Type of the Item property in F#

Consider the interface:

type IVector = 
    abstract Item : int -> float

Now, let us define the class:

type DenseVector(size : int) = 
    let mutable data = Array.zeroCreate size

    interface IVector with 
        member this.Item with get n = data.[n]

What about supply a method to mutate the n-th entry of the dense vector? Then, it would be nice to modify the above code as:

type DenseVector(size : int) = 
    let mutable data = Array.zeroCreate size

    interface IVector with 
        member this.Item with get n = data.[n]
                          and set n value = data.[n] <- value

However, I get the following error because of the signature of the abstract method Item in the IVector interface:

No abstract property was found that corresponds to this override.

So, what should be the signature o开发者_运维知识库f Item in IVector?

type IVector =  
    abstract Item : int -> float with get, set

You can implement DenseVector without changing the original interface while also providing a setter like this:

type IVector = 
    abstract Item: int -> float with get

type DenseVector(size : int) = 
    let data = Array.zeroCreate size
    interface IVector with 
        member this.Item with get i = data.[i]
    member this.Item 
        with get i = (this :> IVector).[i]
        and set i value = data.[i] <- value