octavian - 1 year ago 61
Scala Question

# Type mismatch for function composition

I have defined an identity function and a composition function:

``````def identity[T](x: T): T = x
def composition[A, B, C](f: A => B, g: B => C)(x: A) = g(f(x))
``````

I am trying to assert that the identity function can be applied on both sides with the same result:

``````assert(composition((x: Int) => x + 1, identity)(3) == composition(identity, (x: Int) => x + 1)(3))
``````

However, I am getting these errors:

``````Error:(7, 40) type mismatch;
found   : Nothing => Nothing
required: Int => Nothing
assert(composition((x: Int) => x + 1, identity)(3) == composition(identity, (x: Int) => x + 1)(3));}
``````

And:

``````Error:(7, 68) type mismatch;
found   : Nothing => Nothing
required: A => Nothing
assert(composition((x: Int) => x + 1, identity)(3) == composition(identity, (x: Int) => x + 1)(3));}
``````

Why is this the case?

This is the case because the compiler is having difficulty inferring the types properly, specifically inferring what `A` is. You can help him by placing `A` as the first argument and each function in a separate parameter list:

``````def composition[A, B, C](x: A)(f: A => B)(g: B => C) = g(f(x))
``````

And now this works as expected:

``````scala> :pa
// Entering paste mode (ctrl-D to finish)

def identity[T](x: T): T = x
def composition[A, B, C](x: A)(f: A => B)(g: B => C) = g(f(x))

// Exiting paste mode, now interpreting.

identity: [T](x: T)T
composition: [A, B, C](x: A)(f: A => B)(g: B => C)C

scala> println(composition(3)((x: Int) => x + 1)(identity) == composition(3)(identity)((x: Int) => x + 1))
true
``````

Alternatively, you can specify the type parameter explicitly to help the compiler infer the right type:

``````println(composition((x: Int) => x + 1, identity[Int], 3) ==
composition(identity[Int], (x: Int) => x + 1, 3))
``````
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