[Haskell-cafe] weird type signature in Arrow Notation

[Brent Yorgey]

On Tue, Aug 02, 2011 at 05:08:33PM -0400, bob zhang wrote:
> hi, all
> testB :: (ArrowChoice t1, Num a1, Num a) => (a -> a1 -> t2) -> t1 a t3
> -> t1 a1 t3 -> t1 (a, a1) t
> testB f g h = proc (x,y) -> do
> if (f x y)then g -< x + 1 else h -< y + 2
> 
> it's very strange that the type of _f_ is (a->a1->t2) which I thought
> should be a -> a1 -> Bool,
> 
> btw, is there any way to get the output of preprocessing using -XArrow
> extensions,
> 
> Thanks a lot
> best, bob

Congratulations, you have definitely found a GHC bug!  Note there are
actually two things wrong with testB's type signature: first, t2 ought
to be Bool, as you note.  But even worse, notice that the return type
of the result arrow, t, has nothing to do with any of the other types!
This means that we can use testB along with the (->) instance for
Arrow to construct elements of arbitrary types:

  ghci> let anythingYouWant = testB (\x y -> False) (const 3) (const 2) (2,2)
  ghci> :t anythingYouWant
  anythingYouWant :: t
  ghci> anythingYouWant :: Integer
  2
  ghci> anythingYouWant :: Int
  2
  ghci> anythingYouWant :: Double
  1.0e-323
  ghci> anythingYouWant :: Char
  '\STX'
  ghci> (anythingYouWant :: (Double -> Double) -> [Double]) sqrt
  [
  [1]    17391 segmentation fault  ghci

whoops!

I'm using GHC 7.0.3, but Daniel Wagner and I also tried it (with the
same results) on GHC 7.2.0rc1 and GHC HEAD.

I wasn't able to find a ticket for this on the GHC bug tracker, I
guess we should file one!

I tried to find a way to get the output of preprocessing using -XArrow
but wasn't able to find one (other than -ddump-ds which gives you the
unoptimized *GHC core* output, which is quite hard to read).

-Brent