Copyright | (c) Tristan Wibberley 2017 |
---|---|

License | GPL-2 |

Maintainer | tristan.wibberley@gmail.com |

Stability | experimental |

Safe Haskell | None |

Language | Haskell2010 |

Here is a longer description of this module, containing some
commentary with `some markup`

.

- data SubZero f g a
- points :: (Functor f, Alternative g) => (a -> Bool) -> f a -> SubZero f g a
- reveal :: (Functor f, Applicative g) => f a -> SubZero f g a
- flatten :: Applicative f => f a -> SubZero f Maybe a -> f a
- class (Alternative g, Alternative h) => Superposition g h where
- simplify :: Superposition g h => g a -> Maybe (h a)
- collapse :: Superposition g h => (a -> a -> a) -> g a -> h a
- keep :: Alternative f => (a -> Bool) -> a -> f a

# Documentation

Converts a functor so that each point at the source has alternatives.

It's just like Compose but the applicative instance appends new alternative values in the rightmost (inner/minor) functor instead of in the leftmost (outer/major) functor.

The result is that two

s of alternatives zip together,
providing alternatives to each point.`ZipList`

Given the immediate utility of this, I do wonder if the

instance of `Alternative`

is the wrong one.`Compose`

`f`

- The major functor, overall mapping/view
`g`

- This has a a few key useful interpretations depending on its instances, examples below.
`a`

- Transformed/contained value type.

Some example instances that you might want to rely on from `g`

:

`Alternative`

- Superposition functor.
- How do individual items have a set of possible values?
- How do those possible values collapse to form one optional value?
- etc.

- etc
- There are a lot of other utilities for this type.

(Functor g, Functor f) => Functor (SubZero f g) Source # | |

(Applicative g, Applicative f) => Applicative (SubZero f g) Source # | |

(Applicative f, Alternative g) => Alternative (SubZero f g) Source # | |

(Applicative f, Superposition g h) => Superposition (SubZero f g) (SubZero f h) Source # | Superposition within |

(Eq a, Eq1 g, Eq1 f) => Eq (SubZero f g a) Source # | |

(Ord a, Ord1 g, Ord1 f) => Ord (SubZero f g a) Source # | |

(Read a, Read1 g, Read1 f) => Read (SubZero f g a) Source # | |

(Show a, Show1 g, Show1 f) => Show (SubZero f g a) Source # | |

# Constructors

:: (Functor f, Alternative g) | |

=> (a -> Bool) | A predicate that indicates whether a point is occupied by its original value or vacant. |

-> f a | The seed points with their values. |

-> SubZero f g a | The constructed |

Turns a container of values to a container of either retained or destroyed values based on a predicate

The type constraint allows us to model possible outcomes so destroyed values are just "no possible outcomes" while retained values represent "the only possible outcome".

To represent that "no value" is a possible outcome, `a`

should be some type like (

) or (`Maybe`

a

).`Either`

`String`

a

`f`

- This
`Functor`

defines the broad scale behaviours but its`Alternative`

instance is overridden. This in particular might change during upcoming design validation. `g`

- This
`Functor`

supplies the supercedent`Alternative`

instance and thus the finer behaviours.

:: (Functor f, Applicative g) | |

=> f a | Initial flat structure |

-> SubZero f g a | enhanced structure, albeit with no changes |

Provides structure for values at the other end of a `Functor`

# Destructors

:: Applicative f | |

=> f a | Default values |

-> SubZero f Maybe a | Structured container |

-> f a | Destructured container |

If the type constructor of the possibilities concept is

then you can use `Maybe`

to provide default values for
impossible points.`flatten`

*NOTE*: This uses the applicative instance of the broad scale

which means exact behaviour can vary depending on the type of`Functor`

because each has a different technique to ensure a value is found for every point:`Applicative`

f`list of a`

- Cross-product; Providing all default values once for all points.
`ZipList`

a- zipWith; Providing one default value for each point until there are either no defaults remaining or no more points.
`Identity`

a- One default must surely be provided and it is used if a default is required.
`Maybe`

a- Not sure exactly what this does, TBC.
`Either`

a- Not sure exactly what this does, TBC.

# Restructors

class (Alternative g, Alternative h) => Superposition g h where Source #

collapse f empty = simplify empty

collapse f (pure x) = simplify (pure x)

collapse f (x <|> y) = pure (f x y)

`g`

must form a monoid under `f`

when

is the monoid's identity.`empty`

Alternative h => Superposition [] h Source # | Superposition within a nondeterminism list (ie, []) |

(Applicative f, Superposition g h) => Superposition (SubZero f g) (SubZero f h) Source # | Superposition within |

simplify :: Superposition g h => g a -> Maybe (h a) Source #

Tries to convert from one alternative to another

collapse :: Superposition g h => (a -> a -> a) -> g a -> h a Source #

keep :: Alternative f => (a -> Bool) -> a -> f a Source #

Turns a value "`a`

" to

or `Just`

a

based on a predicate assuming you use it in a
context that wants `Nothing`

instead of some other representation of `Maybe`

a

s`Alternative`