What is this type?

Question

Haskell novice here. I know from type classes that =>means "in the context of". Yet, I can't read the following type, found in module Statistics.Sample

(Vector v (Double, Double), Vector v Double) => v (Double, Double) -> Double

What constraints are being applied on v left of => ?

Answer 1

The Data.Vector.Generic.Vector typeclass takes two type arguments, v and a where v :: * -> * is the type of the container and a :: * is the type of the elements in the container. This is simply a generic interface for the vector types defined in the vector package, notably Data.Vector.Unboxed.Vector.

This is essentially saying that the type v must be able to hold (Double, Double) and Double, although not simultaneously. If you were to use v ~ Data.Vector.Unboxed.Vector then this works just fine. The reason is due to the implementation of correlation, which uses unzip. This function splits a v (a, b) into (v a, v b). Since correlation is working on v (Double, Double), it needs the additional constraint that v can hold Doubles.

This generic type is meant to make the correlation function work with more types than Data.Vector.Vector, including any vector style types that might be implemented in other libraries.

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I want to stress that these constraints

Data.Vector.Generic.Vector v (Double, Double)
Data.Vector.Generic.Vector v Double

State that whatever type you choose for v is capable of holding (Double, Double) and is also capable of holding Double. This is specifying certain prerequisites for your vector type, not the actual contents of the vector. The actual contents of the vector is specified in the first argument to the correlation function.