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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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