On 9/5/07, Tomi Owens <t.owens@hautlieu.sch.je> wrote:

Hi there. I'm a teacher of Maths and am working my way through the Euler Project problems for fun. I have mostly been using Basic, but have read up about Haskell and think it looks like a sensible way to solve many of the problems.

OK, so I've downloaded GHCi and am trying to teach myself.

So far I have done this:

___         ___ _
/ _ \ /\ /\/ __(_)
/ /_\// /_/ / / | |      GHC Interactive, version 6.6.1, for Haskell 98.
/ /_\\/ __ / /___| |      http://www.haskell.org/ghc/
\____/\/ /_/\____/|_|      Type :? for help.

Loading package base ... linking ... done.
Prelude> let f (a,b) = a * floor (100000/b)
Prelude> f(2,5)
40000

Here you can find out type ghci has inferred for this function.
> :t f
f :: (RealFrac b, Integral b1) => (b1, b) -> b1

This function works just as I want it to.

Now I try creating a list:

Prelude> [(a²+b²,a)| a <- [1..4] , b<- [1..4], a²+b²<20, b<=a]
[(2,1),(5,2),(8,2),(10,3),(13,3),(18,3),(17,4)]

Let's assign this to an intermediate variable so we can query it's type:

Prelude> let lst = [(a ^ 2 + b ^ 2, a) | a <- [1..4], b <- [1..4], a^2 + b^2 < 20, b <= a]
Prelude> lst
[(2,1),(5,2),(8,2),(10,3),(13,3),(18,3),(17,4)]
Prelude> :t lst
lst :: [(Integer, Integer)]

aha; here's the source of the type mismatch:
Prelude> :t floor
floor :: (RealFrac a, Integral b) => a -> b

Floor has to take a RealFrac. According to hoogle[1], we can use various floating-point approximations (Float, Double, CFloat, etc) or we can use the exact Rational type.
[1] http://haskell.org/hoogle/?q=RealFrac

You can get your types to match by declaring your list to be of type [(Rational, Rational)] either by explicitly typing one of the untyped variables or the entire expression:
Prelude> let lst = [(a ^ 2 + b ^ 2, a) | (a::Rational) <- [1..4], b <- [1..4], a^2 + b^2 < 20, b <= a]
Prelude> :t lst
lst :: [(Rational, Rational)]
Prelude> let lst :: [(Rational, Rational)] = [(a ^ 2 + b ^ 2, a) | a <- [1..4], b <- [1..4], a^2 + b^2 < 20, b <= a]
Prelude> :t lst
lst :: [(Rational, Rational)]

and this works
So now I try to apply the function to the list:

Prelude> map (f) [(a²+b²,a)| a <- [1..4] , b<- [1..4], a²+b²<20, b<=a]

and I get this result:

<interactive>:1:5:
   Ambiguous type variable `t' in the constraints:
     `Integral t' arising from use of `f' at <interactive>:1:5
     `RealFrac t' arising from use of `f' at <interactive>:1:5
   Probable fix: add a type signature that fixes these type variable(s)

I'm sorry, but I don't quite get how to set the type signature and how it will apply to my function...

Thanks,

Hope this helps

Tomi --------------------------------------------------------------------------------
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