F# allows ".NET" and "OCaml" formatting of signatures. This can be confusing when you fall into the habit of using one style, and then find a situation where you cannot properly format the signature you need. Consider this code, which requires a flexible type as the output of the function input to foo:
let foo n (bar: int -> #seq<'a>) =
(fun () -> Vector.ofSeq (bar n))
let foobar n = Array.ofSeq([1..n])
let x = foo 10 foobar
I could not figure out how to express #seq<'a> in OCaml format. Is it possible?
The following compiles just fine:
type A<'a>(x) =
member __.Get : 'a = x
abstract PairWith : 'b -> ('a * 'b * int)
default __.PairWith y = x, y, 1
type B<'a>(x) =
inherit A<'a>(x)
override __.PairWith y = x, y, 2
let pairAB (x : #A<'a>) y =
x, x.PairWith y
type 'a X (x) =
member __.Get : 'a = x
abstract PairWith : 'b -> ('a * 'b * int)
default __.PairWith y = x, y, 1
type 'a Y (x) =
inherit X<'a>(x)
override __.PairWith y = x, y, 2
let pairXY (x : #('a X)) y =
x, x.PairWith y
So you can guess (and then confirm with F# Interactive) that you are looking for #('a seq).
I'm not exactly sure what you mean, but I assume that you want to put the type variable in front of the type name, e.g. 'a #seq.
According to the language specification (§5.1.5) it's not possible since:
A type of the form #type is an anonymous type with a subtype constraint and is equivalent to 'a when 'a :> type, where 'a is a fresh type inference variable.
So you could write your type like: 'a when 'a :> seq<'b>.
EDIT: You could actually use #('a seq), but it looks awkward and I doubt it's what you want.
EDIT2: Didn't see Ramon Snir's answer :).
Related
RE: What is the best way to pass generic function that resolves to multiple types
Please read the referenced link before going further below
I am trying to extend the concept and pass a generic function that takes 2 parameters and does something with them.
The static approach works, however the interface based one causes a compile error (see the code lines marked with //error):
The declared type parameter '?' cannot be used here since the type parameter cannot be resolved at compile time.
Does anyone know how to fix it?
module MyModule
type T = Content of int
with
static member (+) ((Content i1), (Content i2)) = Content (i1 + i2)
static member (*) ((Content i1), (Content i2)) = Content (i1 * i2)
type W = { Content: int }
with
static member (+) ({Content = i1}, {Content = i2}) = { Content = i1 + i2 }
static member (*) ({Content = i1}, {Content = i2}) = { Content = i1 * i2 }
type Sum = Sum with static member inline ($) (Sum, (x, y)) = x + y
type Mul = Mul with static member inline ($) (Mul, (x, y)) = x * y
let inline f1 (la: 'a list) (lb: 'b list) reducer =
let a = la |> List.reduce (fun x y -> reducer $ (x, y))
let b = lb |> List.reduce (fun x y -> reducer $ (x, y))
(a, b)
type I = abstract member Reduce<'a> : 'a -> 'a -> 'a
let f2 (la: 'a list) (lb: 'b list) (reducer: I) =
let a = la |> List.reduce reducer.Reduce
let b = lb |> List.reduce reducer.Reduce
(a, b)
let main ()=
let lt = [Content 2; Content 4]
let lw = [{ Content = 2 }; { Content = 4 }]
let _ = f1 lt lw Sum
let _ = f1 lt lw Mul
let _ = f2 lt lw { new I with member __.Reduce x y = x + y} //error
let _ = f2 lt lw { new I with member __.Reduce x y = x * y} //error
0
The problem with your attempt is that you can't use operators + or * on parameters x and y, because it's not known that their type 'a has those operators defined.
To answer your further question in comments about how to achieve it anyway - if you want to use multiplication and addition on any type 'a that the caller chooses, you have to specify that. For an interface method, the only way to do this is by constraining the type parameter 'a, and the only two kinds of constraints that .NET runtime supports are "has a parameterless constructor" and "implements a given interface or inherits from a given class".
