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User:Zzo38/Proposal for additional kinds

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==New kinds==
 
==New kinds==
 
## -- New name for (#) kind (although (#) is available for compatibility)
 
## -- 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 classes
 
+ -- Kind for type-level natural numbers
 
+ -- Kind for type-level natural numbers
 
$ -- Means make up a kind from a Template Haskell code
 
$ -- Means make up a kind from a Template Haskell code
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==Kind of classes==
 
==Kind of classes==
 
Example:
 
Example:
[*] -- Kind of Eq class.
+
* -> & -- Kind of Eq class.
[* -> *] -- Kind of Monad class.
+
(* -> *) -> & -- Kind of Monad class.
* -> [*] -- A class that requires a type as a parameter to make a class.
+
(* -> &) -> & -- Class of classes.
[<b></b>[*]] -- Class of classes.
+
+ -> * -> & -- Infinite series of classes, selected by a natural number.
+ -> [*] -- Infinite series of classes, selected by a natural number.
 
k -> [k] -- Polymorphic class that corresponds to any given kind.
 
<!-- <b></b> means make it appear correctly on HTML view -->
 
   
 
==Natural number kind==
 
==Natural number kind==

Revision as of 01:48, 5 September 2011

This document is proposal about additional kinds.

1 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

2 Kind of classes

Example:

* -> & -- Kind of Eq class.
(* -> *) -> & -- Kind of Monad class.
(* -> &) -> & -- Class of classes.
+ -> * -> & -- Infinite series of classes, selected by a natural number.

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.