hrm, wouldn't your proposed extension be largely accomplished by using Record pun and Record WildCards? eg {-# LANGUAGE RecordWildCards #-} {-# LANGUAGE RecordPuns #-} module Foo where data Relation a = Rel{related :: a -> a ->Bool,unrelated :: a -> a -> Bool} foo :: Relation A -> A -> A -> Bool foo Rel{..} x y = related x y ------ or am i over looking something? I do realize this may not quite be what youre suggesting, and if so, could you help me understand better? :) On Fri, Apr 24, 2015 at 4:26 PM, Ertugrul Söylemez wrote:

...

3. NonStrictPoSet, which is the class of all partially ordered set-like things, but without the requirement that a <= b and b <= a implies a Equal b.

Those are preorders. An antisymmetric preorder is a non-strict poset.

Also it's difficult to capture all of those various order types in Haskell's class system. A type can have many orders and many underlying equivalence relations in the case of partial and total orders, and there are different ways to combine them. For example equality is a partial order, modular equivalence is a preorder, etc. Those denote bags and groups more than sequences or trees.

Perhaps it's time to add a type class-like system to Haskell, but for explicitly passed arguments:

record Relation a where related :: a -> a -> Bool

unrelated :: a -> a -> Bool unrelated x y = not (related x y)

func1 :: Relation A -> A -> A -> A func1 _ x y = ... related x y ...

func2 :: Relation A -> Relation A -> A -> A -> A func2 r1 r2 x y = ... r1.related x y ... r2.unrelated x y ...

In a lot of cases this is much more appropriate than a type class, and it would turn many things that are currently types into regular functions, thus making them a lot more composable:

down :: Ord a -> Ord a down o = Ord { compare x y = o.compare y x } -- The remaining Ord functions are defaulted.

Perhaps all we need is to generalise default definitions to data types and add module-like dot syntax for records (mainly to preserve infix operators). Formally speaking there is also little that prevents us From having associated types in those records that can be used on the type level.

For actual record types (i.e. single-constructor types) we could even have specialisation and get a nice performance boost that way, if we ask for it:

{-# SPECIALISE down someOrder :: Ord SomeType #-}

This would be extremely useful.

...

4. Things like above, but with the requirement of a Zero, with the requirement of a One, and the requirement fo both a Zero and a One.

Zero and one as in minBound and maxBound or rather as in Monoid and a hypothetical Semiring? In the latter case I believe they don't really belong into an additional class, unless you have some ordering-related laws for the zeroes and ones. If not, you can always simply use an Ord+Semiring constraint.

There may be some motivation to make Bounded a subclass of Ord though.

Greets, Ertugrul

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