A library for pattern matching on symbolic expressions.

## Project description

MatchPy

=======

MatchPy is a library for pattern matching on symbolic expressions in Python.

**Work in progress**

|pypi| |conda| |coverage| |build| |docs| |joss| |doi|

Installation

------------

MatchPy is available via `PyPI <https://pypi.python.org/pypi/matchpy>`_, and for Conda via `conda-forge <https://anaconda.org/conda-forge/matchpy>`_. It can be installed with ``pip install matchpy`` or ``conda install -c conda-forge matchpy``.

Overview

--------

This package implements `pattern matching <https://en.wikipedia.org/wiki/Pattern_matching>`_ in Python. Pattern matching is a powerful tool for symbolic computations, operating on symbolic expressions. Given a pattern and an expression (which is usually called *subject*), the goal of pattern matching is to find a substitution for all the variables in the pattern such that the pattern becomes the subject. As an example, consider the pattern :math:`f(x)`, where :math:`f` is a function and :math:`x` is a variable, and the subject :math:`f(a)`, where :math:`a` is a constant symbol. Then the substitution that replaces :math:`x` with :math:`a` is a match. MatchPy supports associative and/or commutative function symbols, as well as sequence variables, similar to pattern matching in `Mathematica <https://reference.wolfram.com/language/guide/Patterns.html>`_.

A detailed example of how to use MatchPy can be found `here <https://matchpy.readthedocs.io/en/latest/example.html>`_.

MatchPy supports both one-to-one and many-to-one pattern matching. The latter makes use of similarities between patterns to efficiently find matches for multiple patterns at the same time.

A list of publications about MatchPy can be found `below <#publications>`_.

Expressions

...........

Expressions are tree-like data structures, consisting of operations (functions, internal nodes) and symbols (constants, leaves):

>>> 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 may contain wildcards (variables):

>>> from matchpy import Pattern, Wildcard

>>> x = Wildcard.dot('x')

>>> print(Pattern(f(a, x)))

f(a, x_)

In the previous example, x is the name of the variable. However, it is also possible to use wildcards without names:

>>> w = Wildcard.dot()

>>> print(Pattern(f(w, w)))

f(_, _)

It is also possible to assign variable names to entire subexpressions:

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

y: f(_, a)

Pattern Matching

................

Given a pattern and an expression (which is usually called subject), the idea of pattern matching is to find a substitution that maps wildcards to expressions such that the pattern becomes the subject. In MatchPy, a substitution is a dict that maps variable names to expressions.

>>> from matchpy import match

>>> y = Wildcard.dot('y')

>>> b = Symbol('b')

>>> subject = f(a, b)

>>> pattern = Pattern(f(x, y))

>>> substitution = next(match(subject, pattern))

>>> print(substitution)

{x ↦ a, y ↦ b}

Applying the substitution to the pattern results in the original expression.

>>> from matchpy import substitute

>>> print(substitute(pattern, substitution))

f(a, b)

Sequence Wildcards

..................

Sequence wildcards are wildcards that can match a sequence of expressions instead of just a single expression:

>>> z = Wildcard.plus('z')

>>> pattern = Pattern(f(z))

>>> subject = f(a, b)

>>> substitution = next(match(subject, pattern))

>>> print(substitution)

{z ↦ (a, b)}

Associativity and Commutativity

...............................

MatchPy natively supports associative and/or commutative operations. Nested associative operators are automatically flattened, the operands in commutative operations are sorted:

>>> g = Operation.new('g', Arity.polyadic, associative=True, commutative=True)

>>> print(g(a, g(b, a)))

g(a, a, b)

Associativity and commutativity is also considered for pattern matching:

>>> pattern = Pattern(g(b, x))

>>> subject = g(a, a, b)

>>> print(next(match(subject, pattern)))

{x ↦ g(a, a)}

>>> h = Operation.new('h', Arity.polyadic)

>>> pattern = Pattern(h(b, x))

>>> subject = h(a, a, b)

>>> list(match(subject, pattern))

[]

Many-to-One Matching

....................

