User:Zzo38/Proposal for additional kinds
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This document is proposal about additional kinds.
New kinds
## -- New name for (#) kind (although (#) is available for compatibility) & -- Kind for classes + -- Kind for type-level natural numbers $ -- Means make up a kind from a Template Haskell code
Kind of classes
Example:
* -> & -- Kind of Eq class. (* -> *) -> & -- Kind of Monad class. (* -> &) -> & -- Class of classes. + -> * -> & -- Infinite series of classes, selected by a natural number.
Natural number kind
If a type requires a parameter, it can be a + kind, meaning numbers.
There should be some way to specify a type taking natural numbers by defining it for zero and them for a successor, so that it applies for all natural numbers.
It also means a type of kind + -> + -> + can be a type of adding numbers or other stuff like that, too.
A natural number type would be a type with the number of values being that number, for example 4 is Maybe (Maybe (Maybe (Maybe Zero))), and (->) would be the type for a array with a specific number of elements fixed by the type.