System.Array [] not compatible with float [] [] in F# - f#

I need to call a function that takes System.Array [] as one parameter in F#. (The function is in a library).
I need to pass an argument of type float [] [] [] but the compiler refuses to compile. To replicate the problem, I wrote the following code
let x : float [] [] = Array.init 2 (fun x -> Array.zeroCreate 3)
x :> System.Array;; // This is OK
val x : float [] [] = [|[|0.0; 0.0; 0.0|]; [|0.0; 0.0; 0.0|]|]
> x :> System.Array [];; //Error
x :> System.Array [];;
^^^^^^^^^^^^^^^^^^^^
stdin(14,1): warning FS0059: The type 'System.Array []' does not have any proper subtypes and need not be used as the target of a static coercion
x :> System.Array [];;
^^^^^^^^^^^^^^^^^^^^
stdin(14,1): error FS0193: Type constraint mismatch. The type
float [] []
is not compatible with type
System.Array []
The type 'System.Array' does not match the type 'float []'
How can I solve this problem?
Thanks in advance.

The ability to treat an 's[] as a 't[] when 's :> 't makes the .NET type system unsound (and is probably due to the fact that Java does the same thing). Unfortunately, C# follows .NET in allowing this.
Because it's a .NET runtime feature, you can also do it in F# via boxing and unboxing:
let x : float[][] = Array.init 2 (fun x -> Array.zeroCreate 3)
let x' = (box x) :?> System.Array[]
This avoids the overhead of mapping each element as in Ramon's solution.
To see why this makes the .NET type system unsound, consider this:
x'.[0] <- upcast [| "test" |] // System.ArrayTypeMismatchException
Even though we are storing a value of type System.Array into a System.Array[], we get an exception at runtime because the true type of the underlying array can't support the operation (x and x' are just two views of the same array, and obviously a string[] can't be stored into x). This unsoundness in the .NET type system therefore has the undesirable side effect of requiring additional overhead for most stores into arrays to ensure that the stored value has a type compatible with the underlying array. In my opinion, it's a good thing that F# prevents you from doing this directly.

You could do this:
let x : float [] [] = Array.init 2 (fun x -> Array.zeroCreate 3)
let toArray (xs : #System.Array []) =
Array.map (fun x -> x :> System.Array) xs
let x' : System.Array [] = toArray x

Related

How can I use Seq.sum for any .Net value types?

I'm looking to make a function that handles a seq of any numeric type of data (int, float, double), does a little computation on it via mapping, then does a summation of these calculated values. The problem I am running into is that Seq.sum (or really just '(+)' in general) causes the type parameters to be integer, or just give a flat out error. It seems there there should be a way to make this work by using type constraints but I can't seem to get it.
type ValueWithComputation<'v> = {Value: seq<'v>; Computation: 'v -> 'v}
let calculateAndCombine (x: ValueWithComputation<'v>) =
x.Value
|> Seq.map x.Computation
|> Seq.sum // sometimes gives error: "Could not resolve the ambiguity inherent in the use of operator '(+)'
let x = {Value= {1..10}; Computation= (fun x->x*2)}
let y = {Value= {(1.0)..(10.0)}; Computation= (fun x->x*x)}
let totalX = calculateAndCombine x //this causes the code force 'v to be int
let totalY = calculateAndCombine y //gives an error since this isn't an int
This seems similar to F# generics / function overloading syntax but it didn't really explain how to get it to work for all value types.
I got it to work like this. Read the answer linked by Foggy Finder. Then you need additionally the static member Zero for the sum to work.
type ValueWithComputation< ^T when ^T: (static member (+): ^T * ^T -> ^T) and ^T: (static member Zero: ^T)> =
{ Value: seq< ^T>
Computation: ^T -> ^T }
let inline calculateAndCombine x =
x.Value
|> Seq.map x.Computation
|> Seq.sum
let x = {Value= {1..10}; Computation= (fun x->x*2)}
let y = {Value= {(1.0)..(10.0)}; Computation= (fun x->x*x)}
let totalX = calculateAndCombine x
let totalY = calculateAndCombine y

Value restriction woes

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 ยง14.7 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

FsUnit `should equal` fails on `Some []`

When I run this FsUnit test with NUnit 2.6.3,
let f xs = Some (List.map ((+) 2) xs)
[<Test>]
let test() =
f []
|> should equal (Some [])
I get:
Result Message:
Expected: <Some([])>
But was: <Some([])>
Result StackTrace:
at FsUnit.TopLevelOperators.should[a,a](FSharpFunc`2 f, a x, Object y)
The test fails even though the Expected and Actual in the message are the same. What happened?
The reason is that FsUnit uses untyped mechanism under the hood so Expected is inferred as object by the type checker (see the Object y part in the stacktrace).
A workaround is to add type annotation for generic values i.e.
[<Test>]
let test() =
f []
|> should equal (Some ([]: int list))
Several people have been bitten by this e.g. Weird None behaviour in type providers.
Beauty of fluent assertions is pointless to me once they're no longer type-safe. I suggest to create a type-safe alternative:
let shouldEqual (x: 'a) (y: 'a) =
Assert.AreEqual(x, y, sprintf "Expected: %A\nActual: %A" x y)
This is because your two empty lists are of different types. See the types of actual and expected in this version of your test:
[<Test>]
let test() =
let expected = Some []
let actual = f []
actual |> should equal expected
expected is 'a list option and actual is int list option, so they are not equal.
If you give the compiler some hints about the expected result then it will work.
[<Test>]
let test() =
f []
|> should equal (Some List.empty<int>)

Storing multidimensional points in F#

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.

For loops in 2D arrays giving incorrect types in F#

I suspect that I am missing something very obvious here but this doesn't work:
let t = Array2D.create 1 1 1.0
for x in t do printfn "%f" x;;
It fails with
error FS0001: The type 'obj' is not compatible with any of the types float,float32,decimal, arising from the use of a printf-style format string
Interestingly using printf "%A" or "%O" prints the expected values which suggests to me that the problem is with the type inference
The corresponding code for a 1D array works fine
let t = Array.create 1 1.0
for x in t do printfn "%f" x;;
For reference this is on version 2.0 (both interactive and compiler) running on the latest mono
In .NET, a 1D array implicitly implements IList, which means it also implements (by inheritance) IEnumerable<T>. So, when you run:
let t = Array.create 1 1.0
for x in t do printfn "%f" x;;
the F# compiler emits code which gets an implementation of IEnumerable<T> (seq<T> in F#) from t, then iterates over it. Since it's able to get an IEnumerable<T> from the array, x will have type T.
On the other hand, multi-dimensional arrays (2d, 3d, etc.) only implement IEnumerable (not IEnumerable<T>) so the F# compiler infers the type of x as System.Object (or obj, in F#).
There are two solutions for what you want:
Cast each individual value within the loop, before printing it:
for x in t do printfn "%f" (x :?> float);;
Or, use Seq.cast to create and iterate over a strongly-typed enumerator:
for x in (Seq.cast<float> t) do printfn "%f" x;;
As Jack pointed out, this is a problem. One easy solution is:
let t = Array2D.create 2 2 1.0
t |> Array2D.iter (printfn "%f");;
And if you really like the for .. in .. do syntax:
type Array2DForLoopBuilder() =
member __.Zero() = ()
member __.For(a, f) = Array2D.iter f a
member __.Run e = e
let a2dfor = Array2DForLoopBuilder()
let t = Array2D.init 2 2 (fun a b -> float a + float b)
a2dfor { for x in t do printfn "%f" x }

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