How come that I can do:
let printTeams x : unit =
let rnd = new Random()
Seq.toList x |> List.sortBy (fun x -> rnd.Next()) |> printTeams'
but not:
let printTeams x : unit =
let rnd = new Random()
printTeamsRec' <| Seq.toList x <| List.sortBy(fun x -> rnd.Next())
I'm just getting an error on the last one, which says:
Type mismatch. Expecting a string
list -> 'a -> 'b but given a
string list -> unit The type ''a
-> 'b' does not match the type 'unit'
The error occures on the third line at printTeamsRec'
Any help would be appreciate.
Two things: the translation of the forward pipe to backwards pipe is incorrect, and precedence is different.
let printTeams x : unit =
let rnd = new Random()
printTeamsRec' <| (List.sortBy(fun x -> rnd.Next()) <| Seq.toList x)
Related
type Identity<'T> = Identity of 'T
type IdentityBuilder() =
member __.Bind (Identity x) (k : 'a -> Identity<'b>) = k x
member __.Return x = Identity x
let identity = new IdentityBuilder()
let three = Identity 3
let four = Identity 4
let twelve =
identity.Bind three <| fun t ->
identity.Bind four <| fun f ->
identity.Return (t * f)
let twelve2 = identity {
let! t = three
let! f = four
return t * f
}
twelve does not introduce any problem, but twelve2 gives
FS0001: This expression was expected to have type
'Identity<'a>' but here has type
''b * 'c'
on the line let! t = three.
I thought twelve and twelve2 should be equivalent... Was I mistaken?
As noted in the comment by Szer, you need to use tupled parameters for the Computation Builder methods. However, it is often convenient to use the curried versions for pipelining, as in your example. Therefore, what I usually do is create a module that contains all the functions required for the Computation Builder in curried form, and then use them in the builder itself. That way I can use either the computation expression syntax or the pipelining syntax depending on the scenario.
In your case, that would look something like this:
type Identity<'T> = Identity of 'T
[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]
module Identity =
let bind (f: 'T -> Identity<'U>) (Identity x) = f x
let create x = Identity x
type IdentityBuilder() =
member __.Bind (x, f) = Identity.bind f x
member __.Return x = Identity.create x
let identity = new IdentityBuilder()
let three = Identity 3
let four = Identity 4
let twelve =
three |> Identity.bind (fun t ->
four |> Identity.bind (fun f ->
Identity.create (t * f)))
let twelve2 = identity {
let! t = three
let! f = four
return t * f
}
Another common practice is to define an operator >>= for the bind function so that you can streamline the syntax even more:
let (>>=) f x = Identity.bind x f
let twelve3 = three >>= (fun t -> four >>= (fun f -> Identity.create (t * f)))
I'm trying to explore the dynamic capabilities of F# for situations where I can't express some function with the static type system. As such, I'm trying to create a mapN function for (say) Option types, but I'm having trouble creating a function with a dynamic number of arguments. I've tried:
let mapN<'output> (f : obj) args =
let rec mapN' (state:obj) (args' : (obj option) list) =
match args' with
| Some x :: xs -> mapN' ((state :?> obj -> obj) x) xs
| None _ :: _ -> None
| [] -> state :?> 'output option
mapN' f args
let toObjOption (x : #obj option) =
Option.map (fun x -> x :> obj) x
let a = Some 5
let b = Some "hi"
let c = Some true
let ans = mapN<string> (fun x y z -> sprintf "%i %s %A" x y z) [a |> toObjOption; b |> toObjOption; c |> toObjOption]
(which takes the function passed in and applies one argument at a time) which compiles, but then at runtime I get the following:
System.InvalidCastException: Unable to cast object of type 'ans#47' to type
'Microsoft.FSharp.Core.FSharpFunc`2[System.Object,System.Object]'.
I realize that it would be more idiomatic to either create a computation expression for options, or to define map2 through map5 or so, but I specifically want to explore the dynamic capabilities of F# to see whether something like this would be possible.
Is this just a concept that can't be done in F#, or is there an approach that I'm missing?
I think you would only be able to take that approach with reflection.
However, there are other ways to solve the overall problem without having to go dynamic or use the other static options you mentioned. You can get a lot of the same convenience using Option.apply, which you need to define yourself (or take from a library). This code is stolen and adapted from F# for fun and profit:
module Option =
let apply fOpt xOpt =
match fOpt,xOpt with
| Some f, Some x -> Some (f x)
| _ -> None
let resultOption =
let (<*>) = Option.apply
Some (fun x y z -> sprintf "%i %s %A" x y z)
<*> Some 5
<*> Some "hi"
<*> Some true
To explain why your approach does not work, the problem is that you cannot cast a function of type int -> int (represented as FSharpFunc<int, int>) to a value of type obj -> obj (represented as FSharpFunc<obj, obj>). The types are the same generic types, but the cast fails because the generic parameters are different.
