Cardinality

Measure container capacity. Use it to safely change container.

This module introduces typeclasses

• HasCard = "Has cardinality". In other words, "it's possible to measure current count of elements for this container"

• HasCardT = "Has cardinality (for container types of kind (* -> *))". In other words, "it's possible to measure current count of elements for this container (for container types of kind (* -> *))"

• HasCardConstr = "Has cardinality constraint". In other words, "there is a capacity constraint for this container".

• HasCardConstrT = "Has cardinality constraint (for container types of kind (* -> *))". In other words, "there is a capacity constraint for this container type of kind (* -> *)".

• HasCardUCT = "Has cardinality-unsafe container transform". Define transform that may thow an error, if contents of from don't fit in to .

• HasCardUCT_T = "Has cardinality-unsafe container transform (for container types of kind (* -> *))". Same thing as HasCardUCT, but for containers of kind (* -> *).

No, it's not about playing cards. It's about cardinalities. Wikipedia: "/In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3./" In this package I dare to extend the definition a bit to "C. is a measure of the number of elements in a container"

Usual containers are (together with their cardinality ranges):

• Identity a (1 element)

• Maybe a (0..1 element)

• [a] (0..inf elements)

• Map k e (0..inf elements)

I extended this to the folowing list:

• EmptySet a (0 elements)

• Identity a (1 element)

• Maybe a (0..1 element)

• [a] (0..inf elements)

• NeverEmptyList a (1..inf elements)

• Map k e (0..inf elements)

Typeclass HasCardUCT together with function sContTrans (safe container transform) provides a facility to safely change container from one to another keepeng the content. If content doesn't fit to target container, Nothing is returned. However, when transforming from list [a] to (Maybe a) it won't check list length further first 2 elements. The complexity and power of this package is that it provides a facility to lazily evaluate amount of content in the container.

To interface package functions

import Data.Cardinality