mathnet-numerics/tools/FSharp_1.9.6.16/lib/FSharp.Core/seq.fs

//=========================================================================
// (c) Microsoft Corporation 2005-2009. 
//=========================================================================

namespace Microsoft.FSharp.Collections

    open System.Diagnostics
    open Microsoft.FSharp.Core
    open Microsoft.FSharp.Core.LanguagePrimitives.IntrinsicOperators
    open Microsoft.FSharp.Core.Operators
    open Microsoft.FSharp.Control
    open Microsoft.FSharp.Collections
    open Microsoft.FSharp.Primitives.Basics
    open System.Collections
    open System.Collections.Generic

    module IEnumerator = 


      let noReset() = raise (new System.NotSupportedException("Reset is not supported on this enumerator."))
      let notStarted() = raise (new System.InvalidOperationException("Enumeration has not started. Call MoveNext."))
      let alreadyFinished() = raise (new System.InvalidOperationException("Enumeration already finished."))
      let check started = if not started then notStarted()
      let dispose (r : System.IDisposable) = r.Dispose()

      let cast (e : IEnumerator) : IEnumerator<'T> = 
          { new IEnumerator<'T> with 
                member x.Current = unbox e.Current
            interface IEnumerator with 
                member x.Current = unbox  e.Current
                member x.MoveNext() = e.MoveNext()
                member x.Reset() = noReset();
            interface System.IDisposable with 
                member x.Dispose() = 
                    match e with 
                    | :? System.IDisposable as e -> e.Dispose()
                    | _ -> ()   }
      
      /// A concrete implementation of an enumerator that returns no values
      [<Sealed>]
      type EmptyEnumerator<'T>() = 
          let mutable started = false 
          interface IEnumerator<'T> with 
                member x.Current = 
                  check started; 
                  (alreadyFinished() : 'T)
                  
          interface System.Collections.IEnumerator with 
              member x.Current = 
                  check started; 
                  (alreadyFinished() : obj)
              member x.MoveNext() = 
                  if not started then started <- true;
                  false
              member x.Reset() = noReset()
          interface System.IDisposable with 
                member x.Dispose() = () 
        
      let Empty () = (new EmptyEnumerator<'T>() :> IEnumerator<'T>)

      let rec nth index (e : IEnumerator<'T>) = 
          if not (e.MoveNext()) then  invalidArg "index" "not enough elements in the sequence";
          if index < 0 then invalidArg "index" "negative index requested";
          if index = 0 then e.Current
          else nth (index-1) e

      type MapEnumeratorState = NotStarted | InProcess | Finished

      [<AbstractClass>]
      type MapEnumerator<'T> () =
          let mutable state = NotStarted
          [<DefaultValue(false)>]
          val mutable curr : 'T
          
          member this.GetCurrent () =
              match state with
              |   NotStarted -> notStarted()
              |   Finished -> alreadyFinished()
              |   InProcess -> ()
              this.curr
          
          abstract DoMoveNext : byref<'T> -> bool
          abstract Dispose : unit -> unit
          
          interface IEnumerator<'T> with
              member this.Current = this.GetCurrent()
          
          interface IEnumerator with
              member this.Current = box(this.GetCurrent())
              member this.MoveNext () =
                  state <- InProcess
                  if this.DoMoveNext(&this.curr) then
                      true
                  else
                      state <- Finished
                      false
              member this.Reset() = noReset()
          interface System.IDisposable with
              member this.Dispose() = this.Dispose()
       
      let map f (e : IEnumerator<_>) : IEnumerator<_>=
          upcast 
              { new MapEnumerator<_>() with
                    member this.DoMoveNext (curr : byref<_>) =
                        if e.MoveNext() then
                            curr <- (f e.Current)
                            true
                        else
                            false
                    member this.Dispose() = e.Dispose()
              }
          
      let mapi f (e : IEnumerator<_>) : IEnumerator<_> =
          let i = ref (-1) 
          upcast
              {  new MapEnumerator<_>() with
                     member this.DoMoveNext curr =
                        i := !i + 1
                        if e.MoveNext() then
                           curr <- f !i e.Current
                           true
                        else
                           false
                     member this.Dispose() = e.Dispose()
              }
              
      let map2 f (e1 : IEnumerator<_>) (e2 : IEnumerator<_>) : IEnumerator<_>=
          upcast 
              {  new MapEnumerator<_>() with
                     member this.DoMoveNext curr = 
                        let n1 = e1.MoveNext()
                        let n2 = e2.MoveNext()
                        if n1 && n2 then
                           curr <- f e1.Current e2.Current
                           true
                        else 
                           false
                     member this.Dispose() = e1.Dispose(); e2.Dispose()
              }


