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MVC + Agents (MailboxProcessor) + Immutable Model

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open System
open System.Drawing
open System.Windows.Forms

type Agent<'a> = MailboxProcessor<'a>

module Utils =
  let doEvents () = Application.DoEvents()

module Model =
  type ('a) Model = { state: 'a; events: 'a list }
  // Add functions here to load/persist state and events

module View =
  // Main form
  let title = @"Time Traveling Debugger"
  let width,height = 1024,768
  let form = 
    new Form(
      Visible=true, TopMost=true, ClientSize=Size(width,height),
      MaximizeBox=false, FormBorderStyle=FormBorderStyle.FixedDialog,Text=title)
  let canvas = new Rectangle(0, 0, width, height)
  form.Paint.Add(fun e -> e.Graphics.FillRectangle(Brushes.Black, canvas))

  // Time Traveling Debugger
  let debug = new TrackBar()
  debug.Location <- Point(0,height - 100)
  debug.TickStyle <- TickStyle.Both
  debug.AutoSize <- false
  debug.Width <- width
  debug.Height <- 100
  debug.Minimum <- 0
  debug.Maximum <- 0
  debug.Value <- 0
  form.Controls.Add(debug)

  // Time Traveling Debugger info text
  let debugText = new Label()
  debugText.Location <- Point(0, 50)
  debugText.Width <- width
  debugText.TextAlign <- ContentAlignment.MiddleCenter
  debug.Controls.Add(debugText)

  // Update functions "hardcoded" to above formular and formular controls
  let updateTitle point = form.Text <- sprintf "%s: %A" title point
  let updateCanvas p1 p2 =
    let prev = new Rectangle(fst p1, snd p1, 30, 30)
    form.Paint.Add(fun e -> e.Graphics.FillRectangle(Brushes.Black, prev))
    let next = new Rectangle(fst p2, snd p2, 30, 30)
    form.Paint.Add(fun e -> e.Graphics.FillRectangle(Brushes.LimeGreen, next))
    form.Invalidate(next)
    form.Invalidate(prev)
  let updateDebug n = 
    debug.Maximum <- n
    debug.Value <- n
  let updateDebugText n s p = 
    debugText.Text <- sprintf "Nr. events: %i\nDebug step: %i %A" (n+1) (s+1) p

module Controller =
  open Model
  open View

  type Action = | Event of Event | Debug of Debug
  and Event = int * int
  and Debug = int

  // By using Agents, the model stays inmutable
  let agent = Agent.Start(fun inbox ->
    let rec loop model = async {
      let! msg = inbox.Receive()
      match msg with
      | Event(point) ->
        let model' = { model with state = point; events = point::model.events }
        let n = (model'.events |> List.length) - 1
        updateTitle model'.state
        updateCanvas model.state model'.state
        updateDebug n
        updateDebugText n n point
        return! loop model'
      | Debug(index) ->
        let n = (model.events |> List.length) - 1
        let point = model.events |> List.skip (n-index) |> List.head
        let model' = { model with state = point }
        updateTitle model'.state
        updateCanvas model.state model'.state
        updateDebugText n index point
        return! loop model' }
    loop { Model.state = (0,0); events = [] })

  // Hook-up model events
  form.MouseClick
  |> Event.add (fun e -> agent.Post (Action.Event(e.X,e.Y)))

  // Hook-up Time Traveling Debugger events
  debug.Scroll
  |> Event.add(fun _ -> agent.Post (Action.Debug(debug.Value)))

// Program event loop, not to use with F# Interactive (FsiAnyCpu)
open Utils
open View

let rec main = function | true -> doEvents(); main form.Created | false -> ()

main form.Created

Code output:

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References:

Code Snippet:

