Multiple arity static type constraint - f#

Let's say I have a bunch of vector types (a la XNA) and some of them have static member Cross:
type Vector3 =
...
static member Cross (a : Vector3, b : Vector3) = new Vector3(...)
I can define the cross function and it compiles:
let inline cross (x : ^T) (y : ^T) = (^T : (static member Cross : (^T * ^T) -> ^T) ((x,y)))
Unfortunately I'm not able to use it and have following error:
let res = cross a b
^
The member or object constructor Cross
takes 2 argument(s) but is here given
1. The required signature is static member Vector3.Cross :
a:Vector3 * b:Vector3 ->
Vector3
Is it even possible at all? Thanks for helping!

You've over-parenthesized your static member signature. Try this instead:
let inline cross (x : ^T) (y : ^T) =
(^T : (static member Cross : ^T * ^T -> ^T) (x,y))
Given your definition, F# was looking for a member Cross which takes a single argument of tuple type.

Related

Assign a name to a set of type constraints in F#?

Suppose I have a generic type with some complex type constraints in F#:
[<Struct>]
type Vec2<'t when 't : equality
and 't : comparison
and 't : (static member get_Zero : Unit -> 't)
and 't : (static member (+) : 't * 't -> 't)
and 't : (static member (-) : 't * 't -> 't)
and 't : (static member (*) : 't * 't -> 't)
and 't : (static member (/) : 't * 't -> 't)> =
{
X : 't
Y : 't
}
Now I want to create another generic type that builds on this:
// Does not work
[<Struct>]
type AABB<'t> =
{
Min : Vec2<'t>
Max : Vec2<'t>
}
This does not work unless I replicate the type constraints:
[<Struct>]
type AABB<'t when 't : equality
and 't : comparison
and 't : (static member get_Zero : Unit -> 't)
and 't : (static member (+) : 't * 't -> 't)
and 't : (static member (-) : 't * 't -> 't)
and 't : (static member (*) : 't * 't -> 't)
and 't : (static member (/) : 't * 't -> 't)> =
{
Min : Vec2<'t>
Max : Vec2<'t>
}
This gets old fast!
Is there a way to bind the type constraints to a name so that I can reuse them throughout my code?
// Not real code
constraint IsNumeric 't =
't : equality
and 't : comparison
and 't : (static member get_Zero : Unit -> 't)
and 't : (static member (+) : 't * 't -> 't)
and 't : (static member (-) : 't * 't -> 't)
and 't : (static member (*) : 't * 't -> 't)
and 't : (static member (/) : 't * 't -> 't)
[<Struct>]
type Vec2<'t when IsNumeric 't> =
{
X : 't
Y : 't
}
[<Struct>]
type AABB<'t when IsNumeric 't> =
{
Min : Vec2<'t>
Max : Vec2<'t>
}
A reasonable workaround in this case is to create an interface that represents the constraints. This does not automatically work as named constraint, but you can define a helper function that captures the required operations and then pass the interface around (so that you can invoke the operations you want).
Let's say we want just addition and multiplication:
type INumericalOps<'T> =
abstract Add : 'T * 'T -> 'T
abstract Mul : 'T * 'T -> 'T
[<Struct>]
type Vec2<'T> =
{ X : 'T
Y : 'T }
[<Struct>]
type AABB<'T, 'O when 'O :> INumericalOps<'T>> =
{ Min : Vec2<'T>
Max : Vec2<'T>
Ops : 'O }
Now, the AABB type also contains an implementation of the INumericalOps interface, which is somewhat shorter than specifying all the constraints. We can create an inline function that captures the implementation of * and + for any type that supports those:
let inline capture () =
{ new INumericalOps<_> with
member x.Add(a, b) = a + b
member x.Mul(a, b) = a * b }
When creating a value, the type inference will make sure we get the right implementation of numerical operations:
let aabb =
{ Min = { X = 1.0; Y = 2.0 }
Max = { X = 1.0; Y = 2.0 }
Ops = capture() }
I believe this is essentially this request https://github.com/fsharp/fslang-suggestions/issues/641
Short answer, not supported in F# at this stage but I think it would be a great feature to add.
Your example looks like generic math. This thing will be supported in net6 as preview feature. This has advantages over all others approaches: native support in runtime, C# support it (more libs available), no runtime cost (performance is same as with direct call)
Even though there's no support for this in F# yet, it could look like this (not final, syntax may change)
type IAdditionOperators<'a> =
static abstract (+) : 'a * 'a -> 'a
type IAdditionIdentity<'a> =
inherit IAdditionOperators<'a>
static abstract Zero : 'a
/// This vector type supports addition of 2 generic values
[<Struct>]
type Vector2<'a when 'a : IAdditionIdentity<'a>>(x, y) =
member val X = x
member val Y = y
static member (+) (left, right) =
Vector<'a>('a.(+)(left.X, right.X), 'a.(+)(left.Y, right.Y))
/// This vector supports all methods from INumber
[<Struct>]
type RichVector2<'a when 'a : INumber<'a>>(x, y) =
member val X = x
member val Y = y
static member (+) (left, right) =
Vector<'a>('a.(+)(left.X, right.X), 'a.(+)(left.Y, right.Y))
interface INumber<'a> with
static member (+) (left, right) =
RichVector<'a>.(+)(left, right)
// Requires implementation for +, -, *, /, DivRem,
// Zero, One, Abs, Max, Min, Sign, Clamp,
// Create, CreateSaturating, CreateTruncating, TryCreate,
// Parse, TryParse

