我对F＃很新，发现类型推断真的很酷。但目前似乎它也可能导致代码重复，这不是一件很酷的事情。我想总结这样一个数字的数字：
let rec crossfoot n =
if n = 0 then 0
else n % 10 + crossfoot (n / 10)
crossfoot 123
这正确打印6。但是现在我的输入数字不适合32位，所以我必须将其转换为。
let rec crossfoot n =
if n = 0L then 0L
else n % 10L + crossfoot (n / 10L)
crossfoot 123L
然后，BigInteger来到我的路上，猜猜是什么......
当然，我只能拥有bigint版本并输出输入参数并根据需要输出参数。但首先我假设使用BigInteger而不是int会有一些性能损失。第二个let cf = int (crossfoot (bigint 123))不好看。
是否有通用的方式来写这个？
答案 0 :(得分：25)
以Brian和Stephen的答案为基础，这里有一些完整的代码：
module NumericLiteralG =
let inline FromZero() = LanguagePrimitives.GenericZero
let inline FromOne() = LanguagePrimitives.GenericOne
let inline FromInt32 (n:int) =
let one : ^a = FromOne()
let zero : ^a = FromZero()
let n_incr = if n > 0 then 1 else -1
let g_incr = if n > 0 then one else (zero - one)
let rec loop i g =
if i = n then g
else loop (i + n_incr) (g + g_incr)
loop 0 zero
let inline crossfoot (n:^a) : ^a =
let (zero:^a) = 0G
let (ten:^a) = 10G
let rec compute (n:^a) =
if n = zero then zero
else ((n % ten):^a) + compute (n / ten)
compute n
crossfoot 123
crossfoot 123I
crossfoot 123L
这是一个独立的实现，没有NumericLiteralG模块，而且限制性稍强的推断类型：
let inline crossfoot (n:^a) : ^a =
let zero:^a = LanguagePrimitives.GenericZero
let ten:^a = (Seq.init 10 (fun _ -> LanguagePrimitives.GenericOne)) |> Seq.sum
let rec compute (n:^a) =
if n = zero then zero
else ((n % ten):^a) + compute (n / ten)
compute n
<强>解释
F＃中实际上有两种类型的泛型：1）运行类型多态，通过.NET接口/继承，以及2）编译时泛型。需要编译时泛型来容纳诸如泛型数字操作之类的东西以及诸如鸭子打字（explicit member constraints）之类的东西。这些功能是F＃的组成部分，但在.NET中不受支持，因此必须在编译时由F＃处理。
插入符号（^）用于区分statically resolved (compile-time) type parameters和普通的（使用撇号）。简而言之，'a在运行时处理，^a在编译时处理 - 这就是函数必须标记为inline的原因。
我之前从未尝试过写这样的东西。结果比我想象的更笨拙。我在F＃中编写通用数字代码的最大障碍是：创建一个非零或一个通用数字的实例。请参阅this answer中FromInt32的实施情况，了解我的意思。 GenericZero和GenericOne是内置的，它们是使用用户代码中不可用的技术实现的。在这个函数中，由于我们只需要一个小数（10），我创建了一个10 GenericOne s的序列并将它们相加。
我无法解释为什么需要所有类型注释，除了说每次编译器遇到泛型类型的操作时它似乎都认为它处理的是新类型。因此，它最终推断出一些具有重复重复的奇怪类型（例如，它可能多次需要(+)）。添加类型注释让它知道我们在整个处理相同的类型。代码在没有它们的情况下工作正常，但添加它们可以简化推断的签名。
答案 1 :(得分：16)
除了使用Numeric Literals（Brian的链接）的kvb技术之外，我使用不同的技术取得了很大成功，这种技术可以产生更好的推断结构类型签名，也可以用于创建预先计算的类型特定函数以获得更好的效果性能以及对受支持的数字类型的控制（因为您通常希望支持所有整数类型，但不支持有理类型）：F# Static Member Type Constraints。
继续讨论Daniel和我一直在讨论由不同技术产生的推断类型签名，这里有一个概述：
module NumericLiteralG =
let inline FromZero() = LanguagePrimitives.GenericZero
let inline FromOne() = LanguagePrimitives.GenericOne
let inline FromInt32 (n:int) =
let one = FromOne()
let zero = FromZero()
let n_incr = if n > 0 then 1 else -1
let g_incr = if n > 0 then one else (zero - one)
let rec loop i g =
if i = n then g
else loop (i + n_incr) (g + g_incr)
loop 0 zero
Crossfoot没有添加任何类型的注释：
let inline crossfoot1 n =
let rec compute n =
if n = 0G then 0G
else n % 10G + compute (n / 10G)
compute n
val inline crossfoot1 :
^a -> ^e
when ( ^a or ^b) : (static member ( % ) : ^a * ^b -> ^d) and
^a : (static member get_Zero : -> ^a) and
( ^a or ^f) : (static member ( / ) : ^a * ^f -> ^a) and
^a : equality and ^b : (static member get_Zero : -> ^b) and
