Partial type constructors

[jgbm]

This issue is to track the different work needed to support partial type constructors.

Core features

• Support partial data type constructors #1
• Support partial newtypes #2
• Support partial type families #3
• Support partial type synonyms #4
• Support Partial Data Families #8

Low-level libraries and language features

• Worker-wrapper transformations
• Rules
• Deriving
• Generics
• Total and its kin (following Richard's cheat)

[fxdpntthm]

Rules that don't behave

GHC.Control.Category

class Category cat where
    -- | the identity morphism
    id :: cat a a

    -- | morphism composition
    (.) :: cat b c -> cat a b -> cat a c

{-# RULE
"association"   forall p q r .
                 (p . q) . r = p . (q . r)
 #-}

the association rule fails to compile as it gives rise to different constraints on each side of the equality.

GHC.Control.Arrow

class Category a => Arrow a where
....

{-# RULES
-- "compose/arr"   forall f g .
--                 (arr f) . (arr g) = arr (f . g)
"first/arr"     forall f .
                first (arr f) = arr (first f)
"second/arr"    forall f .
                second (arr f) = arr (second f)
"product/arr"   forall f g .
                arr f *** arr g = arr (f *** g)
"fanout/arr"    forall f g .
                arr f &&& arr g = arr (f &&& g)
-- "compose/first" forall f g .
--                 (first f) . (first g) = first (f . g)
-- "compose/second" forall f g .
--                 (second f) . (second g) = second (f . g)
 #-}


class Arrow a => ArrowChoice a where
...

{-# RULES
"compose/left"  forall f g .
                 left f . left g = left (f . g)
"compose/right" forall f g .
                 right f . right g = right (f . g)
 #-}

Update:

Don't actually need to comment out these after adding Total2 as a class constraint: 90d3c63
class Total2 cat => Category cat where, class (Total2 a, Arrow a) => ArrowChoice a etc.