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        "author": "Manuel Krebber",
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            "Development Status :: 3 - Alpha",
            "Intended Audience :: Developers",
            "License :: OSI Approved :: MIT License",
            "Programming Language :: Python",
            "Programming Language :: Python :: 3",
            "Programming Language :: Python :: 3.6",
            "Programming Language :: Python :: 3.7",
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        "description": "MatchPy\n=======\n\nMatchPy is a library for pattern matching on symbolic expressions in Python.\n\n**Work in progress**\n\n|pypi| |conda| |coverage| |build| |docs| |joss| |doi|\n\nInstallation\n------------\n\nMatchPy 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``.\n\nOverview\n--------\n\nThis 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>`_. \n\nA detailed example of how to use MatchPy can be found `here <https://matchpy.readthedocs.io/en/latest/example.html>`_.\n\nMatchPy 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.\n\nA list of publications about MatchPy can be found `below <#publications>`_.\n\nExpressions\n...........\n\nExpressions are tree-like data structures, consisting of operations (functions, internal nodes) and symbols (constants, leaves):\n\n>>> from matchpy import Operation, Symbol, Arity\n>>> f = Operation.new('f', Arity.binary)\n>>> a = Symbol('a')\n>>> print(f(a, a))\nf(a, a)\n\nPatterns are expressions which may contain wildcards (variables):\n\n>>> from matchpy import Pattern, Wildcard\n>>> x = Wildcard.dot('x')\n>>> print(Pattern(f(a, x)))\nf(a, x_)\n\nIn the previous example, x is the name of the variable. However, it is also possible to use wildcards without names:\n\n>>> w = Wildcard.dot()\n>>> print(Pattern(f(w, w)))\nf(_, _)\n\nIt is also possible to assign variable names to entire subexpressions:\n\n>>> print(Pattern(f(w, a, variable_name='y')))\ny: f(_, a)\n\nPattern Matching\n................\n\nGiven 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.\n\n>>> from matchpy import match\n>>> y = Wildcard.dot('y')\n>>> b = Symbol('b')\n>>> subject = f(a, b)\n>>> pattern = Pattern(f(x, y))\n>>> substitution = next(match(subject, pattern))\n>>> print(substitution)\n{x \u21a6 a, y \u21a6 b}\n\nApplying the substitution to the pattern results in the original expression.\n\n>>> from matchpy import substitute\n>>> print(substitute(pattern, substitution))\nf(a, b)\n\nSequence Wildcards\n..................\n\nSequence wildcards are wildcards that can match a sequence of expressions instead of just a single expression:\n\n>>> z = Wildcard.plus('z')\n>>> pattern = Pattern(f(z))\n>>> subject = f(a, b)\n>>> substitution = next(match(subject, pattern))\n>>> print(substitution)\n{z \u21a6 (a, b)}\n\nAssociativity and Commutativity\n...............................\n\nMatchPy natively supports associative and/or commutative operations. Nested associative operators are automatically flattened, the operands in commutative operations are sorted:\n\n>>> g = Operation.new('g', Arity.polyadic, associative=True, commutative=True)\n>>> print(g(a, g(b, a)))\ng(a, a, b)\n\nAssociativity and commutativity is also considered for pattern matching:\n\n>>> pattern = Pattern(g(b, x))\n>>> subject = g(a, a, b)\n>>> print(next(match(subject, pattern)))\n{x \u21a6 g(a, a)}\n>>> h = Operation.new('h', Arity.polyadic)\n>>> pattern = Pattern(h(b, x))\n>>> subject = h(a, a, b)\n>>> list(match(subject, pattern))\n[]\n\nMany-to-One Matching\n....................\n\nWhen 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.\n\n>>> pattern1 = Pattern(f(a, x))\n>>> pattern2 = Pattern(f(y, b))\n>>> matcher = ManyToOneMatcher(pattern1, pattern2)\n>>> subject = f(a, b)\n>>> matches = matcher.match(subject)\n>>> for matched_pattern, substitution in sorted(map(lambda m: (str(m[0]), str(m[1])), matches)):\n...     print('{} matched with {}'.format(matched_pattern, substitution))\nf(a, x_) matched with {x \u21a6 b}\nf(y_, b) matched with {y \u21a6 a}\n\nRoadmap\n-------\n\nBesides the existing features, we plan on adding the following to MatchPy:\n\n- Support for Mathematica's ``Alternatives``: For example ``f(a | b)`` would match either ``f(a)`` or ``f(b)``.