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#r "System.IdentityModel"
#r "System.ServiceModel"
#r "System.ServiceModel.Http"
#r "System.ServiceModel.Primitives"
#r "System.Runtime.Serialization"
#r "FSharp.Data.TypeProviders.dll"

open System
open System.IO
open System.Net
open System.Runtime.Serialization
open System.ServiceModel
open System.ServiceModel.Description
open System.ServiceModel.Dispatcher
open System.Text
open System.Web.Services.Protocols
open Microsoft.FSharp.Data.TypeProviders

type AuthorizationHeader(basicAuth) = 
  interface IClientMessageInspector with
    member x.AfterReceiveReply(reply, correlationState) = ()
    member x.BeforeSendRequest(request, channel) = 
      let prop = new Channels.HttpRequestMessageProperty()
      prop.Headers.Add(name = "Authorization", value = basicAuth)
      request.Properties.Add(Channels.HttpRequestMessageProperty.Name, prop) :> obj

type BasicAuthorization(usr : string, pwd : string) = 
  let bytes = Encoding.UTF8.GetBytes(usr + ":" + pwd)
  let auth = "Basic " + Convert.ToBase64String(bytes)
  interface IEndpointBehavior with
    member x.Validate(endpoint) = ()
    member x.AddBindingParameters(endpoint, bindingParameters) = ()
    member x.ApplyDispatchBehavior(endpoint, endpointDispatcher) = ()
    member x.ApplyClientBehavior(endpoint, clientRuntime) = 
      clientRuntime.ClientMessageInspectors.Add(new AuthorizationHeader(auth))

[<Literal>]
let baseurl = "https://DOMAIN_GOES_HERE.flexnetoperations.com/flexnet/services/"

[<Literal>]
let fnauth = baseurl + "FlexnetAuthentication?wsdl"

[<Literal>]
let userorghierarchy = baseurl + "UserOrgHierarchyService?wsdl"

type FlexnetAuthentication = WsdlService< ServiceUri=fnauth >
type UserOrgHierarchyService = WsdlService< ServiceUri=userorghierarchy >

let usr = "USERNAME_GOES_HERE"
let pwd = "PASSWORD_GOES_HERE"

/// Example 1: (require Basic Auth)
let user = new UserOrgHierarchyService.ServiceTypes.getUserPermissionsRequestType()
do user.userName <- "USERNAME_GOES_HER"
do user.domainName <- "FLEXnet"

let client1 = UserOrgHierarchyService.GetUserOrgHierarchyService()
do client1.DataContext.Endpoint.Behaviors.Add(new BasicAuthorization(usr, pwd))

let result1 = client1.getUserPermissions (user)

match result1.statusInfo.status with
| UserOrgHierarchyService.ServiceTypes.StatusType.SUCCESS -> 
  result1.responseData.permissions |> Array.iter (printfn "Permission: %s")
| _ -> printfn "%A" result1.statusInfo.status

/// Example 2: (doesn't requiere Basic Auth)
let auth = new FlexnetAuthentication.ServiceTypes.AuthenticateUserInputType()
do auth.userName <- usr
do auth.password <- pwd
do auth.domainName <- "FLEXnet"

let client2 = FlexnetAuthentication.GetFlexnetAuthentication()

let result2 = client2.authenticateUser (auth)

printfn "Access granted to %s: %b" usr result2.Success

References:

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Code Snippet:

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#nowarn "40"

open System

/// Types (alias types)
type Agent<'a> = MailboxProcessor<'a>

/// Domain agents
let print fn =
  Agent.Start(fun inbox ->
    let rec loop = async {
      let! msg = inbox.Receive()
      fn msg
      return! loop }
    loop)

let duplicate a1 a2 fn =
  Agent.Start(fun inbox ->
    let rec loop = async {
      let! msg = inbox.Receive()
      fn a1 a2 msg
      return! loop }
    loop)

let delay a fn =
  Agent.Start(fun inbox ->
    let rec loop = async {
      let! msg = inbox.Receive()
      fn a msg
      return! loop }
    loop)

let add a fn =
  Agent.Start(fun inbox ->
    let rec loop state = async {
      let! msg = inbox.Receive()
      state |> function | None -> () | Some v -> fn a (0I+v+msg);
      return! loop (Some (msg))}
    loop (None))

