[GHC] #12363: Type application for infix

[GHC]

#12363: Type application for infix
-------------------------------------+-------------------------------------
        Reporter:  Iceland_jack      |                Owner:
            Type:  feature request   |               Status:  new
        Priority:  lowest            |            Milestone:
       Component:  Compiler          |              Version:  8.0.1
  (Parser)                           |             Keywords:
      Resolution:                    |  TypeApplications
Operating System:  Unknown/Multiple  |         Architecture:
                                     |  Unknown/Multiple
 Type of failure:  None/Unknown      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:                    |  Differential Rev(s):
       Wiki Page:                    |
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Comment (by Iceland_jack):

 Just passing by

 ----

 A [http://sf.snu.ac.kr/jeehoon.kang/assets/bs_math.pdf definition] of
 composition of an opposite category. The different instantiations of
 composition are made explicit but the arrows are cast implicitly:

 {{{
 f ∘_C^op g = g ∘_C f
 }}}

 Awodey uses the notation `f* : B* -> A*` in `ℂ^op` for `f : A -> B` in `ℂ`
 making conversions between categories explicit. The category of the
 identity arrow is named but not of composition:
 {{{
 1_ℂ* = (1_ℂ)*
 f* ∘ g* = (g ∘ f)*
 }}}

 Haskell makes switching between categories explicit, using `Op f :: (Op ℂ)
 B A` for `f :: ℂ A B`
 {{{#!hs
 type Cat k = k -> k -> Type

 newtype Op :: Cat i -> Cat i where
   Op :: cat b a -> (Op cat) a b

 instance Category cat => Category (Op cat) where
   id :: (Op cat) a a
   id = Op id

   (.) :: (Op cat) b c -> (Op cat) a b -> (Op cat) a c
   Op f . Op g = Op (g . f)
 }}}

 can be made more explicit by

 {{{#!hs
   id :: (Op cat) a a
   id = Op (id @cat)

   (.) :: (Op cat) b c -> (Op cat) a b -> (Op cat) a c
   Op f . Op g = Op (g . @cat f)
 }}}

 ----

 A separate proposal is visible type applications on methods, corresponding
 to their instance type arguments (`Op cat` in this case) which gives us an
 (overly?) explicit definition


 {{{#!hs
 id @(Op cat) = Op (id @cat)

 Op f . @(Op cat) Op g = Op (g . @cat f)
 }}}

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/12363#comment:7>
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