The latter one would be useful in your case: make both types implement the interface and then constrain type parameter 'a to implement that interface:
type IArithmetic<'a> =
abstract member add : 'a -> 'a
abstract member mult : 'a -> 'a
type T = Content of int
with
interface IArithmetic<T> with
member this.add (Content y) = let (Content x) = this in Content (x + y)
member this.mult (Content y) = let (Content x) = this in Content (x * y)
type W = { Content: int }
with
interface IArithmetic<W> with
member this.add y = { Content = this.Content + y.Content }
member this.mult y = { Content = this.Content * y.Content }
type I = abstract member Reduce<'a when 'a :> IArithmetic<'a>> : 'a -> 'a -> 'a
// ^^^^^^^^^^^^^^^^^^^^^^^^^^
// the constraint right here
...
let _ = f2 lt lw { new I with member __.Reduce x y = x.add y }
let _ = f2 lt lw { new I with member __.Reduce x y = x.mult y }
Is this a bit awkward? I guess so, but you're kind of doing the same thing for the SRTP version, so why not?
The core idea is: if you want your Reduce method to work not with just any type, but only with types that can do certain things, you have to specify what those things are. In the SRTP case you're doing that by defining the (+) and (*) operators. In the interface case you're doing that by implementing the interface.
Q: But can I make the interface somehow pick up the (+) and (*) operators?
A: In general, no. The .NET runtime just doesn't support the kind of constraints like "any type that has a method with certain signature". This means that such constraints can't be compiled down to IL, which means they can't be used in an interface implementation.
And this is the price you pay for using SRTPs: all those inline functions - they don't get compiled to IL, they always get expanded (inserted, substituted) at use sites. For small, simple functions, this is no big deal. But if your whole program is like that, you might see some unexpected compiled code bloat, potentially translating to slower startup time etc.
Having said all that, I must note that the code you're showing is toy POC kind of code, not intended to solve any real, practical problem. And as such, most musings on it are in danger of being completely useless.
If you have an actual problem in mind, perhaps try sharing it, and somebody would suggest the best solution for that specific case.
In particular, I have a nagging feeling that you might not actually need higher-rank functions (that's what it's called when a function doesn't lose genericity when passed as parameter).
I am trying to make a class which implements a generic .NET IComparer interface for use with the various System.Collections.Generic collections. This IComparer will map the collection's values into an ordering key using an externally provided function.
An example application might be a SortedSet<City> which sorts by population, but where the population is dynamically retrieved from an external data source which is separately maintained and updated.
open System
open System.Collections.Generic
type ExternalComparer<'T>(compareBy: ('T -> 'U) when 'U :> IComparable) =
let compareBy = compareBy
interface IComparer<'T> with
member this.Compare(a, b) =
let x = compareBy a
let y = compareBy b
if x < y then -1 else if x > y then 1 else 0
The compiler issues the following warning on the if x < y expression, specifically on the x:
Warning FS0064 This construct causes code to be less generic than
indicated by the type annotations. The type variable 'U has been
constrained to be type 'IComparable'.
In fact, I intend the type variable 'U to be constrained to be the type 'IComparable,' and I tried to express that intent with the when 'U :> IComparable constraint in the definition of the compareBy function type.
Is this warning message erroneous, or am I doing something wrong?
I think your solution - just accept a function of type 'T -> IComparable is the right thing to do, even if it means that the users of your ExternalComparer might need to insert an upcast to make the code compile.
To explain why you were getting the error, your class has only one generic type parameter 'T and the 'U parameter is missing there - so the compiler constrained it to IComparable. If you wanted to fix that, you'd have to add another generic parameter:
type ExternalComparer<'T, 'U when 'U :> IComparable>(compareBy: ('T -> 'U)) =
let compareBy = compareBy
interface IComparer<'T> with
member this.Compare(a, b) =
let x = compareBy a :> IComparable
let y = compareBy b :> IComparable
if x < y then -1 else if x > y then 1 else 0
Additionally, I also had to add :> IComparable so that we convert the results from whatever 'U is to IComparable that can be compared. This adds another generic parameter, which is quite silly.
If you wanted to avoid that, you could use a static member that converts a 'T -> 'U function to
'T -> IComparable function before passing it to the constructor:
type ExternalComparer<'T>(compareBy: ('T -> IComparable)) =
let compareBy = compareBy
interface IComparer<'T> with
member this.Compare(a, b) =
let x = compareBy a
let y = compareBy b
if x < y then -1 else if x > y then 1 else 0
static member Create(compareBy : 'T -> #IComparable) =
ExternalComparer(fun v -> compareBy v :> IComparable)
Now you can use the Create method nicely:
ExternalComparer<string>(fun v -> int v :> _) // Requires upcast
ExternalComparer<string>.Create(fun v -> int v) // Works directly!
The problem is that you're defining the compareBy type to return a 'U, constrained to IComparable, when you could more clearly have defined it to return an IComparable directly, like this:
type ExternalComparer<'T>(compareBy: ('T -> IComparable)) =
Since you know 'U will always be an IComparable, the use of a generic type is incorrect.