( ^b or ^c) : (static member ( - ) : ^b * ^c -> ^c) and
( ^b or ^c) : (static member ( + ) : ^b * ^c -> ^b) and
^c : (static member get_One : -> ^c) and
( ^d or ^e) : (static member ( + ) : ^d * ^e -> ^e) and
^e : (static member get_Zero : -> ^e) and
^f : (static member get_Zero : -> ^f) and
( ^f or ^g) : (static member ( - ) : ^f * ^g -> ^g) and
( ^f or ^g) : (static member ( + ) : ^f * ^g -> ^f) and
^g : (static member get_One : -> ^g)
Crossfoot添加了一些类型的注释：
let inline crossfoot2 (n:^a) : ^a =
let (zero:^a) = 0G
let (ten:^a) = 10G
let rec compute (n:^a) =
if n = zero then zero
else ((n % ten):^a) + compute (n / ten)
compute n
val inline crossfoot2 :
^a -> ^a
when ^a : (static member get_Zero : -> ^a) and
( ^a or ^a0) : (static member ( - ) : ^a * ^a0 -> ^a0) and
( ^a or ^a0) : (static member ( + ) : ^a * ^a0 -> ^a) and
^a : equality and ^a : (static member ( + ) : ^a * ^a -> ^a) and
^a : (static member ( % ) : ^a * ^a -> ^a) and
^a : (static member ( / ) : ^a * ^a -> ^a) and
^a0 : (static member get_One : -> ^a0)
module LP =
let inline zero_of (target:'a) : 'a = LanguagePrimitives.GenericZero<'a>
let inline one_of (target:'a) : 'a = LanguagePrimitives.GenericOne<'a>
let inline two_of (target:'a) : 'a = one_of(target) + one_of(target)
let inline three_of (target:'a) : 'a = two_of(target) + one_of(target)
let inline negone_of (target:'a) : 'a = zero_of(target) - one_of(target)
let inline any_of (target:'a) (x:int) : 'a =
let one:'a = one_of target
let zero:'a = zero_of target
let xu = if x > 0 then 1 else -1
let gu:'a = if x > 0 then one else zero-one
let rec get i g =
if i = x then g
else get (i+xu) (g+gu)
get 0 zero
type G<'a> = {
negone:'a
zero:'a
one:'a
two:'a
three:'a
any: int -> 'a
}
let inline G_of (target:'a) : (G<'a>) = {
zero = zero_of target
one = one_of target
two = two_of target
three = three_of target
negone = negone_of target
any = any_of target
}
open LP
Crossfoot，没有明确推断签名所需的注释：
let inline crossfoot3 n =
let g = G_of n
let ten = g.any 10
let rec compute n =
if n = g.zero then g.zero
else n % ten + compute (n / ten)
compute n
val inline crossfoot3 :
^a -> ^a
when ^a : (static member ( % ) : ^a * ^a -> ^b) and
( ^b or ^a) : (static member ( + ) : ^b * ^a -> ^a) and
^a : (static member get_Zero : -> ^a) and
^a : (static member get_One : -> ^a) and
^a : (static member ( + ) : ^a * ^a -> ^a) and
^a : (static member ( - ) : ^a * ^a -> ^a) and ^a : equality and
^a : (static member ( / ) : ^a * ^a -> ^a)
Crossfoot，没有注释，接受预先计算的G实例：
let inline crossfootG g ten n =
let rec compute n =
if n = g.zero then g.zero
else n % ten + compute (n / ten)
compute n
val inline crossfootG :
G< ^a> -> ^b -> ^a -> ^a
when ( ^a or ^b) : (static member ( % ) : ^a * ^b -> ^c) and
( ^c or ^a) : (static member ( + ) : ^c * ^a -> ^a) and
( ^a or ^b) : (static member ( / ) : ^a * ^b -> ^a) and
^a : equality
我在实践中使用上述内容，因为那时我可以制作预先计算的类型特定版本，这些版本不会受到通用语言原理的性能成本的影响：
let gn = G_of 1 //int32
let gL = G_of 1L //int64
