Portability | portable |
---|---|

Stability | experimental |

Maintainer | Luke Palmer <lrpalmer@gmail.com> |

A monad for enumerating sets: like the list monad, but impervious to infinite descent.

A depth-first search of a data structure can fail to give a full traversal if it has an infinitely deep path. Likewise, a breadth-first search of a data structure can fall short if it has an infinitely branching node. Omega addresses this problem by using a "diagonal" traversal that gracefully dissolves such data.

So while `liftM2 (,) [0..] [0..]`

gets "stuck" generating tuples whose
first element is zero, ```
runOmega $ liftM2 (,) (each [0..]) (each
[0..])
```

generates all pairs of naturals.

More precisely, if `x`

appears at a finite index in
`xs`

, and `y`

appears at a finite index in `f x`

,
then `y`

will appear at a finite index in `each xs >>= f`

.

This monad gets its name because it is a monad over sets of order type omega.

Warning: Omega is only a monad when the results of `runOmega`

are
interpreted as a set; that is, a valid transformation according to the
monad laws may change the order of the results. However, the same
set of results will always be reachable.