      let choose f (e : IEnumerator<'T>) = 
          let started = ref false 
          let curr = ref None 
          let get() =  check !started; (match !curr with None -> alreadyFinished() | Some x -> x) 
          { new IEnumerator<'b> with 
                member x.Current = get()
            interface IEnumerator with 
                member x.Current = box (get())
                member x.MoveNext() = 
                    if not !started then started := true;
                    curr := None; 
                    while ((!curr).IsNone && e.MoveNext()) do 
                        curr := f e.Current;
                    Option.isSome !curr
                member x.Reset() = noReset()
            interface System.IDisposable with 
                member x.Dispose() = e.Dispose()  }

      let filter f (e : IEnumerator<'T>) = 
          let started = ref false 
          let this = 
              { new IEnumerator<'T> with 
                    member x.Current = check !started; e.Current
                interface IEnumerator with 
                    member x.Current = check !started; box e.Current
                    member x.MoveNext() = 
                        let rec next() =
                            if not !started then started := true;
                            e.MoveNext() && (f  e.Current || next()) 
                        next()
                    member x.Reset() = noReset()
                interface System.IDisposable with 
                    member x.Dispose() = e.Dispose()  } 
          this
          
      let unfold f x : IEnumerator<_> =
          let state = ref x
          upcast 
              {  new MapEnumerator<_>() with
                    member this.DoMoveNext curr =
                        match f !state with
                        |   None -> false
                        |   Some(r,s) ->
                                curr <- r
                                state := s
                                true
                    member this.Dispose() = ()
              }

      let upto lastOption f =
          match lastOption with
          | Some b when b<0 -> Empty()    // a request for -ve length returns empty sequence
          | _ ->          
              let unstarted   = -1  // index value means unstarted (and no valid index)
              let completed   = -2  // index value means completed (and no valid index)
              let unreachable = -3  // index is unreachable from 0,1,2,3,...
              let finalIndex  = match lastOption with
                                | Some b -> b             // here b>=0, a valid end value.
                                | None   -> unreachable   // run "forever", well as far as Int32.MaxValue since indexing with a bounded type.                    
              // The Current value for a valid index is "f i".
              // Lazy<_> values are used as caches, to store either the result or an exception if thrown.
              // These "Lazy<_>" caches are created only on the first call to current and forced immediately.
              // The lazy creation of the cache nodes means enumerations that skip many Current values are not delayed by GC.
              // For example, the full enumeration of Seq.initInfinite in the tests.
              // state
              let index   = ref unstarted
              // a Lazy node to cache the result/exception
              let current = ref (Unchecked.defaultof<_>)
              let setIndex i = index := i; current := (Unchecked.defaultof<_>) // cache node unprimed, initialised on demand.
              let getCurrent() = 
                  if !index = unstarted then notStarted()
                  if !index = completed then alreadyFinished()
                  match box !current with 
                  | null -> current := Lazy.Create(fun () -> f !index); 
                  | _ ->  ()
                  // forced or re-forced immediately.          
                  (!current).Force() 
              { new IEnumerator<'b> with 
                    member x.Current = getCurrent()
                interface IEnumerator with 
                    member x.Current = box (getCurrent())
                    member x.MoveNext() = 
                        if !index = completed then
                            false
                        elif !index = unstarted then
                            setIndex 0
                            true
                        else (
                            if !index = System.Int32.MaxValue then failwith "Enumeration based on System.Int32 exceeded System.Int32.MaxValue"
                            if !index = finalIndex then
                                false
                            else
                                setIndex (!index + 1)
                                true
                        )
                    member self.Reset() = noReset()
                interface System.IDisposable with 
                    member x.Dispose() = () } 
                
      let readAndClear r = 
          lock r (fun () -> match !r with None -> None | Some x as res -> r := None; res)
      
      let generateWhileSome openf compute closef : IEnumerator<'b> = 
          let started = ref false 
          let curr = ref None
          let state = ref (Some(openf())) 
          let getCurr() = 
              check !started;
              match !curr with None -> alreadyFinished() | Some x -> x 
          let start() = if not !started then (started := true) 

          let dispose() = readAndClear state |> Option.iter closef
          let finish() = (dispose(); curr := None) 
          {  new IEnumerator<'b> with 
                 member x.Current = getCurr()
             interface IEnumerator with 
                 member x.Current = box (getCurr())
                 member x.MoveNext() = 
                     start();
                     match !state with 
                     | None -> false (* we started, then reached the end, then got another MoveNext *)
                     | Some s -> 
                         match (try compute s with e -> finish(); rethrow ()) with 
                         | None -> finish(); false
                         | Some(r) as x -> curr := x; true

                 member x.Reset() = noReset()
             interface System.IDisposable with 
                 member x.Dispose() = dispose() } 