If you insert a lot of boxing and unboxing, then your function actually works, but this is probably not something you want to write:
let ans = mapN<string> (fun (x:obj) -> box (fun (y:obj) -> box (fun (z:obj) ->
box (Some(sprintf "%i %s %A" (unbox x) (unbox y) (unbox z))))))
[a |> toObjOption; b |> toObjOption; c |> toObjOption]
If you wanted to explore more options possible thanks to dynamic hacks - then you can probably do more using F# reflection. I would not typically use this in production (simple is better - I'd just define multiple map functions by hand or something like that), but the following runs:
let rec mapN<'R> f args =
match args with
| [] -> unbox<'R> f
| x::xs ->
let m = f.GetType().GetMethods() |> Seq.find (fun m ->
m.Name = "Invoke" && m.GetParameters().Length = 1)
mapN<'R> (m.Invoke(f, [| x |])) xs
mapN<obj> (fun a b c -> sprintf "%d %s %A" a b c) [box 1; box "hi"; box true]
Suppose I have the following data:
var1,var2,var3
0.942856823,0.568425866,0.325885379
1.227681099,1.335672206,0.925331054
1.952671045,1.829479996,1.512280854
2.45428731,1.990174152,1.534456808
2.987783477,2.78975186,1.725095748
3.651682331,2.966399127,1.972274564
3.768010479,3.211381506,1.993080807
4.509429614,3.642983433,2.541071547
4.81498729,3.888415006,3.218031802
Here is the code:
open System.IO
open MathNet.Numerics.LinearAlgebra
let rows = [|for line in File.ReadAllLines("Z:\\mypath.csv")
|> Seq.skip 1 do yield line.Split(',') |> Array.map float|]
let data = DenseMatrix.ofRowArrays rows
let data_logdiff =
DenseMatrix.init (data.RowCount-1) (data.ColumnCount)
(fun j i -> if j = 0 then 0. else data.At(j, i) / data.At(j-1, i) |> log)
let alpha = vector [for i in data_logdiff.EnumerateColumns() -> i |> Statistics.Mean]
let sigsq (values:Vector<float>) (avg: float) =
let sqr x = x * x
let result = values |> (fun i -> sqr (i - avg))
result
sigsq (data_logdiff.Column(i), alpha.[0]) |> printfn "%A"
Error: The type ''a * 'b' is not compatible with the type 'Vector<float>'
This is all for a broadcast operation between a matrix and a vector. All these acrobatics to do a simple mean((y-alpha).^2) in MATLAB.
You have a mistake in your code, and the F# compiler complains about it, albeit in a somewhat obscure way. You define your function:
let sigsq (values:Vector<float>) (avg: float) =
This is a function that takes two arguments. (Actually it's a function taking one argument, returning another function taking one argument.) But you call it like this:
sigsq (data_logdiff.Column(i), alpha.[0]) |> printfn "%A"
You tuple the arguments, and for F# functions (a,b) is one argument, which is a tuple. You should call your function like this:
sigsq (data_logdiff.Column(0)) (alpha.[0])
or
sigsq <| data_logdiff.Column(0) <| alpha.[0]
and my favorite one:
data_logdiff.Column(0) |> sigsq <| alpha.[0]
I replaced the (i) with 0 in your code. You can map through the columns if you want to loop:
data_logdiff.EnumerateColumnsIndexed() |> Seq.map (fun (i,col) -> sigsq col alpha.[i])
[<ReflectedDefinition>]
module Foo =
let x = 5
let y () = 6
let z a = a
I tried to find out how to get the AST in this situation a couple of times now and keep failing. Time to ask the question here.
So far, I thought that a module would be mappped to a class with static members internally and as such, it should be the equivalent of:
[<ReflectedDefinition>]
type Foo =
static member x = 5
static member y () = 6
static member z a = a
let bar_members =
typeof<Bar>.GetMethods()
|> Array.filter (fun mi -> match mi with | MethodWithReflectedDefinition x -> true | _ -> false)
|> Array.map (fun m -> sprintf "%s: %A" (m.Name) (Expr.TryGetReflectedDefinition(m :> MethodBase) ) )
In the latter case, I could use typeof<Foo>.GetMembers() (or GetMethods()?!), cast it to Reflection.MethodBase and use this as an argument for Expr.TryGetReflectedDefinition().
