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?
Please explain the magic behind drawShape function. 1) Why it works at all -- I mean how it calls the Draw member, 2) why it needs to be inline?
type Triangle() =
member x.Draw() = printfn "Drawing triangle"
type Rectangle() =
member x.Draw() = printfn "Drawing rectangle"
let inline drawShape (shape : ^a) =
(^a : (member Draw : unit->unit) shape)
let triangle = Triangle()
let rect = Rectangle()
drawShape triangle
drawShape rect
And the next issue is -- is it possible to write drawShape function using parameter type annotation like below? I found that it has exactly the same signature as the first one, but I'm unable to complete the body.
let inline drawShape2 (shape : ^a when ^a : (member Draw : unit->unit)) =
...
Thanks in advance.
This Voodoo-looking syntax is called "statically resolved type parameter". The idea is to ask the compiler to check that the type passed as generic argument has certain members on it (in your example - Draw).
Since CLR does not support such checks, they have to be done at compile time, which the F# compiler is happy to do for you, but it also comes with a price: because there is no CLR support, there is no way to compile such function to IL, which means that it has to be "duplicated" every time it's used with a new generic argument (this technique is also sometimes known as "monomorphisation"), and that's what the inline keyword is for.
As for the calling syntax: for some reason, just declaring the constraint on the parameter itself doesn't cut it. You need to declare it every time you actually reference the member:
// Error: "x" is unknown
let inline f (a: ^a when ^a: (member x: unit -> string)) = a.x()
// Compiles fine
let inline f a = (^a: (member x: unit -> string)( a ))
// Have to jump through the same hoop for every call
let inline f (a: ^a) (b: ^a) =
let x = (^a: (member x: unit -> string)( a ))
let y = (^a: (member x: unit -> string)( b ))
x+y
// But can wrap it up if it becomes too messy
let inline f (a: ^a) (b: ^a) =
let callX t = (^a: (member x: unit -> string) t)
(callX a) + (callX b)
// This constraint also implicitly carries over to anybody calling your function:
> let inline g x y = (f x y) + (f y x)
val inline g : x: ^a -> y: ^a -> string when ^a : (member x : ^a -> string)
// But only if those functions are also inline:
> let g x y = (f x y) + (f y x)
Script.fsx(49,14): error FS0332: Could not resolve the ambiguity inherent in the use of the operator 'x' at or near this program point. Consider using type annotations to resolve the ambiguity.
There's a generic function LanguagePrimitives.DivideByInt to divide by int without losing generic behavior, we can use it like this:
let inline Divideby2 n = LanguagePrimitives.DivideByInt n 2
val inline Divideby2 :
^a -> ^a when ^a : (static member DivideByInt : ^a * int -> ^a)
But there's no function called MultiplyByInt to perform generic multiplication by int. Is there anything to perform generic multiplication? Like this:
let inline MultiplyBy2 n = SomeGenericFunctionsModule.MultiplybyInt n 2;
P.S. we can always use some non-standard approach like:
let inline MultiplyByInt n m = seq { for i in 1..m -> n} |> Seq.sum
but I'm interested if it is possible to do in the right way.
I'm afraid there's no built-in function, but I can propose two alternative solutions:
type MulExtension = MulExtension of int with
static member (=>) (x:float , MulExtension y) = x * (float y)
static member (=>) (x:decimal, MulExtension y) = x * (decimal y)
static member (=>) (x:int64 , MulExtension y) = x * (int64 y)
// More overloads
let inline MultiplyByInt x y = x => MulExtension y
But you'll have to specify each type.
I would rather use this function:
let inline MultiplyByInt x y =
let fromInt (n:int) : ^a when ^a : (static member (*) : ^a * ^a -> ^a) =
System.Convert.ChangeType(n, typeof<'a>) :?> 'a
x * (fromInt y)
I can't see any difference in performance between both methods.
I managed to get a solution in O(log(N)) which beats yours, but it still feels very ugly
let inline MulInt (m:^t) (n:int) =
let r : ^t ref = ref LanguagePrimitives.GenericZero
let addv : ^t ref= ref LanguagePrimitives.GenericOne
while ((int) !r) < n do
if int(!r + !addv + !addv) < n then
addv := !addv + !addv
else
r := !r + !addv
addv := LanguagePrimitives.GenericOne
!r * m
Using some of the library only features could make this a little better, but would result in warnings.
Note: This solution assumes that n is representable in ^t - i.e.
MulInt 2uy 5000
will loop forever
let inline MultiplyByInt n (x: ^a) =
let zero : ^a = LanguagePrimitives.GenericZero
let one : ^a = LanguagePrimitives.GenericOne
if n = 0 then zero
else
let mutable q, r = System.Math.DivRem(abs n, 2)
let mutable y = x
while q > 0 do
y <- y + y
q <- q / 2
let y = if r = 0 then y else y + x
if n > 0 then y
else y * (zero - one)
I've received an answer from Don Syme (via fsbugs email) when I've asked about missing MutliplyByInt and limited support of DivideByInt:
Don's answer:
This operator exists to support “Seq.averageBy” etc. This represents pseudo-precise division of the total by the count. We didn’t extend the mechanism beyond what was needed for that.
So it looks like I've misunderstood the purpose of this mechanism.
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.
I'm looking for a shorter way (if there is one) to constraint a function. E.g.
let inline sincos (a:'T) =
let y = sin a
let x = cos a
y, x
For using this function, 'T will need to support both Sin and Cos static members.
I can constraint it to work on float32 with:
let sincosf = sincos : float32 -> float32 -> float32
or using some wildcard:
let sincosf = sincos : float32 -> _
My question is, would it be possible to add a type parameter to sincos so I just have to write:
let sincosf = sincos<float32>
Thanks in advance.
Indeed, let sincosf = sincos<float32> will give you a warning, but will work as is.
As I noted in the comments, it should be possible to explicitly provide a type parameter on the definition of sincos which would remove the warning. However, this also requires all of the inferred constraints on that parameter to be specified, which can be a bit ugly. In this case, the F# compiler unexpectedly rejects the definition anyway:
let inline sincos< ^t when ^t : (static member Sin : ^t -> ^t)
and ^t : (static member Cos : ^t -> ^t)> (a: ^t) =
let y = sin a
let x = cos a
y, x
I believe that this is a compiler bug.