是否需要具有签名类型 [英] Need and impossibility of having a type of a signature

问题描述

我定义了2个签名和4个模块，如下所示:

I have defined 2 signature and 4 modules as follows, and it works fine:

module type TRIANGLE =
  sig
    type 'a t
    val get ...
    val set ...
    ...
  end

module type MATRIX =
  sig
    type 'a t
    val unionArrayArray: 'a TriangleArray.t -> 'a TriangleArray.t -> 'a t
    val unionListList: 'a TriangleList.t -> 'a TriangleList.t -> 'a t
    val unionArrayList: 'a TriangleArray.t -> 'a TriangleList.t -> 'a t
    val unionListArray: 'a TriangleList.t -> 'a TriangleArray.t -> 'a t
    ...
  end

module rec MatrixArray: MATRIX =
  struct
    type 'a t = 'a array array
    ...
  end

and MatrixList: MATRIX =
  struct
    type 'a t = 'a list list
    ...
  end

and TriangleArray: TRIANGLE =
  struct
    type 'a t = 'a array array
    ...
  end

and TriangleList: TRIANGLE =
  struct
    type 'a t = 'a list list
    ...
  end

TRIANGLE和MATRIX是两个并行签名.函数unionXXXX取两个直角三角形，如果它们的边长相同，则建立一个矩阵.

TRIANGLE and MATRIX are two parallel signatures. The function unionXXXX takes two right triangles, if their sides have same length, builds a matrix.

模块XXXXArray在内部由array的数组实现，而模块XXXXList在内部由list的列表实现.但是它们可能具有相同的签名XXXX，其中包括诸如set，get ...

The module XXXXArray is internally realized by array of array, and the module XXXXList is internally realized by list of list. But they could have same signature XXXX which includes such functions as set, get...

此设计的问题在于，对于TRIANGLE的set，get之类的功能，4个unionXXXX函数可以具有相同的实现.我们只需要一个函数union，它的类型实际上是: 'a TRIANGLE.t -> 'a TRIANGLE.t -> 'a MATRIX.t.

The problem of this design is that, with the functions like set, get of TRIANGLE, 4 unionXXXX functions can have same implementation. We just need one function union, and its type is actually : 'a TRIANGLE.t -> 'a TRIANGLE.t -> 'a MATRIX.t.

但是，如果我按以下方式定义签名MATRIX，则编译器将在union的签名处停止并给出Error: Unbound module Triangle:

But if I define the signature MATRIX as follows, the compiler stops at the signature of union and gives an Error: Unbound module Triangle:

module type TRIANGLE =
  sig
    type 'a t
    val get ...
    val set ...
    ...
  end

module type MATRIX =
  sig
    type 'a t
    val union: 'a TRIANGLE.t -> 'a TRIANGLE.t -> 'a t
    ...
  end

我希望我已经展示了将4个unionXXXX函数合并为一个union更好，但是很遗憾我们不能指定其类型，因为缺少'a TRIANGLE.t，或者签名MATRIX或模块MatrixXXXX中.

I hope I have shown it is better to combine 4 unionXXXX functions to one union, but it is really a pity that we can't specify its type, because of the lack of 'a TRIANGLE.t, either in the signature MATRIX or in the modules MatrixXXXX.

我希望我的需求和关注已得到清晰描述，有人能找到解决方案或更好的设计吗?

I hope my need and concern has been clearly described, and does anyone have a solution or a better design?

Edit1 :根据评论的建议更改字母大小写...

Edit1 : change case of letters as the comment suggests...

推荐答案

首先，请遵循约定:通常期望模块名称具有CamelCase格式，而模块类型名称具有ALL_UPPERCASE格式.我花了两遍才知道您正在处理模块类型而不是模块.

First, a word on conventions : it's usually expected that module names have CamelCase formatting and module type names have ALL_UPPERCASE formatting. It took me two reads to notice you were dealing with module types instead of modules.

因此，您在这里要说的是，对于实现TRIANGLE的任何模块Triangle，任何实现模块类型MATRIX的模块都应该能够提供以下签名:

So, what you are trying to say here is that any module which implements module type MATRIX should be able, for any module Triangle that implements TRIANGLE, provide this signature:

type 'a t
val union : 'a Triangle.t -> 'a Triangle.t -> 'a t

不可能这样表达通用量词.您应该做的是使用一个存在量词和一个仿函数:

It's not possible to express universal quantifiers like that. What you should do is use an existential quantifier and a functor :

module type MATRIX = sig
  module Triangle : TRIANGLE 
  type 'a t 
  val union : 'a Triangle.t -> 'a Triangle.t -> 'a t
end

module MatrixOfTriangle = functor (Triangle:TRIANGLE) -> struct
  module Triangle = Triangle
  type 'a t = ...
  let union t1 t2 = ...
end

这确实迫使您指定在代码的任何给定点上正在处理的三角形，但是可以将函子与TRIANGLE参数一起使用，以避免建立在一种三角形上.

This does force you to specify what triangle you are working on at any given point in your code, but you can use functors with TRIANGLE arguments to avoid settling on one type of triangle.

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