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Divergence using free monads

I am trying to use a la carte data types to define a free monad for template purposes. I wrote some combinators, but I'm stuck. My program continues to diverge, and I do not understand why.

Consider:

math :: Math :<: f => MathExpr a -> Free f ()
blank :: f :<: (Textual :+: Math) => Free f () -> Free (Blank k f) ()
equals :: Free (Math :+: (Blank L Math)) ()
       -> Free (Math :+: (Blank R Math)) ()
       -> Free Equation ()

Composition (empty mathematics) has the type:

blank . math :: ( f :<: (Textual :+: Math)
                , Math :<: f
                ) => MathExpr a -> Free (Blank k f) ()

Note that f must be both smaller than the mix of Textual and Math, and larger than Math. So the only option for f is math. (I understand that the compiler cannot do this without additional work on my part, if at all)

The problem occurs when I try to evaluate:

test :: Free Equation ()
test = (hoistFree (inj :: Blank 'L Math a -> (Math :+: Blank 'L Math) a)
     . blank
     . (math :: MathExpr x -> Free Math ())
     $ "hi"
     )
     `equals` (math $ "world")

which apparently loops, tying my processor 100%. The calculation of the results is calculated as follows:

Free (Equation (Free (DirectSum {unDirectSum = Right

GHCi . , -, , , .

, , . ?

: : http://lpaste.net/93471      Data.Domain : http://lpaste.net/93472

+4
1

( , ...)

lpastes () GHC 7.6.3 free-3.4.2

- , typecheck, .

  • (MathExpr a) .

  • -XKindSignatures -XOloadloadStrings.

  • (Show Blank).

    ( (g (Free g())), f) = > ( k g f)

, .

ghci:

*> test
Free (Equation (Free (DirectSum {unDirectSum = Right (Blank (Free (Math "hi" (Pure ()))) (Pure ()))})) (Free (DirectSum {unDirectSum = Left (Math "hello" (Pure ()))})) (Pure ()))

, , / GHC ? .

+1

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