\n- Support for Mathematica's ``Repeated``: For example ``f(a..)`` would match ``f(a)``, ``f(a, a)``, ``f(a, a, a)``, etc.\n- Support pattern sequences (``PatternSequence`` in Mathematica). These are mainly useful in combination with\n  ``Alternatives`` or ``Repeated``, e.g. ``f(a | (b, c))`` would match either ``f(a)`` or ``f(b, c)``.\n  ``f((a a)..)`` would match any ``f`` with an even number of ``a`` arguments.\n- All these additional pattern features need to be supported in the ``ManyToOneMatcher`` as well.\n- Better integration with existing types such as ``dict``.\n- 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.\n- Improving the documentation with more examples.\n- Better test coverage with more randomized tests.\n- 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.\n\nContributing\n------------\n\nIf you have some issue or want to contribute, please feel free to open an issue or create a pull request. Help is always appreciated!\n\nThe Makefile has several tasks to help development:\n\n- To install all needed packages, you can use ``make init`` .\n- To run the tests you can use ``make test``. The tests use `pytest <https://docs.pytest.org/>`_.\n- To generate the documentation you can use ``make docs`` .\n- To run the style checker (`pylint <https://www.pylint.org/>`_) you can use ``make check`` .\n\nIf you have any questions or need help with setting things up, please open an issue and we will try the best to assist you.\n\nPublications\n------------\n\n`MatchPy: Pattern Matching in Python <http://joss.theoj.org/papers/10.21105/joss.00670>`_ |br|\nManuel Krebber and Henrik Barthels |br|\nJournal of Open Source Software, Volume 3(26), pp. 2, June 2018.\n\n`Efficient Pattern Matching in Python <https://dl.acm.org/citation.cfm?id=3149871>`_ |br|\nManuel Krebber, Henrik Barthels and Paolo Bientinesi |br|\nProceedings of the 7th Workshop on Python for High-Performance and Scientific Computing, November 2017.\n\n`MatchPy: A Pattern Matching Library <http://conference.scipy.org/proceedings/scipy2017/manuel_krebber.html>`_ |br|\nManuel Krebber, Henrik Barthels and Paolo Bientinesi |br|\nProceedings of the 15th Python in Science Conference, July 2017.\n\n`Non-linear Associative-Commutative Many-to-One Pattern Matching with Sequence Variables <https://arxiv.org/abs/1705.00907>`_ |br|\nManuel Krebber |br|\nMaster Thesis, RWTH Aachen University, May 2017\n\nIf you want to cite MatchPy, please reference the JOSS paper::\n\n    @article{krebber2018,\n        author    = {Manuel Krebber and Henrik Barthels},\n        title     = {{M}atch{P}y: {P}attern {M}atching in {P}ython},\n        journal   = {Journal of Open Source Software},\n        year      = 2018,\n        pages     = 2,\n        month     = jun,\n        volume    = {3},\n        number    = {26},\n        doi       = \"10.21105/joss.00670\",\n        web       = \"http://joss.theoj.org/papers/10.21105/joss.00670\",\n    }\n\n.. |br| raw:: html\n\n   <br />\n\n.. |pypi| image:: https://img.shields.io/pypi/v/matchpy.svg?style=flat\n    :target: https://pypi.org/project/matchpy/\n    :alt: Latest version released on PyPi\n\n.. |conda| image:: https://img.shields.io/conda/vn/conda-forge/matchpy.svg\n    :target: https://anaconda.org/conda-forge/matchpy\n    :alt: Latest version released via conda-forge\n\n.. |coverage| image:: https://coveralls.io/repos/github/HPAC/matchpy/badge.svg?branch=master\n    :target: https://coveralls.io/github/HPAC/matchpy?branch=master\n    :alt: Test coverage\n\n.. |build| image:: https://travis-ci.org/HPAC/matchpy.svg?branch=master\n    :target: https://travis-ci.org/HPAC/matchpy\n    :alt: Build status of the master branch\n\n.. |docs| image:: https://readthedocs.org/projects/matchpy/badge/?version=latest\n    :target: https://matchpy.readthedocs.io/en/latest/?badge=latest\n    :alt: Documentation Status\n\n.. |joss| image:: http://joss.theoj.org/papers/e456bc05880b533652980aee6550a3cb/status.svg\n    :target: http://joss.theoj.org/papers/e456bc05880b533652980aee6550a3cb\n    :alt: The Journal of Open Source Software\n\n.. |doi| image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1294930.svg\n   :target: https://doi.org/10.5281/zenodo.1294930\n   :alt: Digital Object Identifier\n\n\n",
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