/// Domain functions
let out = lazy print (fun msg -> printfn "%A" msg)
let rec delta2int =
  lazy
    duplicate out (pairsInt:Lazy<Agent<bigint>>)
      (fun a1 a2 msg -> a1.Value.Post msg; a2.Value.Post msg)
and prefixInt0 = lazy delay delta2int (fun a msg -> a.Value.Post msg)
and prefixInt1 = lazy delay prefixInt0 (fun a msg -> a.Value.Post msg)
and pairsInt = lazy add prefixInt1 (fun a msg -> a.Value.Post msg)

prefixInt0.Value.Post 0I
prefixInt1.Value.Post 1I

// Main (recursive loop)
let rec main () : unit = main ()
main ()

Code output:

type Agent<'a> = MailboxProcessor<'a>
val print : fn:('a -> unit) -> MailboxProcessor<'a>
val duplicate :
  a1:'a -> a2:'b -> fn:('a -> 'b -> 'c -> unit) -> MailboxProcessor<'c>
val delay : a:'a -> fn:('a -> 'b -> unit) -> MailboxProcessor<'b>
val add :
  a:'a ->
    fn:('a -> Numerics.BigInteger -> unit) ->
      MailboxProcessor<Numerics.BigInteger>
val out : Lazy<MailboxProcessor<bigint>> = Value is not created.
val delta2int : Lazy<MailboxProcessor<bigint>> = Value is not created.
val prefixInt0 : Lazy<MailboxProcessor<bigint>> = Value is not created.
val prefixInt1 : Lazy<MailboxProcessor<bigint>> = Value is not created.
val pairsInt : Lazy<Agent<bigint>> = Value is not created.
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44945570212853
72723460248141
117669030460994
190392490709135
308061521170129
498454011879264
806515533049393
1304969544928657
...

Error output (only on Mono):

Unhandled Exception:
System.NullReferenceException: Object reference not set to an instance of an object
  at Microsoft.FSharp.Control.AsyncBuilderImpl+bindA@783[Microsoft.FSharp.Core.Unit,Microsoft.FSharp.Core.Unit].Invoke (Microsoft.FSharp.Control.AsyncParams`1 args) [0x00000] in <filename unknown>:0
  at Microsoft.FSharp.Control.AsyncBuilderImpl+callA@805[Microsoft.FSharp.Core.Unit,Microsoft.FSharp.Core.Unit].Invoke (Microsoft.FSharp.Control.AsyncParams`1 args) [0x00000] in <filename unknown>:0
  at Microsoft.FSharp.Control.AsyncBuilderImpl+tryWithA@839[Microsoft.FSharp.Core.Unit].Invoke (Microsoft.FSharp.Control.AsyncParams`1 args) [0x00000] in <filename unknown>:0
  at Microsoft.FSharp.Control.AsyncBuilderImpl+callA@805[Microsoft.FSharp.Core.Unit,Microsoft.FSharp.Core.Unit].Invoke (Microsoft.FSharp.Control.AsyncParams`1 args) [0x00000] in <filename unknown>:0
  at Microsoft.FSharp.Control.AsyncBuilderImpl+queueAsync@727[Microsoft.FSharp.Core.Unit].Invoke (Microsoft.FSharp.Core.Unit unitVar0) [0x00000] in <filename unknown>:0
  at <StartupCode$FSharp-Core>.$Control.loop@426-40 (Microsoft.FSharp.Control.Trampoline this, Microsoft.FSharp.Core.FSharpFunc`2 action) [0x00000] in <filename unknown>:0
  at Microsoft.FSharp.Control.Trampoline.ExecuteAction (Microsoft.FSharp.Core.FSharpFunc`2 firstAction) [0x00000] in <filename unknown>:0
  at Microsoft.FSharp.Control.TrampolineHolder.Protect (Microsoft.FSharp.Core.FSharpFunc`2 firstAction) [0x00000] in <filename unknown>:0
  at <StartupCode$FSharp-Core>.$Control+-ctor@512-1.Invoke (System.Object state) [0x00000] in <filename unknown>:0 
Mono JIT compiler version 4.0.0 ((detached/d136b79 Mon Apr 13 14:40:59 EDT 2015)
Copyright (C) 2002-2014 Novell, Inc, Xamarin Inc and Contributors. www.mono-project.com
        TLS:           normal
        SIGSEGV:       altstack
        Notification:  kqueue
        Architecture:  x86
        Disabled:      none
        Misc:          softdebug
        LLVM:          yes(3.6.0svn-mono-(detached/a173357)
        GC:            sgen

