Re: [Haskell-cafe] GHCi gives type signature that won't compile.

5 Jun 2008

      On Thu, Jun 5, 2008 at 9:36 AM, Miguel Mitrofanov  wrote:
...
Check your types for typos.
On 5 Jun 2008, at 20:31, A A wrote:
...
Hi All
I can successfully compile the following code using ghci
import Data.Array.IArray
makeArray (lower, upper) f = listArray (lower, upper) [(f i) | i <-
[lower..upper]
tridiagonal_solve (a, b, c, d, (lower, upper)) = x
   where
       gen_array f = (makeArray (lower, upper) f)
       x = gen_array x_f
           where
               x_f i
                   | i == upper     = (d_dash ! upper)
                   | otherwise         = (d_dash ! i) - (c_dash ! i) * (x
! (i + 1))
       d_dash = gen_array d_dash_f
           where
               d_dash_f i
                   | i == lower     = (d ! lower) / (b ! lower)
                   | otherwise        = ((d ! i) - (d_dash ! (i - 1)) * (a
! i)) /
                                         ((b ! i) - (c_dash ! (i - 1)) *
(a ! i))
       c_dash = gen_array c_dash_f
           where
               c_dash_f i
                   | i == lower    = (c ! lower) / (b ! lower)
                   | otherwise     = (c ! i) /
                                         ((b ! i) - (c_dash ! (i - 1)) *
(a ! i))
I then attempted to write a type signature for tridiagonal_solve. I didn't
succeed at this however, all of my type signatures gave compile errors when
attempting to load them in ghci. I asked in the #haskell channel, and they
suggested that I try the type signature from ghci :type function.
So I removed any type signatures, and reloaded the file in ghci, and typed
":type tridiagonal_solve" which produced the following output:
tridiagonal_solve :: (IArray a3 e,
                     IArray a6 e,
                     IArray a7 e,
                     Fractional e,
                     Ix a,
                     Num a,
                     IArray a4 e,
                     IArray a2 e,
                     IArray a5 e,
                     IArray a1 e,
                     Enum a) =>
                    (a4 a e, a2 a e, a1 a e, a5 a e, (a, a)) -> a7 a e
I then attempted to paste this into my code, the resulting code looking
like this:
import Data.Array.IArray
makeArray (lower, upper) f = listArray (lower, upper) [(f i) | i <-
[lower..upper]]
tridiagonal_solve :: (IArray a3 e,
                     IArray a6 e,
                     IArray a7 e,
                     Fractional e,
                     Ix a,
                     Num a,
                     IArray a4 e,
                     IArray a2 e,
                     IArray a5 e,
                     IArray a1 e,
                     Enum a) =>
                    (a4 a e, a2 a e, a1 a e, a5 a e, (a, a)) -> a7 a e
tridiagonal_solve (a, b, c, d, (lower, upper)) = x
   where
       gen_array f = (makeArray (lower, upper) f)
       x = gen_array x_f
           where
               x_f i
                   | i == upper     = (d_dash ! upper)
                   | otherwise        = (d_dash ! i) - (c_dash ! i) * (x !
(i + 1))
       d_dash = gen_array d_dash_f
           where
               d_dash_f i
                   | i == lower     = (d ! lower) / (b ! lower)
                   | otherwise        = ((d ! i) - (d_dash ! (i - 1)) * (a
! i)) /
                                         ((b ! i) - (c_dash ! (i - 1)) *
(a ! i))
       c_dash = gen_array c_dash_f
           where
               c_dash_f i
                   | i == lower    = (c ! lower) / (b ! lower)
                   | otherwise     = (c ! i) /
                                         ((b ! i) - (c_dash ! (i - 1)) *
(a ! i))
When I attempt to load this into ghci, I recieve the following error:
[1 of 1] Compiling Main             ( main.lhs, interpreted )
main.lhs:29:11:
   Could not deduce (IArray a1 e)
     from the context (IArray a3 e,
                       IArray a6 e,
                       IArray a7 e,
                       Fractional e,
                       Ix a2,
                       Num a2,
                       IArray a4 e,
                       IArray a21 e,
                       IArray a5 e,
                       IArray a11 e,
                       Enum a2)
     arising from a use of `gen_array' at main.lhs:29:11-28
   Possible fix:
     add (IArray a1 e) to the context of
       the type signature for `tridiagonal_solve'
   In the expression: gen_array d_dash_f
   In the definition of `d_dash':
       d_dash = gen_array d_dash_f
              where
                  d_dash_f i | i == lower = (d ! lower) / (b ! lower)
                             | otherwise
                             = ((d ! i) - (d_dash ! (i - 1)) * (a ! i))
                             / ((b ! i) - (c_dash ! (i - 1)) * (a ! i))
   In the definition of `tridiagonal_solve':
       tridiagonal_solve (a, b, c, d, (lower, upper))
                           = x
                           where
                               gen_array f = (makeArray (lower, upper) f)
