MatchPy is a library for pattern matching on symbolic expressions in Python.
Work in progress
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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.
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 f(x), where f is a function and x is a variable, and the subject f(a), where a is a constant symbol. Then the substitution that replaces x with 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}
Besides the existing features, we plan on adding the following to MatchPy:
Alternatives: For example f(a | b) would match either f(a) or f(b).Repeated: For example f(a..) would match f(a), f(a, a), f(a, a, a), etc.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.ManyToOneMatcher as well.dict.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:
make init .make test. The tests use pytest <https://docs.pytest.org/>_.make docs .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.
| MatchPy: Pattern Matching in Python <http://joss.theoj.org/papers/10.21105/joss.00670>_
| Manuel Krebber and Henrik Barthels
| 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>_
| Manuel Krebber, Henrik Barthels and Paolo Bientinesi
| 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>_
| Manuel Krebber, Henrik Barthels and Paolo Bientinesi
| 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>_
| Manuel Krebber
| 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",
}
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FAQs
A library for pattern matching on symbolic expressions.
We found that matchpy demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 2 open source maintainers collaborating on the project.
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