References:

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#load @"Utils/ListLazy.fs"

open Stermon.Research.Utils

let corruptStartPoint l =
  let rec loopStart = function
    | Cons(h1,t1),Cons(h2,t2) -> (h1 = h2) |> function
      | true -> Some h1
      | false ->
        loopStart (t1.Force(),t2.Force())
    | _,_ -> None
  let rec meetPoint = function
    | Cons(h1,t1),Cons(h2,t2) -> (h1 = h2) |> function
      | true -> loopStart (l,t2.Force())
      | false ->
        meetPoint (t1.Force(),(t2.Force() |> List.Lazy.skip 1I))
    | _,_ -> None
  meetPoint (l,(l |> List.Lazy.skip 1I))

Code output:

[Loading Utils/ListLazy.fs]

namespace FSI_0002.Stermon.Research.Utils
  type 'a ListLazy =
    | Cons of 'a * Lazy<'a ListLazy>
    | Nil
  module Lazy = begin
    val single : h:'a -> 'a ListLazy
    val cons : h:'a -> l:'a ListLazy -> 'a ListLazy
    val head : _arg1:'a ListLazy -> 'a
    val tail : _arg1:'a ListLazy -> 'a ListLazy
    val iter : f:('a -> unit) -> _arg1:'a ListLazy -> unit
    val map : f:('a -> 'b) -> _arg1:'a ListLazy -> 'b ListLazy
    val fold : f:('a -> 'b -> 'a) -> init:'a -> _arg1:'b ListLazy -> 'a
    val foldBack :
      f:('a -> Lazy<'b> -> 'b) -> init:'b -> _arg1:'a ListLazy -> 'b
    val unfold : f:('a -> ('b * 'a) option) -> init:'a -> 'b ListLazy
    val reduce : f:('a -> 'a -> 'a) -> _arg1:'a ListLazy -> 'a
    val reduceBack : f:('a -> Lazy<'a> -> 'a) -> _arg1:'a ListLazy -> 'a
    val skip :
      n:System.Numerics.BigInteger -> _arg1:'a ListLazy -> 'a ListLazy
    val take :
      n:System.Numerics.BigInteger -> _arg1:'a ListLazy -> 'a ListLazy
    val append : l1:'a ListLazy -> l2:'a ListLazy -> 'a ListLazy
    val concat : _arg1:'a ListLazy ListLazy -> 'a ListLazy
    val ofList : _arg1:'a list -> 'a ListLazy
    val toList : l:'a ListLazy -> 'a list
  end

val corruptStartPoint :
  l:'a Stermon.Research.Utils.ListLazy -> 'a option when 'a : equality

Non corrupt linked list

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let example1 = List.Lazy.unfold(fun s -> Some(s,s+1)) 0 |> List.Lazy.take 26I

example1
|> List.Lazy.iter(printf "%i ")

corruptStartPoint example1
> val example1 : int ListLazy = Cons (0,Value is not created.)
> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 val it : unit = ()
> val it : int option = None