When a fixed set of patterns is matched repeatedly against different subjects, matching can be sped up significantly by using many-to-one matching. The idea of many-to-one matching is to construct a so called discrimination net, a data structure similar to a decision tree or a finite automaton that exploits similarities between patterns. In MatchPy, there are two such data structures, implemented as classes: `DiscriminationNet <https://matchpy.readthedocs.io/en/latest/api/matchpy.matching.syntactic.html>`_ and `ManyToOneMatcher <https://matchpy.readthedocs.io/en/latest/api/matchpy.matching.many_to_one.html>`_. The DiscriminationNet class only supports syntactic pattern matching, that is, operations are neither associative nor commutative. Sequence variables are not supported either. The ManyToOneMatcher class supports associative and/or commutative matching with sequence variables. For syntactic pattern matching, the DiscriminationNet should be used, as it is usually faster.

>>> pattern1 = Pattern(f(a, x))

>>> pattern2 = Pattern(f(y, b))

>>> matcher = ManyToOneMatcher(pattern1, pattern2)

>>> subject = f(a, b)

>>> matches = matcher.match(subject)

>>> for matched_pattern, substitution in sorted(map(lambda m: (str(m[0]), str(m[1])), matches)):

... print('{} matched with {}'.format(matched_pattern, substitution))

f(a, x_) matched with {x ↦ b}

f(y_, b) matched with {y ↦ a}

Roadmap

-------

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. There is already an experimental implementation, but it still has some dependencies on MatchPy which can probably be removed.

- Improving the documentation with more examples.

- Better test coverage with more randomized tests.

- Implementation of the matching algorithms in a lower-level language, for example C, both for performance and to make MatchPy's functionality available in other languages.

Contributing

------------

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 <https://docs.pytest.org/>`_.

- To generate the documentation you can use ``make docs`` .

- To run the style checker (`pylint <https://www.pylint.org/>`_) 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.

Publications

------------

`MatchPy: Pattern Matching in Python <http://joss.theoj.org/papers/10.21105/joss.00670>`_ |br|

Manuel Krebber and Henrik Barthels |br|

Journal of Open Source Software, Volume 3(26), pp. 2, June 2018.

`Efficient Pattern Matching in Python <https://dl.acm.org/citation.cfm?id=3149871>`_ |br|

Manuel Krebber, Henrik Barthels and Paolo Bientinesi |br|

Proceedings of the 7th Workshop on Python for High-Performance and Scientific Computing, November 2017.

`MatchPy: A Pattern Matching Library <http://conference.scipy.org/proceedings/scipy2017/manuel_krebber.html>`_ |br|

Manuel Krebber, Henrik Barthels and Paolo Bientinesi |br|

Proceedings of the 15th Python in Science Conference, July 2017.

`Non-linear Associative-Commutative Many-to-One Pattern Matching with Sequence Variables <https://arxiv.org/abs/1705.00907>`_ |br|

Manuel Krebber |br|

Master Thesis, RWTH Aachen University, May 2017

If you want to cite MatchPy, please reference the JOSS paper::

@article{krebber2018,

author = {Manuel Krebber and Henrik Barthels},

title = {{M}atch{P}y: {P}attern {M}atching in {P}ython},

journal = {Journal of Open Source Software},

year = 2018,

pages = 2,

month = jun,

volume = {3},

number = {26},

doi = "10.21105/joss.00670",

web = "http://joss.theoj.org/papers/10.21105/joss.00670",

}

.. |br| raw:: html

<br />

.. |pypi| image:: https://img.shields.io/pypi/v/matchpy.svg?style=flat

:target: https://pypi.org/project/matchpy/

:alt: Latest version released on PyPi

.. |conda| image:: https://img.shields.io/conda/vn/conda-forge/matchpy.svg

:target: https://anaconda.org/conda-forge/matchpy

:alt: Latest version released via conda-forge

.. |coverage| image:: https://coveralls.io/repos/github/HPAC/matchpy/badge.svg?branch=master

:target: https://coveralls.io/github/HPAC/matchpy?branch=master

:alt: Test coverage

.. |build| image:: https://travis-ci.org/HPAC/matchpy.svg?branch=master

:target: https://travis-ci.org/HPAC/matchpy

:alt: Build status of the master branch

.. |docs| image:: https://readthedocs.org/projects/matchpy/badge/?version=latest

:target: https://matchpy.readthedocs.io/en/latest/?badge=latest

:alt: Documentation Status

.. |joss| image:: http://joss.theoj.org/papers/e456bc05880b533652980aee6550a3cb/status.svg

:target: http://joss.theoj.org/papers/e456bc05880b533652980aee6550a3cb

:alt: The Journal of Open Source Software

.. |doi| image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1294930.svg

:target: https://doi.org/10.5281/zenodo.1294930

:alt: Digital Object Identifier

=======

MatchPy is a library for pattern matching on symbolic expressions in Python.