Why does this usage of inline lead to a compilation error in F#?

I am trying to learn more about inline and SRTP. Unfortunately I don't have the understanding to make this sample more minimal, but it's not too big:
type ComponentCollection<'props, 'comp when 'props : comparison> =
{
Components : Map<'props, 'comp>
}
with
static member AddComponent (collection, props, comp) =
{
Components =
collection.Components
|> Map.add props comp
}
module ComponentCollection =
let inline add< ^t, ^props, ^comp
when ^t : (static member AddComponent : ((^t * ^props * ^comp) -> ^t)) >
(props : ^props) (comp : ^comp) (xs : ^t) =
(^t : (static member AddComponent : (^t * ^props * ^comp -> ^t ) ) () ) (xs, props, comp)
type Component<'t> =
{
Props : 't
}
type Foo =
{
Foo : int
}
[<EntryPoint>]
let main argv =
let foo = { Foo = 1 }
let a : ComponentCollection<Foo, Component<Foo>> =
{ Components = Map.empty }
|> ComponentCollection.add foo { Props = foo }
0
The gives a compilation error:
error FS0001: The type 'ComponentCollection<'a,'b>' does not support the operator 'get_AddComponent'
This is very misleading to me, since I am using static member AddComponent, not get_AddComponent. I am not sure where the compiler gets get_AddComponent from.
What am I doing wrong here?
Additionally, it would be very helpful if someone could explain this bit of the code:
(^t : (static member AddComponent : (^t * ^props * ^comp -> ^t ) ) () )
I understand that it somehow provides the static member AddComponent of ^t as a free-function, but I cobbled it together from other examples, and the documentation for this syntax is lacking. For example, why is a () required?
As far as I can see, the only thing that is wrong with your snippet is that you have some excessive parentheses which, unfortunately in this case, actually have semantic meaning. Changing the code as follows resolves the problem:
module ComponentCollection =
let inline add< ^t, ^props, ^comp
when ^t : (static member AddComponent : ^t * ^props * ^comp -> ^t) >
(props : ^props) (comp : ^comp) (xs : ^t) =
(^t : (static member AddComponent : ^t * ^props * ^comp -> ^t) (xs, props, comp))
The issue is that F# actually makes a difference between:
static member AddComponent : ^t * ^props * ^comp -> ^t
static member AddComponent : (^t * ^props * ^comp) -> ^t
static member AddComponent : ((^t * ^props * ^comp) -> ^t)
The first is a regular static method with three arguments
The second is a static method taking three-element tuple as a single argument
The last is a static property returning a function value taking a tuple
Regarding your second question - in the working version, the call looks like this:
(^t : (static member AddComponent : ^t * ^props * ^comp -> ^t) (xs, props, comp))
This tells the compiler to access the static member (which is required by the constraint) and invoke it with arguments xs, props and comp. In your original version, this was invoking a getter method of the property (confusingly though, it somehow allowed you to do this without arguments - I suspect this would lead to another type error later).
From experience, SRTP's are complex and hard to use. They require a lot of inlines and Error messages tend to be very obscure.
I would recommend limiting their use.
Also, they would not be C# compatible if that is something you are interested in.
I also changed your code to fix the issues:
type ComponentCollection<'props, 'comp when 'props : comparison> =
{
Components : Map<'props, 'comp>
}
with
member collection.AddComponent(props, comp) =
{
Components =
collection.Components
|> Map.add props comp
}
module ComponentCollection =
let inline add< ^t, ^props, ^comp
when 'props : comparison and ^t : (member AddComponent : ^props * ^comp -> ^t) >
(props : ^props) (comp : ^comp) (xs : ^t) =
(^t : (member AddComponent : ^props * ^comp -> ^t ) (xs, props, comp ))
type Component<'t> =
{
Props : 't
}
type Foo =
{
Foo : int
}
[<EntryPoint>]
let main argv =
let foo = { Foo = 1 }
let a =
{ Components = Map.empty }
|> ComponentCollection.add foo { Props = foo }
0

