User:Zzo38/Proposal for additional kinds

This document is proposal about additional kinds.

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

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.

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.