It seems to me you could collapse a chunk of the code into an object expression:
let bigCity = {Name="NYC"; population = 1_000_000}
let smallCity = {Name="KC"; population = 1000}
let cityComparer compFunc = { new System.Collections.Generic.IComparer<'T> with
override __.Compare(c1, c2) =
let x = compFunc c1
let y = compFunc c2
if x < y then -1 else if x > y then 1 else 0
}
let comp = cityComparer (fun x -> x.population)
comp.Compare(smallCity,bigCity)
//val it : int = -1
type Interpreter<'a> =
| RegularInterpreter of (int -> 'a)
| StringInterpreter of (string -> 'a)
let add<'a> (x: 'a) (y: 'a) (in_: Interpreter<'a>): 'a =
match in_ with
| RegularInterpreter r ->
x+y |> r
| StringInterpreter r ->
sprintf "(%s + %s)" x y |> r
The error message of it not being able to resolve 'a at compile time is pretty clear to me. I am guessing that the answer to the question of whether it is possible to make the above work is no, short of adding functions directly into the datatype. But then I might as well use an interface, or get rid of generic parameters entirely.
Edit: Mark's reply does in fact do what I asked, but let me extend the question as I did not explain it adequately. What I am trying to do is do with the technique above is imitate what what was done in this post. The motivation for this is to avoid inlined functions as they have poor composability - they can't be passed as lambdas without having their generic arguments specialized.
I was hoping that I might be able to work around it by passing an union type with a generic argument into a closure, but...
type Interpreter<'a> =
| RegularInterpreter of (int -> 'a)
| StringInterpreter of (string -> 'a)
let val_ x in_ =
match in_ with
| RegularInterpreter r -> r x
| StringInterpreter r -> r (string x)
let inline add x y in_ =
match in_ with
| RegularInterpreter r ->
x in_ + y in_ |> r
| StringInterpreter r ->
sprintf "(%A + %A)" (x in_) (y in_) |> r
let inline mult x y in_ =
match in_ with
| RegularInterpreter r ->
x in_ * y in_ |> r
| StringInterpreter r ->
sprintf "(%A * %A)" (x in_) (y in_) |> r
let inline r2 in_ = add (val_ 1) (val_ 3) in_
r2 (RegularInterpreter id)
r2 (StringInterpreter id) // Type error.
This last line gives a type error. Is there a way around this? Though I'd prefer the functions to not be inlined due to the limits they place on composability.
Remove the type annotations:
let inline add x y in_ =
match in_ with
| RegularInterpreter r ->
x + y |> r
| StringInterpreter r ->
sprintf "(%A + %A)" x y |> r
You'll also need to make a few other changes, which I've also incorporated above:
Change the format specifiers used with sprintf to something more generic. When you use %s, you're saying that the argument for that placeholder must be a string, so the compiler would infer x and y to be string values.
Add the inline keyword.
With these changes, the inferred type of add is now:
x: ^a -> y: ^b -> in_:Interpreter<'c> -> 'c
when ( ^a or ^b) : (static member ( + ) : ^a * ^b -> int)
You'll notice that it works for any type where + is defined as turning the input arguments into int. In practice, that's probably going to mean only int itself, unless you define a custom operator.
FSI smoke tests:
> add 3 2 (RegularInterpreter id);;
val it : int = 5
> add 2 3 (StringInterpreter (fun _ -> 42));;
val it : int = 42
The compiler ends up defaulting to int, and the kind of polymorphism you want is difficult to achieve in F#. This article articulates the point.
Perhaps, you could work the dark arts using FSharp.Interop.Dynamic but you lose compile time checking which sort of defeats the point.
I've come to the conclusion that what I am trying to is impossible. I had a hunch that it was already, but the proof is in the following:
let vale (x,_,_) = x
let adde (_,x,_) = x
let multe (_,_,x) = x
let val_ x d =
let f = vale d
f x
let add x y d =
let f = adde d
f (x d) (y d)
let mult x y d =
let f = multe d
f (x d) (y d)
let in_1 =
let val_ (x: int) = x
let add x y = x+y
let mult x y = x*y
val_,add,mult
let in_2 =
let val_ (x: int) = string x
let add x y = sprintf "(%s + %s)" x y
let mult x y = sprintf "(%s * %s)" x y
val_,add,mult
let r2 d = add (val_ 1) (val_ 3) d
//let test x = x in_1, x in_2 // Type error.
let a2 = r2 in_1 // Works
let b2 = r2 in_2 // Works
The reasoning goes that if it cannot be done with plain functions passed as arguments, then it definitely won't be possible with interfaces, records, discriminated unions or any other scheme. The standard functions are more generic than any of the above, and if they cannot do it then this is a fundamental limitation of the language.
