[GHC] #10805: Could not deduce (a ~ b) implies (f a ~ f b), because a type function may not be injective

[GHC]

#10805: Could not deduce (a ~ b) implies (f a ~ f b), because a type function may
not be injective
-------------------------------------+-------------------------------------
              Reporter:  htebalaka   |             Owner:
                  Type:  bug         |            Status:  new
              Priority:  normal      |         Milestone:
             Component:  Compiler    |           Version:  7.10.2
  (Type checker)                     |
              Keywords:              |  Operating System:  Unknown/Multiple
          Architecture:              |   Type of failure:  GHC rejects
  Unknown/Multiple                   |  valid program
             Test Case:              |        Blocked By:
              Blocking:              |   Related Tickets:
Differential Revisions:              |
-------------------------------------+-------------------------------------
 I don't know if the summary I provided is what's really going on here, but
 I'm a little baffled why this doesn't typecheck. I can't see what
 injectivity has to do with it, since we're not trying to deduce that the
 arguments are the same from the result of an application being the same;
 rather we're doing the opposite. I've encountered plenty of obvious
 arithmetic laws that I've needed to unsafeCoerceConstraint away with doing
 type level arithmetic, but this seems like it should be trivial
 regardless.

 {{{#!hs
 {-# LANGUAGE GADTs, ExplicitNamespaces, TypeOperators, DataKinds #-}
 {-# LANGUAGE ConstraintKinds, KindSignatures, PatternGuards #-}

 import Data.Type.Equality ((:~:)(..))
 import GHC.TypeLits (Nat, type (<=), type (-), type (+), type (<=?))

 data SNat :: Nat -> * where
     SSucc   :: SNat a -> SNat (a + 1)
     SZero   :: SNat 0

 heqHet :: SNat a -> SNat b -> Maybe (a :~: b)
 heqHet SZero SZero = Just Refl
 heqHet (SSucc a) (SSucc b)
     | Just Refl <- heqHet a b = Just Refl
 heqHet _ _ = Nothing

 data Slice :: Nat -> Nat -> * where
     Slice   :: ((start + 1) <= end, end <= numElements)
             => SNat numElements -> SNat start -> SNat end
             -> Slice numElements (end - start)

 heqHet' :: Slice a b -> Slice a b' -> Bool
 heqHet' (Slice _ start end) (Slice _ start' end')
     | Just _ <- heqHet start start'
     , Just _ <- heqHet end end' = True
     | otherwise = False
 }}}


 {{{#!hs
 Slice.hs:24:10:
     Could not deduce (((start + 1) <=? a) ~ ((start + 1) <=? a))
     from the context (b ~ (end - start), (start + 1) <= end, end <= a)
       bound by a pattern with constructor
                  Slice :: forall (numElements :: Nat) (start :: Nat) (end
 :: Nat).
                           ((start + 1) <= end, end <= numElements) =>
                           SNat numElements
                           -> SNat start -> SNat end -> Slice numElements
 (end - start),
                in an equation for ‘heqHet'’
       at Slice.hs:24:10-26
     or from (b' ~ (end1 - start1), (start1 + 1) <= end1, end1 <= a)
       bound by a pattern with constructor
                  Slice :: forall (numElements :: Nat) (start :: Nat) (end
 :: Nat).
                           ((start + 1) <= end, end <= numElements) =>
                           SNat numElements
                           -> SNat start -> SNat end -> Slice numElements
 (end - start),
                in an equation for ‘heqHet'’
       at Slice.hs:24:30-48
     NB: ‘GHC.TypeLits.<=?’ is a type function, and may not be injective
     Relevant bindings include
       heqHet' :: Slice a b -> Slice a b' -> Bool (bound at Slice.hs:24:1)
     In the pattern: Slice _ start end
     In an equation for ‘heqHet'’:
         heqHet' (Slice _ start end) (Slice _ start' end')
           | Just _ <- heqHet start start', Just _ <- heqHet end end' =
 True
           | otherwise = False
 Failed, modules loaded: none.
 }}}

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Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/10805>
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