Corrupt linked list

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let corruptGenerator n =
  List.Lazy.unfold(
    fun s -> (s < n) |> function
    | false -> Some((s % n) + n,s+1)
    | true  -> Some(s,s+1)) 0

let example2 = corruptGenerator 7

example2
|> List.Lazy.take 28I
|> List.Lazy.iter(printf "%i ")

corruptStartPoint example2
> val corruptGenerator : n:int -> int ListLazy
> val example2 : int ListLazy = Cons (0,Value is not created.)
> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 7 8 9 10 11 12 13 7 8 9 10 11 12 13 val it : unit = ()
> val it : int option = Some 7

References:

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Code Snippet:

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type 'a ListLazy = Cons of 'a * 'a ListLazy Lazy | Nil

module List =
  module Lazy =
    let single h = Cons(h, lazy (Nil))
    let cons h l = Cons(h, lazy (l))
    let head = function | Nil -> failwith "empty list" | Cons(h,_) -> h
    let tail = function | Nil -> failwith "empty list" | Cons(_,t) -> t.Force()
    let rec iter f = function
      | Nil -> () | Cons(h,t) -> f h; iter f (t.Force())
    let rec map f = function
      | Nil -> Nil | Cons(h,t) -> Cons(f h, lazy (map f (t.Force())))
    let rec fold f init = function
      | Nil -> init | Cons(h,t) -> fold f (f init h) (t.Force())
    let rec foldBack f init = function
      | Nil -> init | Cons(h,t) -> f h (lazy (foldBack f init (t.Force())))
    let rec unfold f init = f init |> function
      | None -> Nil | Some(a,s) -> Cons (a, lazy (unfold f s))
    let rec reduce f = function
      | Nil -> failwith "empty list" | Cons(h,t) -> fold f h (t.Force())
    let rec reduceBack f = function
      | Nil -> failwith "empty list" | Cons(h,t) -> foldBack f h (t.Force())
    let rec skip n = function
      | Nil -> Nil | Cons(h,t) -> (n = 0I) |> function
        | true  -> cons h (t.Force())
        | false -> skip (n-1I) (t.Force())
    let rec take n = function
      | Nil -> Nil | Cons(h,t) -> (n = 0I) |> function
        | true  -> Nil
        | false -> Cons(h, lazy (take (n-1I) (t.Force())))
    let rec append l1 l2 = l1 |> function
      | Nil -> l2 | Cons(h,t) -> Cons(h, lazy (append (t.Force()) l2))
    let rec concat = function
      | Nil -> Nil | Cons(h,t) -> append h (concat (t.Force()))
    let rec ofList = function
      | [] -> Nil | h :: t -> cons h (ofList t)
    let toList l =
      let rec toList' acc = function
        | Nil -> List.rev acc
        | Cons(h,t) -> toList' (h::acc) (t.Force())
      toList' [] l

Code output:

> 
type 'a ListLazy =
  | Cons of 'a * Lazy<'a ListLazy>
  | Nil
module List = begin
  module Lazy = begin
    val single : h:'a -> 'a ListLazy
    val cons : h:'a -> l:'a ListLazy -> 'a ListLazy
    val head : _arg1:'a ListLazy -> 'a
    val tail : _arg1:'a ListLazy -> 'a ListLazy
    val iter : f:('a -> unit) -> _arg1:'a ListLazy -> unit
    val map : f:('a -> 'b) -> _arg1:'a ListLazy -> 'b ListLazy
    val fold : f:('a -> 'b -> 'a) -> init:'a -> _arg1:'b ListLazy -> 'a
    val foldBack :
      f:('a -> Lazy<'b> -> 'b) -> init:'b -> _arg1:'a ListLazy -> 'b
    val unfold : f:('a -> ('b * 'a) option) -> init:'a -> 'b ListLazy
    val reduce : f:('a -> 'a -> 'a) -> _arg1:'a ListLazy -> 'a
    val reduceBack : f:('a -> Lazy<'a> -> 'a) -> _arg1:'a ListLazy -> 'a
    val skip :
      n:System.Numerics.BigInteger -> _arg1:'a ListLazy -> 'a ListLazy
    val take :
      n:System.Numerics.BigInteger -> _arg1:'a ListLazy -> 'a ListLazy
    val append : l1:'a ListLazy -> l2:'a ListLazy -> 'a ListLazy
    val concat : _arg1:'a ListLazy ListLazy -> 'a ListLazy
    val ofList : _arg1:'a list -> 'a ListLazy
    val toList : l:'a ListLazy -> 'a list
  end
end

