| 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 |
Control.Applicative.Cancellative
Description
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.
Minimal complete definition
Nothing
Methods
Invert (or cancel) a Cancellative functor, such that, if the
functor is also a GroupFoldable, then gold . cancel
Examples:
>>>let x = FreeGroup [Left (Sum (2 :: Word8)), Right (Sum 3)]>>>cancel xFreeGroup {runFreeGroup = [Left (Sum {getSum = 3}),Right (Sum {getSum = 2})]}
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)]>>>gold xSum {getSum = 1}>>>gold $ cancel1 (Sum 1) xSum {getSum = 0}
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.