Copyright | (c) 2020 Emily Pillmore |
---|---|

License | BSD-style |

Maintainer | Emily Pillmore <emilypi@cohomolo.gy>, Reed Mullanix <reedmullanix@gmail.com> |

Stability | stable |

Portability | non-portable |

Safe Haskell | Safe |

Language | Haskell2010 |

This module contains definitions for `Cancellative`

functors
along with the relevant combinators.

## Synopsis

- class Alternative f => Cancellative f where
- cancel :: f a -> f a

- cancel1 :: (Group a, Cancellative f) => a -> f a -> f a
- annihilate :: (Cancellative f, Traversable t) => (a -> f a) -> t a -> f (t a)

# Cancellative

class Alternative f => Cancellative f where Source #

A group on `Applicative`

functors.

`Cancellative`

functors have the following laws in addition to those of
`Alternative`

:

This is analogous to a group operation on applicative functors,
in the sense that `Alternative`

forms a monoid. A straight-
forward implementation exists whenever `f a`

forms a `Group`

for all `a`

, in which case, `cancel == invert`

.

Nothing

Invert (or `cancel`

) a `Cancellative`

functor, such that, if the
functor is also a `GroupFoldable`

, then

amounts to evaluating the inverse of a word in the functor.`gold`

`.`

`cancel`

### Examples:

`>>>`

`let x = FreeGroup [Left (Sum (2 :: Word8)), Right (Sum 3)]`

`>>>`

FreeGroup {runFreeGroup = [Left (Sum {getSum = 3}),Right (Sum {getSum = 2})]}`cancel x`

#### Instances

## Cancellative combinators

cancel1 :: (Group a, Cancellative f) => a -> f a -> f a Source #

Cancel a single element in a `Cancellative`

functor.

### Examples:

`>>>`

`let x = FreeGroup [Left (Sum (2 :: Word8)), Right (Sum 3)]`

`>>>`

Sum {getSum = 1}`gold x`

`>>>`

Sum {getSum = 0}`gold $ cancel1 (Sum 1) x`

annihilate :: (Cancellative f, Traversable t) => (a -> f a) -> t a -> f (t a) Source #

Annihilate a `Traversable`

's worth of elements in a `Cancellative`

functor.