let gI = G_of 1I //bigint
let gD = G_of 1.0 //double
let gS = G_of 1.0f //single
let gM = G_of 1.0m //decimal
let crossfootn = crossfootG gn (gn.any 10)
let crossfootL = crossfootG gL (gL.any 10)
let crossfootI = crossfootG gI (gI.any 10)
let crossfootD = crossfootG gD (gD.any 10)
let crossfootS = crossfootG gS (gS.any 10)
let crossfootM = crossfootG gM (gM.any 10)
答案 2 :(得分：14)
由于在使用广义数字文字时如何使类型签名不那么毛茸茸的问题已经出现，我想我会把我的两分钱。主要问题是F＃的运算符可能是非对称的，因此您可以执行System.DateTime.Now + System.TimeSpan.FromHours(1.0)之类的操作，这意味着只要执行算术运算，F＃的类型推断就会添加中间类型变量。
在数值算法的情况下，这种潜在的不对称性通常不常用，并且类型签名中的结果爆炸非常难看（尽管它通常不会影响F＃在给定具体参数时正确应用函数的能力）。此问题的一个可能解决方案是在您关注的范围内限制算术运算符的类型。例如，如果您定义此模块：
module SymmetricOps =
let inline (+) (x:'a) (y:'a) : 'a = x + y
let inline (-) (x:'a) (y:'a) : 'a = x - y
let inline (*) (x:'a) (y:'a) : 'a = x * y
let inline (/) (x:'a) (y:'a) : 'a = x / y
let inline (%) (x:'a) (y:'a) : 'a = x % y
...
然后，只要您希望操作符仅应用于同一类型的两个参数，您就可以打开SymmetricOps模块。所以现在我们可以定义：
module NumericLiteralG =
open SymmetricOps
let inline FromZero() = LanguagePrimitives.GenericZero
let inline FromOne() = LanguagePrimitives.GenericOne
let inline FromInt32 (n:int) =
let one = FromOne()
let zero = FromZero()
let n_incr = if n > 0 then 1 else -1
let g_incr = if n > 0 then one else (zero - one)
let rec loop i g =
if i = n then g
else loop (i + n_incr) (g + g_incr)
loop 0 zero
和
open SymmetricOps
let inline crossfoot x =
let rec compute n =
if n = 0G then 0G
else n % 10G + compute (n / 10G)
compute x
，推断的类型是相对干净的
val inline crossfoot :
^a -> ^a
when ^a : (static member ( - ) : ^a * ^a -> ^a) and
^a : (static member get_One : -> ^a) and
^a : (static member ( % ) : ^a * ^a -> ^a) and
^a : (static member get_Zero : -> ^a) and
^a : (static member ( + ) : ^a * ^a -> ^a) and
^a : (static member ( / ) : ^a * ^a -> ^a) and ^a : equality
虽然我们仍然可以获得crossfoot一个漂亮，可读的定义的好处。
答案 3 :(得分：2)
当我在寻找解决方案并且发布我的答案时，我偶然发现了这个话题，因为我发现了一种表达通用数字的方法，而不是手动建立数字的最佳实现。
open System.Numerics
// optional
open MathNet.Numerics
module NumericLiteralG =
type GenericNumber = GenericNumber with
static member instance (GenericNumber, x:int32, _:int8) = fun () -> int8 x
static member instance (GenericNumber, x:int32, _:uint8) = fun () -> uint8 x
static member instance (GenericNumber, x:int32, _:int16) = fun () -> int16 x
static member instance (GenericNumber, x:int32, _:uint16) = fun () -> uint16 x
static member instance (GenericNumber, x:int32, _:int32) = fun () -> x
static member instance (GenericNumber, x:int32, _:uint32) = fun () -> uint32 x
static member instance (GenericNumber, x:int32, _:int64) = fun () -> int64 x
static member instance (GenericNumber, x:int32, _:uint64) = fun () -> uint64 x
static member instance (GenericNumber, x:int32, _:float32) = fun () -> float32 x
static member instance (GenericNumber, x:int32, _:float) = fun () -> float x
static member instance (GenericNumber, x:int32, _:bigint) = fun () -> bigint x
static member instance (GenericNumber, x:int32, _:decimal) = fun () -> decimal x