It is not the lack of HKTs that make the code ungeneric, but something as simple as this. In fact, going by the Finally Tagless paper linked to in the Reddit post, Haskell has the same problem with needing to duplicate interpreters without the impredicative types extension - though I've looked around and it seem that impredicative types will be removed in the future as the extension is difficult to maintain.
Nevertheless, I do hope this is only a current limitation of F#. If the language was dynamic, the code segment above would in fact run correctly.
Unfortunately, it's not completely clear to me what you're trying to do. However, it seems likely that it's possible by creating an interface with a generic method. For example, here's how you could get the code from your answer to work:
type I = abstract Apply : ((int -> 'a) * ('a -> 'a -> 'a) * ('a -> 'a -> 'a)) -> 'a
//let test x = x in_1, x in_2 // Type error.
let test (i:I) = i.Apply in_1, i.Apply in_2
let r2' = { new I with member __.Apply d = add (val_ 1) (val_ 3) d }
test r2' // no problem
If you want to use a value (e.g. a function input) generically, then in most cases the cleanest way is to create an interface with a generic method whose signature expresses the required polymorphism.
I was experimenting with an implementation of Clojure Transducers in F#, and quickly hit the dreaded Value Restriction error.
The whole point of Transducers is to be composable. This is some sample code:
type Reducer<'a,'b,'c> = ('a -> 'b -> 'a) -> 'a -> 'c -> 'a
module Transducers =
[<GeneralizableValue>]
let inline map proj : Reducer<'result,'output,'input> =
fun xf ->
fun result input ->
xf result (proj input)
let inline conj xs x = x :: xs
let inline toList xf input = List.fold (xf conj) [] input
let xform = map (fun i -> i + 9) >> map (fun a -> a * 5)
//let xs = toList xform [1;2] // if you apply this, type will be fixed to 'a list
// which makes xform unusable with eg 'a seq
Play on dotnetfiddle
GeneralizableValue was supposed to lift the value restriction, but does nothing, it seems. Your mission is to make this code compile without applying toList (Type inference will fix the type to 'a list, so you could not use the same xform with a seq) and without changing the type of xform (at least not in a way so as to make it not composable). Is this simply not possible in F#?
Why would annotating map with [<GeneralizableValue>] affect whether xform is subject to the value restriction? (in any case, map is already generalizable since it's defined by a lambda; also I don't see the point of all the inlines).
If your requirements are:
xform must be generic, but not an explicitly annotated type function
xform is defined by the application of an operator ((>>) in this case)
then you're out of luck; xform's body is not a generalizable expression (see §14.7 in the F# spec), so the value restriction applies here.
Furthermore, I would argue that this makes sense. Imagine that the value restriction didn't apply, and that we tweaked the definition of map:
let map proj : Reducer<_,_,_> =
printfn "Map called!"
fun xf result input ->
xf result (proj input)
Now enter these definitions one-by-one:
let xform<'a> : Reducer<'a,int,int> = map (fun i -> i + 9) >> map (fun a -> a * 5)
let x1 = xform (+)
let x2 = xform (*)
let x3 = xform (fun s i -> String.replicate i s)
When do you expect "Map called!" to be printed? Does the actual behavior match your expectations? In my opinion it's good that F# forces you to go out of your way to treat non-values as generic values.
So you're not going to get exactly what you want. But perhaps there's a different encoding that would work just as well for your use cases. If every reducer will be generic in the result type, then you could do this instead:
type Reducer<'b,'c> = abstract Reduce<'a> : ('a -> 'b -> 'a) -> 'a -> 'c -> 'a
module Transducers =
let map proj =
{ new Reducer<_,_> with
member this.Reduce xf result input = xf result (proj input) }
let (>!>) (r1:Reducer<'b,'c>) (r2:Reducer<'c,'d>) =
{ new Reducer<_,_> with
member this.Reduce xf result input = (r1.Reduce >> r2.Reduce) xf result input }
let conj xs x = x :: xs
let toList (xf:Reducer<_,_>) input = List.fold (xf.Reduce conj) [] input
let xform = map (fun i -> i + 9) >!> map (fun a -> a * 5)
Unfortunately, you've got to lift each operator like (>>) to the reducer level before you can use it, but this at least works for your example, since xform is no longer a generic value, but a non-generic value with a generic method.
