The coproduct (or free product) of monoids M and N.
Conceptually this is an alternating list of M and N values, with
the identity as the empty list, and composition as list concatenation that
combines adjacent elements when possible.
- Companion
- object
Value members
Concrete methods
A homomorphism to a monoid Z (if f and g are homomorphisms).
A homomorphism to a monoid Z (if f and g are homomorphisms).
Take a value from the coproduct monoid where each monoid acts on the
other, and untangle into a pair of values. Before being folded into the answer
an N value is combined with the sum of the M values to its left via g and
an M value is combined with the sum of the N values to its left via f.
This allows you to add up N values while having the opportunity to "track"
an evolving M value, and vice versa.
Take a value from the coproduct monoid where each monoid acts on the
other, and untangle into a pair of values. Before being folded into the answer
an N value is combined with the sum of the M values to its left via g and
an M value is combined with the sum of the N values to its left via f.
This allows you to add up N values while having the opportunity to "track"
an evolving M value, and vice versa.
Like untangle, except M values are simply combined without regard to the
N values to the left of it.
Like untangle, except M values are simply combined without regard to the
N values to the left of it.