Maintainer | diagrams-discuss@googlegroups.com |
---|---|

Safe Haskell | Safe-Inferred |

The coproduct of two monoids.

# Documentation

`m :+: n`

is the coproduct of monoids `m`

and `n`

. Values of
type `m :+: n`

consist of alternating lists of `m`

and `n`

values. The empty list is the identity, and composition is list
concatenation, with appropriate combining of adjacent elements
when possible.

killL :: Monoid n => (m :+: n) -> nSource

`killL`

takes a value in a coproduct monoid and sends all the
values from the left monoid to the identity.

killR :: Monoid m => (m :+: n) -> mSource

`killR`

takes a value in a coproduct monoid and sends all the
values from the right monoid to the identity.

untangle :: (Action m n, Monoid m, Monoid n) => (m :+: n) -> (m, n)Source

Take a value from a coproduct monoid where the left monoid has an action on the right, and "untangle" it into a pair of values. In particular,

m1 <> n1 <> m2 <> n2 <> m3 <> n3 <> ...

is sent to

(m1 <> m2 <> m3 <> ..., (act m1 n1) <> (act (m1 <> m2) n2) <> (act (m1 <> m2 <> m3) n3) <> ...)

That is, before combining `n`

values, every `n`

value is acted on
by all the `m`

values to its left.