What about annotating xform explicitly?
[<GeneralizableValue>]
let xform<'t> : Reducer<'t, _, _> = map (fun i -> i + 9) >> map (fun a -> a * 5) >> map (fun s -> s + 1)
As suggested above, and in the error message itself, can you add arguments explicitly?
let xform x = x |> map ...
F# only plays along so well with point free approaches
I am currently porting some code from Java to F# that deals with multidimensional functions. It supports variable dimension, so in the original implementation each point is represented as an array of doubles. The critical function of the code is an optimisation routine, that basically generates a sequence of points based on some criteria, evaluates a given function at these points and looks for a maximum. This works for any dimension. The operations I need are:
check the dimension of a point
create a new point with the same dimension of a given point
set (in procedural or functional sense) a given coordinate of a point
In F# I could obviously also use arrays in the same way. I was wandering though if there is a better way. If the dimension was fixed in advance, the obvious choice would be to use tuples. Is it possible to use tuples in this dynamic setting though?
No, tuples will be fixed by dimension. Also note that .NET tuples are boxed. If you are operating on large collections of points with small dimension (such as arrays of 2d points), using structs may help.
If you really want to push the F#/.NET advantage over Java, have a look at generics. Writing code with generics allows to write code that works for any dimension, and use different representations for different dimensions (say structs for 1-3 dimensions, and vectors for larger dimensions):
let op<'T where 'T :> IVector> (x: 'T) =
...
This is only relevant though if you are willing to go a long way to get the absolutely best performance and generality. Most projects do not need that, stick with the simplest thing that works.
For the fun of it, here is an extended example of how to utilize generics and F# inlining:
open System.Numerics
type IVector<'T,'V> =
abstract member Item : int -> 'T with get
abstract member Length : int
abstract member Update : int * 'T -> 'V
let lift<'T,'V when 'V :> IVector<'T,'V>> f (v: 'V) : 'V =
if v.Length = 0 then v else
let mutable r = v.Update(0, f v.[0])
for i in 1 .. v.Length - 1 do
r <- r.Update(i, f v.[i])
r
let inline norm (v: IVector<_,_>) =
let sq i =
let x = v.[i]
x * x
Seq.sum (Seq.init v.Length sq)
let inline normalize (v: 'V) : 'V =
let n = norm v
lift (fun x -> x / n) v
[<Struct>]
type Vector2D<'T>(x: 'T, y: 'T) =
member this.X = x
member this.Y = y
interface IVector<'T,Vector2D<'T>> with
member this.Item
with get (i: int) =
match i with
| 0 -> x
| _ -> y
member this.Length = 2
member this.Update(i: int, v: 'T) =
match i with
| 0 -> Vector2D(v, y)
| _ -> Vector2D(x, v)
override this.ToString() =
System.String.Format("{0}, {1}", x, y)
[<Sealed>]
type Vector<'T>(x: 'T []) =
interface IVector<'T,Vector<'T>> with
member this.Item with get (i: int) = x.[i]
member this.Length = x.Length
member this.Update(i: int, v: 'T) =
let a = Array.copy x
a.[i] <- v
Vector(a)
override this.ToString() =
x
|> Seq.map (fun e -> e.ToString())
|> String.concat ", "
[<Struct>]
type C(c: Complex) =
member this.Complex = c
static member Zero = C(Complex(0., 0.))
static member ( + ) (a: C, b: C) = C(a.Complex + b.Complex)
static member ( * ) (a: C, b: C) = C(a.Complex * b.Complex)
static member ( / ) (a: C, b: C) = C(a.Complex / b.Complex)
override this.ToString() = string c
let v1 = Vector2D(10., 30.)
normalize v1
|> printfn "%O"
let v2 = Vector2D(C(Complex(1.25, 0.8)), C(Complex(0.5, -1.)))
normalize v2
|> printfn "%O"
let v3 = Vector([| 10.; 30.; 50.|])
normalize v3
|> printfn "%O"
Note that norm and normalize are fairly general, they cope with specialized 2D vectors and generalized N-dimensional vectors, and with different component types such as complex numbers (you can define your own). The use of generics and F# inlining ensure that while general, these algorithms perform well for the special cases, using compact representations. This is where F# and .NET generics shine compared to Java, where you are obliged to create specialized copies of your code to get decent performance.