# User:Zzo38/Proposal for additional kinds

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[x] -- If x is a kind, [x] is the kind of classes of types of kind x | [x] -- If x is a kind, [x] is the kind of classes of types of kind x | ||

+ -- Kind for type-level natural numbers | + -- Kind for type-level natural numbers | ||

+ | $ -- Means make up a kind from a Template Haskell code | ||

==Kind of classes== | ==Kind of classes== | ||

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* -> [*] -- A class that requires a type as a parameter to make a class. | * -> [*] -- A class that requires a type as a parameter to make a class. | ||

[<b></b>[*]] -- Class of classes. | [<b></b>[*]] -- Class of classes. | ||

+ | + -> [*] -- Infinite series of classes, selected by a natural number. | ||

+ | forall k. k -> [k] -- Polymorphic class that corresponds to any given kind. | ||

<!-- <b></b> means make it appear correctly on HTML view --> | <!-- <b></b> means make it appear correctly on HTML view --> | ||

## Revision as of 21:58, 3 September 2011

This document is proposal about additional kinds.

## 1 New kinds

## -- New name for (#) kind (although (#) is available for compatibility) [x] -- If x is a kind, [x] is the kind of classes of types of kind x + -- Kind for type-level natural numbers $ -- Means make up a kind from a Template Haskell code

## 2 Kind of classes

Example:

[*] -- Kind of Eq class. [* -> *] -- Kind of Monad class. * -> [*] -- A class that requires a type as a parameter to make a class. [[*]] -- Class of classes. + -> [*] -- Infinite series of classes, selected by a natural number. forall k. k -> [k] -- Polymorphic class that corresponds to any given kind.

## 3 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.