**Work in progress**

|pypi| |conda| |coverage| |build| |docs| |joss| |doi|

Installation

------------

MatchPy is available via `PyPI <https://pypi.python.org/pypi/matchpy>`_, and for Conda via `conda-forge <https://anaconda.org/conda-forge/matchpy>`_. It can be installed with ``pip install matchpy`` or ``conda install -c conda-forge matchpy``.

Overview

--------

This package implements `pattern matching <https://en.wikipedia.org/wiki/Pattern_matching>`_ in Python. Pattern matching is a powerful tool for symbolic computations, operating on symbolic expressions. Given a pattern and an expression (which is usually called *subject*), the goal of pattern matching is to find a substitution for all the variables in the pattern such that the pattern becomes the subject. As an example, consider the pattern :math:`f(x)`, where :math:`f` is a function and :math:`x` is a variable, and the subject :math:`f(a)`, where :math:`a` is a constant symbol. Then the substitution that replaces :math:`x` with :math:`a` is a match. MatchPy supports associative and/or commutative function symbols, as well as sequence variables, similar to pattern matching in `Mathematica <https://reference.wolfram.com/language/guide/Patterns.html>`_.

A detailed example of how to use MatchPy can be found `here <https://matchpy.readthedocs.io/en/latest/example.html>`_.

MatchPy supports both one-to-one and many-to-one pattern matching. The latter makes use of similarities between patterns to efficiently find matches for multiple patterns at the same time.

A list of publications about MatchPy can be found `below <#publications>`_.

Expressions

...........

Expressions are tree-like data structures, consisting of operations (functions, internal nodes) and symbols (constants, leaves):

>>> 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 may contain wildcards (variables):

>>> from matchpy import Pattern, Wildcard

>>> x = Wildcard.dot('x')

>>> print(Pattern(f(a, x)))

f(a, x_)

In the previous example, x is the name of the variable. However, it is also possible to use wildcards without names:

>>> w = Wildcard.dot()

>>> print(Pattern(f(w, w)))

f(_, _)

It is also possible to assign variable names to entire subexpressions:

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

y: f(_, a)

Pattern Matching

................

Given a pattern and an expression (which is usually called subject), the idea of pattern matching is to find a substitution that maps wildcards to expressions such that the pattern becomes the subject. In MatchPy, a substitution is a dict that maps variable names to expressions.

>>> from matchpy import match

>>> y = Wildcard.dot('y')

>>> b = Symbol('b')

>>> subject = f(a, b)

>>> pattern = Pattern(f(x, y))

>>> substitution = next(match(subject, pattern))

>>> print(substitution)

{x ↦ a, y ↦ b}

Applying the substitution to the pattern results in the original expression.

>>> from matchpy import substitute

>>> print(substitute(pattern, substitution))

f(a, b)

Sequence Wildcards

..................

Sequence wildcards are wildcards that can match a sequence of expressions instead of just a single expression:

>>> z = Wildcard.plus('z')

>>> pattern = Pattern(f(z))

>>> subject = f(a, b)

>>> substitution = next(match(subject, pattern))

>>> print(substitution)

{z ↦ (a, b)}

Associativity and Commutativity

...............................

MatchPy natively supports associative and/or commutative operations. Nested associative operators are automatically flattened, the operands in commutative operations are sorted:

>>> g = Operation.new('g', Arity.polyadic, associative=True, commutative=True)

>>> print(g(a, g(b, a)))

g(a, a, b)

Associativity and commutativity is also considered for pattern matching:

>>> pattern = Pattern(g(b, x))

>>> subject = g(a, a, b)

>>> print(next(match(subject, pattern)))

{x ↦ g(a, a)}

>>> h = Operation.new('h', Arity.polyadic)

>>> pattern = Pattern(h(b, x))

>>> subject = h(a, a, b)

>>> list(match(subject, pattern))

[]

Many-to-One Matching

....................

