# 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 |
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+ -- Kind for type-level natural numbers |
+ -- Kind for type-level natural numbers |
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+ | $ -- Means make up a kind from a Template Haskell code |
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==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. |
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[<b></b>[*]] -- Class of classes. |
[<b></b>[*]] -- Class of classes. |
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+ | + -> [*] -- Infinite series of classes, selected by a natural number. |
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+ | forall k. k -> [k] -- Polymorphic class that corresponds to any given kind. |
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## 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.