManyToOneMatcher and the DiscriminationNet.

Expressions

Expressions and patterns both have a tree structure. Expressions consist of symbols (leafs) and operations (internal nodes):

>>> from matchpy import Operation, Symbol, Arity
>>> f = Operation.new('f', Arity.binary)
>>> a = Symbol('a')
>>> print(f(a, a))
f(a, a)

Patterns are expressions which can additionally contain wildcards and subexpressions can have a variable name assigned to them. During matching, a subject matching a pattern with a variable will be captured so it can be accessed later. Wildcards are placeholders that stand for any expression. Usually, the wildcards are used in combination with a variable name:

>>> from matchpy import Wildcard
>>> x = Wildcard.dot('x')
>>> print(Pattern(f(a, x)))
f(a, x_)

Here x is the name of the variable. However, unnamed wildcards can also be used:

>>> w = Wildcard.dot()
>>> print(Pattern(f(w, w)))
f(_, _)

Or a more complex expression can be named with a variable:

>>> print(Pattern(f(w, a, variable_name='y')))
y: f(_, a)

In addition, sequence wildcards that can match for multiple expressions are supported:

>>> z = Wildcard.plus('z')
>>> print(Pattern(f(z)))
f(z__)

Substitutions

Matches are given in the form of substitutions, which are a mapping from variable names to expressions:

>>> from matchpy import match
>>> y = Wildcard.dot('y')
>>> b = Symbol('b')
>>> expression = f(a, b)
>>> pattern = Pattern(f(x, y))
>>> substitution = next(match(expression, pattern))
>>> substitution
{'x': Symbol('a'), 'y': Symbol('b')}

Replacing the variables in the pattern according to the substitution will yield the original subject expression:

>>> from matchpy import substitute
>>> print(substitute(pattern, substitution))
f(a, b)