When a fixed set of patterns is matched repeatedly against different subjects, matching can be sped up significantly by using many-to-one matching. The idea of many-to-one matching is to construct a so called discrimination net, a data structure similar to a decision tree or a finite automaton that exploits similarities between patterns. In MatchPy, there are two such data structures, implemented as classes: `DiscriminationNet <https://matchpy.readthedocs.io/en/latest/api/matchpy.matching.syntactic.html>`_ and `ManyToOneMatcher <https://matchpy.readthedocs.io/en/latest/api/matchpy.matching.many_to_one.html>`_. The DiscriminationNet class only supports syntactic pattern matching, that is, operations are neither associative nor commutative. Sequence variables are not supported either. The ManyToOneMatcher class supports associative and/or commutative matching with sequence variables. For syntactic pattern matching, the DiscriminationNet should be used, as it is usually faster.

>>> pattern1 = Pattern(f(a, x))

>>> pattern2 = Pattern(f(y, b))

>>> matcher = ManyToOneMatcher(pattern1, pattern2)

>>> subject = f(a, b)

>>> matches = matcher.match(subject)

>>> for matched_pattern, substitution in sorted(map(lambda m: (str(m[0]), str(m[1])), matches)):

... print('{} matched with {}'.format(matched_pattern, substitution))

f(a, x_) matched with {x ↦ b}

f(y_, b) matched with {y ↦ a}

Roadmap

-------

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. There is already an experimental implementation, but it still has some dependencies on MatchPy which can probably be removed.

- Improving the documentation with more examples.

- Better test coverage with more randomized tests.

- Implementation of the matching algorithms in a lower-level language, for example C, both for performance and to make MatchPy's functionality available in other languages.

Contributing

------------

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 <https://docs.pytest.org/>`_.

- To generate the documentation you can use ``make docs`` .

- To run the style checker (`pylint <https://www.pylint.org/>`_) 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.

Publications

------------

`MatchPy: Pattern Matching in Python <http://joss.theoj.org/papers/10.21105/joss.00670>`_ |br|

Manuel Krebber and Henrik Barthels |br|

Journal of Open Source Software, Volume 3(26), pp. 2, June 2018.

`Efficient Pattern Matching in Python <https://dl.acm.org/citation.cfm?id=3149871>`_ |br|

Manuel Krebber, Henrik Barthels and Paolo Bientinesi |br|

Proceedings of the 7th Workshop on Python for High-Performance and Scientific Computing, November 2017.

`MatchPy: A Pattern Matching Library <http://conference.scipy.org/proceedings/scipy2017/manuel_krebber.html>`_ |br|

Manuel Krebber, Henrik Barthels and Paolo Bientinesi |br|

Proceedings of the 15th Python in Science Conference, July 2017.

`Non-linear Associative-Commutative Many-to-One Pattern Matching with Sequence Variables <https://arxiv.org/abs/1705.00907>`_ |br|

Manuel Krebber |br|

Master Thesis, RWTH Aachen University, May 2017

If you want to cite MatchPy, please reference the JOSS paper::

@article{krebber2018,

author = {Manuel Krebber and Henrik Barthels},

title = {{M}atch{P}y: {P}attern {M}atching in {P}ython},

journal = {Journal of Open Source Software},

year = 2018,

pages = 2,

month = jun,

volume = {3},

number = {26},

doi = "10.21105/joss.00670",

web = "http://joss.theoj.org/papers/10.21105/joss.00670",

}

.. |br| raw:: html

<br />

.. |pypi| image:: https://img.shields.io/pypi/v/matchpy.svg?style=flat

:target: https://pypi.org/project/matchpy/

:alt: Latest version released on PyPi

.. |conda| image:: https://img.shields.io/conda/vn/conda-forge/matchpy.svg

:target: https://anaconda.org/conda-forge/matchpy

:alt: Latest version released via conda-forge

.. |coverage| image:: https://coveralls.io/repos/github/HPAC/matchpy/badge.svg?branch=master

:target: https://coveralls.io/github/HPAC/matchpy?branch=master

:alt: Test coverage

.. |build| image:: https://travis-ci.org/HPAC/matchpy.svg?branch=master

:target: https://travis-ci.org/HPAC/matchpy

:alt: Build status of the master branch

.. |docs| image:: https://readthedocs.org/projects/matchpy/badge/?version=latest

:target: https://matchpy.readthedocs.io/en/latest/?badge=latest

:alt: Documentation Status

.. |joss| image:: http://joss.theoj.org/papers/e456bc05880b533652980aee6550a3cb/status.svg

:target: http://joss.theoj.org/papers/e456bc05880b533652980aee6550a3cb

:alt: The Journal of Open Source Software

.. |doi| image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1294930.svg

:target: https://doi.org/10.5281/zenodo.1294930

:alt: Digital Object Identifier

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