Object Expression as Computation Builder

Given a generic interface declaration like
type IFoo<'T,'MT> =
abstract Return : 'T -> 'MT
abstract Bind : 'MT * ('T -> 'MT) -> 'MT
it's actually possible to use object expressions as computation builder expressions, which could provide for an interesting approach to the division between encapsulation and execution logic of monadic workflows.
let inline addOption mx my =
{ new IFoo<_,_> with
member __.Return x = Some x
member __.Bind(ma, f) = Option.bind f ma }
{ let! x = mx
let! y = my
return x + y }
// val inline addOption :
// mx: ^a option -> my: ^a option -> ^a option
// when ^a : (static member ( + ) : ^a * ^a -> ^a)
addOption (Some 1) (Some 2)
// val it : int option = Some 3
addOption None (Some 2)
// val it : int option = None
The compiler checks on the type of the expression if the expected methods are present. But it is only halfway there; because for real monads, I would need to get the method signature abstract Bind : 'MT * ('T -> 'MU) -> 'MU honoured, a projection to a different non-encapsulated type. Why can't this be done?

Static type variable, member constraint, compiler bug? ("Attempted to parse this as an operator name, but failed")

Compiles:
let inline f< ^T when ^T : (static member (<<<) : ^T * int -> ^T) > (x : ^T) = x <<< 1
Does not compile:
let inline f< ^T when ^T : (static member (>>>) : ^T * int -> ^T) > (x : ^T) = x >>> 1
Errors:
Attempted to parse this as an operator name, but failed
Unexpected symbol '>' in member signature. Expected ')' or other token.
A type parameter is missing a constraint 'when ^T : (static member ( >>> ) : ^T * int32 -> ^T)'
Adding spaces doesn't help; this line yields the same compiler errors:
let inline f< ^T when ^T : (static member ( >>> ) : ^T * int -> ^T) > (x : ^T) = x >>> 1
I've searched both the documentation and the specification, to no avail. Is this a bug? Is there some way to include the > characters in the member signature?
Sure looks like a bug. It's ugly, but one workaround is to use the long form of the operator name:
let inline f< ^T when ^T : (static member op_RightShift : ^T * int -> ^T)> (x : ^T) =
x >>> 1
Do you even need an explicit constraint? This works just as well:
let inline f (x: ^T) : ^T = x >>> 1

How to write a function for generic numbers?