Infinite Fibonacci (and squared) sequence

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let fib =
  (List.Lazy.single 0I,
   List.Lazy.unfold(fun (a1,a2) -> Some(a1+a2,(a2,a1+a2))) (1I,0I))
  ||> List.Lazy.append

let fibSquared =
  fib |> List.Lazy.foldBack(fun x l -> Cons(x*x,l)) Nil

fib
|> List.Lazy.take 10I
|> List.Lazy.iter(printf "%A ")

fibSquared
|> List.Lazy.take 10I
|> List.Lazy.iter(printf "%A ")
> 
val fib : System.Numerics.BigInteger ListLazy = Cons (0,Value is not created.)
val fibSquared : System.Numerics.BigInteger ListLazy =
  Cons (0,Value is not created.)

> 0 1 1 2 3 5 8 13 21 34 val it : unit = ()
> 0 1 1 4 9 25 64 169 441 1156 val it : unit = ()

Runtime errors when skipping/taking on empty sequences (F# Seq)

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fib
|> List.Lazy.take 10I
|> List.Lazy.toList
|> List.toSeq
|> Seq.skip 20 
|> Seq.iter(printf "%A ")
> val it : seq<System.Numerics.BigInteger> =
  Error: The input sequence has an insufficient number of elements.
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fib
|> List.Lazy.take 10I
|> List.Lazy.toList
|> List.toSeq
|> Seq.take 20
|> Seq.iter(printf "%A ")
> 0 1 1 2 3 5 8 13 21 34 System.InvalidOperationException: The input sequence has an insufficient number of elements.
  at Microsoft.FSharp.Collections.SeqModule+Take@999[System.Numerics.BigInteger].GenerateNext (IEnumerable`1& next) [0x00000] in <filename unknown>:0 
  at Microsoft.FSharp.Core.CompilerServices.GeneratedSequenceBase`1[System.Numerics.BigInteger].MoveNextImpl () [0x00000] in <filename unknown>:0 
  at Microsoft.FSharp.Core.CompilerServices.GeneratedSequenceBase`1[System.Numerics.BigInteger].System-Collections-IEnumerator-MoveNext () [0x00000] in <filename unknown>:0 
  at Microsoft.FSharp.Collections.SeqModule.Iterate[BigInteger] (Microsoft.FSharp.Core.FSharpFunc`2 action, IEnumerable`1 source) [0x00000] in <filename unknown>:0 
  at <StartupCode$FSI_0047>.$FSI_0047.main@ () [0x00000] in <filename unknown>:0 
  at (wrapper managed-to-native) System.Reflection.MonoMethod:InternalInvoke (System.Reflection.MonoMethod,object,object[],System.Exception&)
  at System.Reflection.MonoMethod.Invoke (System.Object obj, BindingFlags invokeAttr, System.Reflection.Binder binder, System.Object[] parameters, System.Globalization.CultureInfo culture) [0x00000] in <filename unknown>:0 
Stopped due to error

No runtime errors when skipping/taking on empty lists

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fib
|> List.Lazy.take 10I
|> List.Lazy.skip 20I // Behave as C# Linq.Enumerable.Skip
|> List.Lazy.iter(printf "%A ")

fib
|> List.Lazy.take 10I
|> List.Lazy.take 20I // Behave as C# Linq.Enumerable.Take (or F# Seq.truncate)
|> List.Lazy.iter(printf "%A ")
> val it : unit = ()
> 0 1 1 2 3 5 8 13 21 34 val it : unit = ()

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