http://i.imgur.com/NGKpHbJ.png thats the image of the output ^ . the declarations are here:
let add1 x = x + 1
let multi2 x = x * 2
let wtf x = ((add1 multi2) x)
(wtf 3)
<interactive>:8:1:
No instance for (Num (a0 -> a0)) arising from a use of `it'
In a stmt of an interactive GHCi command: print it
?>
Can anyone explain to me why Haskell says that the type of the invalid expression is Num and why it wont print the number? I can't understand what is going on on the type system.
add1 multi2 applies add1 to a function, but add1 expects a number. So you might expect this to be an error because functions aren't numbers, but the thing is that they could be. In Haskell a number is a value of a type that's an instance of the Num type class and you can add instances whenever you want.
That is, you can write instance Num (a -> a) where ... and then functions will be numbers. So now mult2 + 1 will do something that produces a new function of the same type as mult2 (what exactly that will be depends on how you defined + in the instance of course), so add1 mult2 produces a function of type Num a -> a -> a and applying that function to x gives you a value of the same type as x.
So what the type wtf :: (Num (a -> a), Num a) => a -> a is telling you is "Under the condition that you a is a numeric type and you define an instance for Num (a -> a)", wtf will take a number and produce a number of the same type. And when you then actually try to use the function, you get an error because you did not define an instance for Num (a -> a).
(Re-written somewhat in response to comment)
Your line of code:
((add1 multi2) x)
means: apply the add1 function to the argument multi2, then apply the resulting function to the argument x. Since adding 1 to a function doesn't make sense, this won't work, so we get a compile-time type error.
The error is explaining that the compiler cannot find a typeclass instance to make functions work like numbers. Numbers must be part of the Num typeclass so they can be added, multiplied etc.
No instance for (Num (a0 -> a0)
In other words, the type a0-> a0 (which is a function type) doesn't have a Num typeclass instance, so adding 1 to it fails. This is a compile-time error; the code is never executed, so GHCi cannot print any output from your function.
The type of your wtf function is:
wtf :: (Num (a -> a), Num a) => a -> a
which says:
a is a numeric typea -> a (function) is a numeric typewtf will take a number and return a numberThe second condition fails at compile time because there's no defined way to treat a function as a number.