                               x = gen_array x_f
                                 where
                                     x_f i | i == upper = (d_dash ! upper)
                                           | otherwise
                                           = (d_dash ! i) - (c_dash ! i) *
(x ! (i + 1))
                               d_dash = gen_array d_dash_f
                                      where
                                          d_dash_f i | i == lower = (d !
lower) / (b ! lower)
                                                     | otherwise
                                                     = ((d ! i) - (d_dash
! (i - 1)) * (a ! i))
                                                     / ((b ! i) - (c_dash
! (i - 1)) * (a ! i))
                               c_dash = gen_array c_dash_f
                                      where
                                          c_dash_f i | i == lower = (c !
lower) / (b ! lower)
                                                     | otherwise
                                                     = (c ! i)
                                                     / ((b ! i) - (c_dash
! (i - 1)) * (a ! i))
main.lhs:35:11:
   Could not deduce (IArray a e)
     from the context (IArray a3 e,
                       IArray a6 e,
                       IArray a7 e,
                       Fractional e,
                       Ix a2,
                       Num a2,
                       IArray a4 e,
                       IArray a21 e,
                       IArray a5 e,
                       IArray a11 e,
                       Enum a2)
     arising from a use of `gen_array' at main.lhs:35:11-28
   Possible fix:
     add (IArray a e) to the context of
       the type signature for `tridiagonal_solve'
   In the expression: gen_array c_dash_f
   In the definition of `c_dash':
       c_dash = gen_array c_dash_f
              where
                  c_dash_f i | i == lower = (c ! lower) / (b ! lower)
                             | otherwise = (c ! i) / ((b ! i) - (c_dash !
(i - 1)) * (a ! i))
   In the definition of `tridiagonal_solve':
       tridiagonal_solve (a, b, c, d, (lower, upper))
                           = x
                           where
                               gen_array f = (makeArray (lower, upper) f)
                               x = gen_array x_f
                                 where
                                     x_f i | i == upper = (d_dash ! upper)
                                           | otherwise
                                           = (d_dash ! i) - (c_dash ! i) *
(x ! (i + 1))
                               d_dash = gen_array d_dash_f
                                      where
                                          d_dash_f i | i == lower = (d !
lower) / (b ! lower)
                                                     | otherwise
                                                     = ((d ! i) - (d_dash
! (i - 1)) * (a ! i))
                                                     / ((b ! i) - (c_dash
! (i - 1)) * (a ! i))
                               c_dash = gen_array c_dash_f
                                      where
                                          c_dash_f i | i == lower = (c !
lower) / (b ! lower)
                                                     | otherwise
                                                     = (c ! i)
                                                     / ((b ! i) - (c_dash
! (i - 1)) * (a ! i))
My question is, what should the type signature for tridiagonal_solve
actually be? I would like one that doesn't limit the generality of
tridiagonal_solve because I would like to pass different array types in the
one function invocation, as long as they have the same index and element
types. I'm happy if other functions need type signatures as well.
I'm using ghc 6.8.2 on windows, though I get a similar issue with ghc
6.4.1.
This sounds like a problem I've seen before.  GHCi would infer some
constraint like IArray a e, but when I put that into the type of the
function it would then complain that there's no instance of IArray a1
e, and when I put IArray a1 e in, it complains that there is no
instance for IArray a2 e.... and so on....

The problem was that there were terms of type "a" within the body of
the function (the same "a" from the type of the function), but it
wasn't figuring that out.  The solution was to litter my function body
with type ascriptions, and then in the type of the function introduce
all of the type variables with a "forall".  It also seems like all of
your "as" should be the same?  So... something like this might work:

  tridiagonal_solve :: forall a e . (IArray a e, Fractional e, Ix a, Num a....

Where you ascribe some of the terms in the body of your function to be
of type "a".

Hope that helps.  Sorry if I couldn't explain this problem very well.
...
...
Thanks.
Clinton
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Re: [Haskell-cafe] GHCi gives type signature that won't compile.

Philip Weaver