static member instance (GenericNumber, x:int32, _:Complex) = fun () -> Complex.op_Implicit x
static member instance (GenericNumber, x:int64, _:int64) = fun () -> int64 x
static member instance (GenericNumber, x:int64, _:uint64) = fun () -> uint64 x
static member instance (GenericNumber, x:int64, _:float32) = fun () -> float32 x
static member instance (GenericNumber, x:int64, _:float) = fun () -> float x
static member instance (GenericNumber, x:int64, _:bigint) = fun () -> bigint x
static member instance (GenericNumber, x:int64, _:decimal) = fun () -> decimal x
static member instance (GenericNumber, x:int64, _:Complex) = fun () -> Complex.op_Implicit x
static member instance (GenericNumber, x:string, _:float32) = fun () -> float32 x
static member instance (GenericNumber, x:string, _:float) = fun () -> float x
static member instance (GenericNumber, x:string, _:bigint) = fun () -> bigint.Parse x
static member instance (GenericNumber, x:string, _:decimal) = fun () -> decimal x
static member instance (GenericNumber, x:string, _:Complex) = fun () -> Complex(float x, 0.0)
// MathNet.Numerics
static member instance (GenericNumber, x:int32, _:Complex32) = fun () -> Complex32.op_Implicit x
static member instance (GenericNumber, x:int32, _:bignum) = fun () -> bignum.FromInt x
static member instance (GenericNumber, x:int64, _:Complex32) = fun () -> Complex32.op_Implicit x
static member instance (GenericNumber, x:int64, _:bignum) = fun () -> bignum.FromBigInt (bigint x)
static member instance (GenericNumber, x:string, _:Complex32) = fun () -> Complex32(float32 x, 0.0f)
static member instance (GenericNumber, x:string, _:bignum) = fun () -> bignum.FromBigInt (bigint.Parse x)
let inline genericNumber num = Inline.instance (GenericNumber, num) ()
let inline FromZero () = LanguagePrimitives.GenericZero
let inline FromOne () = LanguagePrimitives.GenericOne
let inline FromInt32 n = genericNumber n
let inline FromInt64 n = genericNumber n
let inline FromString n = genericNumber n
这种实现在演员阵容期间没有复杂的迭代。它使用FsControl作为实例模块。
答案 4 :(得分：1)
十字脚是你想要做的，还是只是将一个长数字的数字相加？
因为如果您只想对数字求和，那么：
let crossfoot (x:'a) = x.ToString().ToCharArray()
|> (Array.fold(fun acc x' -> if x' <> '.'
then acc + (int x')
else acc) 0)
......你完成了。
反正， 你能把东西转换为字符串，删除小数点，记住小数点的位置，将其解释为int，运行crossfoot吗？
这是我的解决方案。当你添加了一个小数点时，我不确定你想要“crossfoot”如何工作。
例如，您想要：crossfoot(123.1) = 7还是crossfoot(123.1) = 6.1？ （我假设你想要后者）
无论如何，代码确实允许您使用数字作为泛型。
let crossfoot (n:'a) = // Completely generic input
let rec crossfoot' (a:int) = // Standard integer crossfoot
if a = 0 then 0
else a%10 + crossfoot' (a / 10)
let nstr = n.ToString()
let nn = nstr.Split([|'.'|]) // Assuming your main constraint is float/int
let n',n_ = if nn.Length > 1 then nn.[0],nn.[1]
else nn.[0],"0"
let n'',n_' = crossfoot'(int n'),crossfoot'(int n_)
match n_' with
| 0 -> string n''
| _ -> (string n'')+"."+(string n_')
如果你需要输入大整数或int64的东西，crossfoot的工作方式，你可以将大数字拆分成bitesize块（字符串）并将它们输入到这个函数中，并将它们加在一起。