[GHC] #11070: Type-level arithmetic of sized-types has weaker inference power than in 7.8

[GHC]

#11070: Type-level arithmetic of sized-types has weaker inference power than in 7.8
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        Reporter:  cactus            |                Owner:
            Type:  bug               |               Status:  new
        Priority:  normal            |            Milestone:
       Component:  Compiler          |              Version:  7.10.2
      Resolution:                    |             Keywords:  TypeFamilies
Operating System:  Unknown/Multiple  |         Architecture:
 Type of failure:  GHC rejects       |  Unknown/Multiple
  valid program                      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:                    |  Differential Rev(s):
       Wiki Page:                    |
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Comment (by cactus):

 The same behaviour can be observed with the closed-type-family version
 below:


 {{{
 data X0 = X0
 data N1 = N1

 data X0_ a = X0_ Integer
 data X1_ a = X1_ Integer
 type X1 = X1_ X0
 type X2 = X0_ (X1_ X0)

 type family APP0 a where
     APP0 X0 = X0
     APP0 N1 = X0_ N1
     APP0 (X1_ a) = X0_ (X1_ a)
     APP0 (X0_ a) = X0_ (X0_ a)

 type family APP1 a where
     APP1 X0 = X1_ X0
     APP1 N1 = N1
     APP1 (X1_ a) = X1_ (X1_ a)
     APP1 (X0_ a) = X1_ (X0_ a)

 type family SUCC a where
     SUCC X0 = X1_ X0
     SUCC N1 = X0
     SUCC (X1_ a) = APP0 (SUCC a)
     SUCC (X0_ a) = APP1 a

 type family ADD a b where
     ADD a X0 = a
     ADD X0 a = a
     ADD N1 N1 = APP0 N1
     ADD N1 (X1_ b) = APP0 b
     ADD N1 (X0_ b) = APP1 (ADD N1 b)
     ADD (X1_ a) N1 = APP0 a
     ADD (X0_ a) N1 = APP1 (ADD a N1)
     ADD (X1_ a) (X1_ b) = APP0 (SUCC (ADD a b))
     ADD (X1_ a) (X0_ b) = APP1 (ADD a b)
     ADD (X0_ a) (X1_ b) = APP1 (ADD a b)
     ADD (X0_ a) (X0_ b) = APP0 (ADD a b)

 type family NOT a where
     NOT X0 = N1
     NOT N1 = X0
     NOT (X1_ a) = APP0 (NOT a)
     NOT (X0_ a) = APP1 (NOT a)

 type SUB a b = ADD a (SUCC (NOT b))

 }}}

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/11070#comment:3>
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