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�

�h?#��d�dZddlZGd�d��Zd�Zd�ZGd�d��Zd	�Zd
�Zd�ZdS)a�
    An implementation of the Knuth-Bendix algorithm,
    as described in (1), p. 143.
    For determining if two paths in a category are equal.

The algorithm as given here,
takes a set of equations in the form of a sequence:

E = [(a, b), (c, d) ...]

where a, b, c, d are 'paths'.

Paths are given as strings, for example:

E = [ ('fhk', 'gh'), ('m', 'kkm') ]

means that the path 'fhk' equals 'gh' and 'm' equals 'kkm'.

Each arrow in the path is here a single character.  If longer arrow
names are required, a delimiter string can be specified as in:

kb(E, delim='.')

The paths must then be given by the delimiter between each arrow;

E = [ ('h_arrow.g_arrow', 'g_arrow.k_arrow') ... ]


The function kb(E) returns an object, say A, which is

o callable: A(a, b)->boolean determines if two paths given by a, b are equal.
o has a method A.reduce(a)->pathstring, which reduces a path to normal form.

An optional parameter to kb, max_iterations, determines the maximum
number of iterations the algorithm should try making the reduction
system 'confluent'. The algorithm is not guaranteed to terminate
with a confluent system in a finite number of iterations, so if the
number of iterations needed exceeds max_iterations an exception
(ValueError) will be raised. The default is 100.

References

(1)
@book{walters91categories,
    title={Categories and Computer Science},
    author={R. F. C. Walters},
    publisher={Cambridge University Press},
    location={Cambridge},
    year=1991}


(2)
@book{grimaldi94discrete,
author="Ralph P. Grimaldi".
title="Discrete and Combinatorial Mathematics: An Applied Introduction",
publisher="Addison-Wesley",
location="Readin, Massachusetts",
year=1994
}


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