F# 中的全局运算符重载 [英] Global operator overloading in F#

问题描述

我正在开始为笛卡尔积和矩阵乘法定义自己的运算符.

I'm starting down the road of defining my own operators for Cartesian products and matrix multiplication.

矩阵和向量别名为列表:

With matrices and vectors aliased as lists:

type Matrix = float list list
type Vector = float list

我可以通过编写自己的初始化代码(并获得笛卡尔积)

I can write my own initialisation code (and get a Cartesian product into the bargain) by writing

let inline (*) X Y =
    X |> List.collect (fun x -> Y |> List.map (fun y -> (x, y)))

let createVector size f = 
    [0..size - 1] |> List.map (fun i -> f i)

let createMatrix rows columns f =
    [0..rows - 1] * [0..columns - 1] |> List.map (fun i j -> f i j)

到目前为止一切顺利.问题是我对 * 的定义消除了正常定义，即使我的版本只为列表定义，列表没有自己的乘法运算符.

So far so good. The problem is that my definition of * wipes out the normal definition, even though my version is only defined for Lists, which don't have their own multiplication operator.

文档http://msdn.microsoft.com/en-us/library/vstudio/dd233204.aspx 声明新定义的运算符优先于内置运算符".然而，我没想到所有的数字化身都会被消灭——静态类型肯定会解决这个问题吗?

The documentation http://msdn.microsoft.com/en-us/library/vstudio/dd233204.aspx states that "newly defined operators take precedence over the built-in operators". However, I wasn't expecting all of the numerical incarnations to be wiped out -- surely static typing would take care of this?

我知道可以定义一个尊重类型的全局运算符，因为 MathNet Numerics 使用 * 进行矩阵乘法.我也想沿着这条路走下去，这需要打字系统将矩阵乘法优先于 Matrix 类型(它们本身就是列表)的笛卡尔积.

I know it is possible to define a global operator that respects types, because MathNet Numerics uses * for matrix multiplication. I would also like to go down that road, which would require the typing system to prioritise matrix multiplication over the Cartesian product of Matrix types (which are themselves lists).

有谁知道如何在 F# 中做到这一点?

Does anyone know how to do this in F#?

推荐答案

这是(非惯用的)解决方案:

Here is the (non idiomatic) solution:

type Mult = Mult with
    static member inline ($) (Mult, v1: 'a list) = fun (v2: 'b list) -> 
        v1 |> List.collect (fun x -> v2 |> List.map (fun y -> (x, y))) : list<'a * 'b>
    static member inline ($) (Mult, v1:'a      ) = fun (v2:'a) -> v1 * v2 :'a

let inline (*) v1 v2 = (Mult $ v1) v2

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