But unfortunately, this is not working with the module version.
So, how to do it?
If you want to play with the code, you might want to open some namespaces:
open Microsoft.FSharp.Quotations
open Microsoft.FSharp.Quotations.DerivedPatterns
open Microsoft.FSharp.Reflection
open System.Reflection
The problem comes go down to actually getting the type of the Module. In order to do that, there's a great answer here by Phillip Trelford: https://stackoverflow.com/a/14706890/5438433
Basically, you add a helper value to your module which returns the type of that module:
[<ReflectedDefinition>]
module Foo =
type internal IMarker = interface end
let fooType = typeof<IMarker>.DeclaringType
let x = 5
let y () = 6
let z a = a
You can then use fooType to retrieve the reflected definitions.
let foo_members =
Foo.fooType.GetMethods()
|> Array.filter (fun mi -> match mi with | MethodWithReflectedDefinition x -> true | _ -> false)
|> Array.map (fun m -> sprintf "%s: %A" (m.Name) (Expr.TryGetReflectedDefinition(m :> MethodBase) ) )
I can then, e.g. print the results:
[|"get_fooType: Some PropertyGet (Some (Call (None, TypeOf, [])), DeclaringType, [])";
"get_x: Some Value (5)";
"y: Some Lambda (unitVar0, Value (6))";
"z: Some Lambda (a, a)"|]
For the use case, when the reflected definitions are in another assembly (like an F# dll, for example), you can do without the marker interface trick, as shown below:
open System
open Microsoft.FSharp.Quotations
open Microsoft.FSharp.Quotations.DerivedPatterns
open Microsoft.FSharp.Reflection
open System.Reflection
open FSharp.Reflection.FSharpReflectionExtensions
let tryGetReflectedModules (a : Assembly) : seq<TypeInfo> =
a.DefinedTypes
|> Seq.filter
(fun dt ->
dt.CustomAttributes
|> Seq.map (fun cad -> cad.AttributeType)
|> Seq.filter ((=) (typeof<ReflectedDefinitionAttribute>))
|> Seq.isEmpty
|> not
)
let astFromReflectedDefinition (mi : MethodInfo) : Expr option =
mi :> MethodBase |> Expr.TryGetReflectedDefinition
let reflectedMethodsOfAModule (m : System.Type) : (MethodInfo * Expr) [] =
m.GetMethods()
|> Array.map (fun m -> (m,astFromReflectedDefinition m))
|> Array.filter (snd >> Option.isSome)
|> Array.map (fun (x,y) -> (x, Option.get y))
let reflectAssembly (assemblyPath : string) =
let a = System.Reflection.Assembly.LoadFile(assemblyPath)
a
|> tryGetReflectedModules
|> Seq.map (fun x -> (x,reflectedMethodsOfAModule (x.AsType())))
Where, for example, the assembly I used for testing the code above looked like this:
namespace Input
[<ReflectedDefinition>]
module Api =
let trace s =
for _ in [0..3] do System.Diagnostics.Trace.WriteLine s
[<ReflectedDefinition>]
module Foo =
let foobar (x : string) : string =
x.ToUpper()
You get the top level types in the assembly, which just so happen to be the (static) classes, representing the modules of the Fsharp assembly and test for the ReflectedDefinitionAttribute presence. Then, you take it from there.
I have asked a related question here. I want to do a similar thing but this time thread an accumulator though the array of functions. I immediately thought of Array.Reduce or Array.Fold but they are not working for me:
let AddTen x =
x + 10
let MultiplyFive x =
x * 5
let SubtractTwo x =
x - 2
let functionArray = [| AddTen; MultiplyFive; SubtractTwo |]
let calculateAnswer functionArray x = functionArray |>Array.reduce(fun acc f -> f acc)
The last line throws this exception:
Type mismatch. Expecting a
'a -> 'b but given a
'b The resulting type would be infinite when unifying ''a' and ''b -> 'a'
Am I thinking about the problem incorrectly?
Take a look at these two:
let calculateReduce = functionArray |> Array.reduce (fun f g -> f >> g)
let calculateFold x = functionArray |> Array.fold (fun acc f -> f acc) x
In the reduce version, you take an array of functions and compose them into a single function which you can later call on x.
In the fold version you fold over the array of functions, threading the accumulator through and applying each function to it in sequence. x is the initial value of the accumulator here.
Your original code didn't work, because a reduce expects a 'a -> 'a -> 'a function, which in case of an array of functions would imply composition, while you were trying to apply one function of type int -> int to another.