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A pattern matching library.

Project description

MatchPy is a pattern matching libary for python.

Work in progress

Latest version released on PyPi Test coverage Build status of the master branch Documentation Status


MatchPy is availiablle via PyPI. You can install it using pip install matchpy.


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. Some of the implemented algorithms have been described in this Master thesis.

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

>>> from matchpy import Operation, Symbol, Arity
>>> f ='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 ='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 =
>>> 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 ='z')
>>> print(Pattern(f(z)))


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

>>> from matchpy import match
>>> y ='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)


Besides the existing features, we plan on adding the following to MatchPy:

  • Support for Mathematica’s Alternatives: For example f(a | b) would match either f(a) or f(b).
  • Support for Mathematica’s Repeated: For example f(a..) would match f(a), f(a, a), f(a, a, a), etc.
  • Support pattern sequences (PatternSequence in Mathematica). These are mainly useful in combination with Alternatives or Repeated, e.g. f(a | (b, c)) would match either f(a) or f(b, c). f((a a)..) would match any f with an even number of a arguments.
  • All these additional pattern features need to be supported in the ManyToOneMatcher as well.
  • Better integration with existing types such as dict.
  • Code generation for both one-to-one and many-to-one matching.
  • Improving the documentation with more examples.
  • Better test coverage with more randomized tests.


If you have some issue or want to contribute, please feel free to open an issue or create a pull request. Help is always appreciated!

The Makefile has several tasks to help development:

  • To install all needed packages, you can use make init .
  • To run the tests you can use make test. The tests use pytest.
  • To generate the documentation you can use make docs .
  • To run the style checker (pylint) you can use make check .

If you have any questions or need help with setting things up, please open an issue and we will try the best to assist you.

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