Control.Applicative.SubZero

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

Documentation

data SubZero f g a

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 ZipLists of alternatives zip together, providing alternatives to each point.

Given the immediate utility of this, I do wonder if the Alternative instance of Compose is the wrong one.

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.

Instances

(Functor g, Functor f) => Functor (SubZero f g)

Methods

fmap :: (a -> b) -> SubZero f g a -> SubZero f g b

(<$) :: a -> SubZero f g b -> SubZero f g a

(Applicative g, Applicative f) => Applicative (SubZero f g)

Methods

pure :: a -> SubZero f g a

(<*>) :: SubZero f g (a -> b) -> SubZero f g a -> SubZero f g b

(*>) :: SubZero f g a -> SubZero f g b -> SubZero f g b

(<*) :: SubZero f g a -> SubZero f g b -> SubZero f g a

(Applicative f, Alternative g) => Alternative (SubZero f g)

Methods

empty :: SubZero f g a

(<|>) :: SubZero f g a -> SubZero f g a -> SubZero f g a

some :: SubZero f g a -> SubZero f g [a]

many :: SubZero f g a -> SubZero f g [a]

(Eq a, Eq1 g, Eq1 f) => Eq (SubZero f g a)

Methods

(==) :: SubZero f g a -> SubZero f g a -> Bool

(/=) :: SubZero f g a -> SubZero f g a -> Bool

(Ord a, Ord1 g, Ord1 f) => Ord (SubZero f g a)

Methods

compare :: SubZero f g a -> SubZero f g a -> Ordering

(<) :: SubZero f g a -> SubZero f g a -> Bool

(<=) :: SubZero f g a -> SubZero f g a -> Bool

(>) :: SubZero f g a -> SubZero f g a -> Bool

(>=) :: SubZero f g a -> SubZero f g a -> Bool

max :: SubZero f g a -> SubZero f g a -> SubZero f g a

min :: SubZero f g a -> SubZero f g a -> SubZero f g a

(Read a, Read1 g, Read1 f) => Read (SubZero f g a)

Methods

readsPrec :: Int -> ReadS (SubZero f g a)

readList :: ReadS [SubZero f g a]

readPrec :: ReadPrec (SubZero f g a)

readListPrec :: ReadPrec [SubZero f g a]

(Show a, Show1 g, Show1 f) => Show (SubZero f g a)

Methods

showsPrec :: Int -> SubZero f g a -> ShowS

show :: SubZero f g a -> String

showList :: [SubZero f g a] -> ShowS

Constructors

points

Arguments

:: (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 SubZero value.

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 (Maybe a) or (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.

reveal

Arguments

:: (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

flatten

Arguments

:: Applicative f

=> f a

Default values

-> SubZero f Maybe a

Structured container

-> f a

Destructured container

If the type of the possibilities concept is Maybe then you can use flatten to provide default values for impossible points.

• NOTE: This uses the applicative instance of the broad scale Functor which means exact behaviour can vary depending on the type of Applicative f because each has a different technique to ensure a value is found for every point:

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

collapse

Arguments

:: (Functor f, Foldable g, Alternative h)

=> (a -> a -> a)

combining function

-> SubZero f g a

full structure

-> SubZero f h a

collapsed structure

Take the alternatives embedded in the SubZero and collapse them with a combining function to a single Alternative value or empty which means no possible outcomes. This is quite free in the type of the possibilities concept of the result. It's compatible with Maybe for further uses with flatten, but you can retain behaviours of more sophisticated types. A consequence of this is that you will probably need to state a type.