I'm quite new to F# and find type inference really is a cool thing. But currently it seems that it also may lead to code duplication, which is not a cool thing. I want to sum the digits of a number like this:
let rec crossfoot n =
if n = 0 then 0
else n % 10 + crossfoot (n / 10)
crossfoot 123
This correctly prints 6. But now my input number does not fit int 32 bits, so I have to transform it to.
let rec crossfoot n =
if n = 0L then 0L
else n % 10L + crossfoot (n / 10L)
crossfoot 123L
Then, a BigInteger comes my way and guess what…
Of course, I could only have the bigint version and cast input parameters up and output parameters down as needed. But first I assume using BigInteger over int has some performance penalities. Second let cf = int (crossfoot (bigint 123)) does just not read nice.
Isn't there a generic way to write this?
Building on Brian's and Stephen's answers, here's some complete code:
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
UPDATE: Simple Answer
Here's a standalone implementation, without the NumericLiteralG module, and a slightly less restrictive inferred type:
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
Explanation
There are effectively two types of generics in F#: 1) run-type polymorphism, via .NET interfaces/inheritance, and 2) compile time generics. Compile-time generics are needed to accommodate things like generic numerical operations and something like duck-typing (explicit member constraints). These features are integral to F# but unsupported in .NET, so therefore have to be handled by F# at compile time.
The caret (^) is used to differentiate statically resolved (compile-time) type parameters from ordinary ones (which use an apostrophe). In short, 'a is handled at run-time, ^a at compile-time–which is why the function must be marked inline.
I had never tried to write something like this before. It turned out clumsier than I expected. The biggest hurdle I see to writing generic numeric code in F# is: creating an instance of a generic number other than zero or one. See the implementation of FromInt32 in this answer to see what I mean. GenericZero and GenericOne are built-in, and they're implemented using techniques that aren't available in user code. In this function, since we only needed a small number (10), I created a sequence of 10 GenericOnes and summed them.
I can't explain as well why all the type annotations are needed, except to say that it appears each time the compiler encounters an operation on a generic type it seems to think it's dealing with a new type. So it ends up inferring some bizarre type with duplicated resitrictions (e.g. it may require (+) multiple times). Adding the type annotations lets it know we're dealing with the same type throughout. The code works fine without them, but adding them simplifies the inferred signature.
In addition to kvb's technique using Numeric Literals (Brian's link), I've had a lot of success using a different technique which can yield better inferred structural type signatures and may also be used to create precomputed type-specific functions for better performance as well as control over supported numeric types (since you will often want to support all integral types, but not rational types, for example): F# Static Member Type Constraints.
Following up on the discussion Daniel and I have been having about the inferred type signatures yielded by the different techniques, here is an overview:
NumericLiteralG Technique
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 without adding any type annotations:
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 adding some type annotations:
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)
Record Type Technique
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, no annotations required for nice inferred signature:
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, no annotations, accepts precomputed instances of G:
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
I use the above in practice since then I can make precomputed type specific versions which don't suffer from the performance cost of Generic LanguagePrimitives:
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)
Since the question of how to make the type signatures less hairy when using the generalized numeric literals has come up, I thought I'd put in my two cents. The main issue is that F#'s operators can be asymmetric so that you can do stuff like System.DateTime.Now + System.TimeSpan.FromHours(1.0), which means that F#'s type inference adds intermediary type variables whenever arithmetic operations are being performed.
In the case of numerical algorithms, this potential asymmetry isn't typically useful and the resulting explosion in the type signatures is quite ugly (although it generally doesn't affect F#'s ability to apply the functions correctly when given concrete arguments). One potential solution to this problem is to restrict the types of the arithmetic operators within the scope that you care about. For instance, if you define this module:
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
...
then you can just open the SymmetricOps module whenever you want have the operators apply only to two arguments of the same type. So now we can define:
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
and
open SymmetricOps
let inline crossfoot x =
let rec compute n =
if n = 0G then 0G
else n % 10G + compute (n / 10G)
compute x
and the inferred type is the relatively clean
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
while we still get the benefit of a nice, readable definition for crossfoot.
I stumbled upon this topic when I was looking for a solution and I am posting my answer, because I found a way to express generic numeral without the less than optimal implementation of building up the number by hand.
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
this implementation comes by without complicated iteration during the cast. It uses FsControl for the Instance module.
http://www.fssnip.net/mv
Is crossfoot exactly what you want to do, or is it just summing the digits of a long number?
because if you just want to sum the digits, then:
let crossfoot (x:'a) = x.ToString().ToCharArray()
|> (Array.fold(fun acc x' -> if x' <> '.'
then acc + (int x')
else acc) 0)
... And you are done.
Anyways,
Can you convert stuff to a string, drop the decimal point, remember where the decimal point is, interpret it as an int, run crossfoot?
Here is my solution. I am not sure exactly how you want "crossfoot" to work when you have a decimal point added.
For instance, do you want: crossfoot(123.1) = 7 or crossfoot(123.1) = 6.1? (I'm assuming you want the latter)
Anyways, the code does allow you to work with numbers as generics.
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_')
If you need to input big integers or int64 stuff, the way crossfoot works, you can just split the big number into bitesize chunks (strings) and feed them into this function, and add them together.

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