      [<Sealed>]
      type ArrayEnumerator<'T>(arr: 'T array) = 
          let mutable curr = -1
          let mutable len = arr.Length
          member x.Get() =
               if curr >= 0 then 
                 if curr >= len then alreadyFinished()
                 else arr.[curr]
               else 
                 notStarted()
          interface IEnumerator<'T> with 
                member x.Current = x.Get()
          interface System.Collections.IEnumerator with 
                member x.MoveNext() = 
                       if curr >= len then false
                       else 
                         curr <- curr + 1;
                         (curr < len)
                member x.Current = box(x.Get())
                member x.Reset() = noReset()
          interface System.IDisposable with 
                member x.Dispose() = () 

      let of_array arr = (new ArrayEnumerator<'T>(arr) :> IEnumerator<'T>)

      [<Sealed>]    
      type Singleton<'T>(v:'T) = 
          let mutable started = false
          interface IEnumerator<'T> with
                member x.Current = v
          interface IEnumerator with
              member x.Current = box v
              member x.MoveNext() = if started then false else (started <- true; true)
              member x.Reset() = noReset()
          interface System.IDisposable with
              member x.Dispose() = () 

      let Singleton x = (new Singleton<'T>(x) :> IEnumerator<'T>)

      let EnumerateThenFinally f (e : IEnumerator<'T>) = 
          { new IEnumerator<'T> with
                member x.Current = e.Current
            interface IEnumerator with
                member x.Current = (e :> IEnumerator).Current
                member x.MoveNext() = e.MoveNext()
                member x.Reset() = noReset()
            interface System.IDisposable with
                member x.Dispose() = f(); e.Dispose()  }

    // Use generators for some implementations of IEnumerables.
    //
    module Generator = 

        open System.Collections
        open System.Collections.Generic
        
        type Step<'T> = 
            | Stop
            | Yield of 'T
            | Goto of Generator<'T>

        and Generator<'T> = 
            abstract Apply: (unit -> Step<'T>)
            abstract Disposer: (unit -> unit) option

        let disposeG (g:Generator<'T>) = 
            match g.Disposer with 
            | None -> () 
            | Some f -> f()
        
        let chainDisposeG d1 (g:Generator<'T>) =
            let app = g.Apply
            let disp = match g.Disposer with Some f2 -> Some(fun () -> f2(); d1()) | None -> Some d1
            { new Generator<_> with 
                  member x.Apply = app 
                  member x.Disposer = disp }

        let appG (g:Generator<_>) =
            //System.Console.WriteLine("{0}.appG", box g)
            let res = g.Apply()
            match res with 
            | Goto(next) -> 
                Goto(next)
            | Yield _ ->  
                res
            | Stop -> 
                //System.Console.WriteLine("appG: Stop")
                disposeG g; 
                res
        
        // Binding. 
        //
        // We use a type defintion to apply a local dynamic optimization. 
        // We automatically right-associate binding, i.e. push the continuations to the right.
        // That is, bindG (bindG G1 cont1) cont2 --> bindG G1 (cont1 o cont2)
        // This makes constructs such as the following linear rather than quadratic:
        //
        //  let rec rwalk n = { if n > 0 then 
        //                         yield! rwalk (n-1)
        //                         yield n }

        type GenerateThen<'T>(g:Generator<'T>, cont : unit -> Generator<'T>) =
            member self.Generator = g
            member self.Cont = cont
            interface Generator<'T> with 
                 member x.Apply = (fun () -> 
                      match appG g with 
                      | Stop -> 
                          // OK, move onto the generator given by the continuation
                          Goto(cont())

                      | Yield v as res -> 
                          res
                      
                      | Goto next -> 
                          Goto(GenerateThen<_>.Bind(next,cont)))
                 member x.Disposer = 
                      g.Disposer


            static member Bind (g:Generator<'T>, cont) = 
                match g with
                | :? GenerateThen<'T> as g -> GenerateThen<_>.Bind(g.Generator,(fun () -> GenerateThen<_>.Bind (g.Cont(), cont)))
                | g -> (new GenerateThen<'T>(g, cont) :> Generator<'T>)


        let bindG g cont = GenerateThen<_>.Bind(g,cont)

        //let emptyG () = 
        //    { new Generator<_> with 
        //           member x.Apply = (fun () -> Stop)
        //           member x.Disposer = None }
        //
        //let delayG f  = 
        //    { new Generator<_> with 
        //           member x.Apply = fun () -> Goto(f())
        //           member x.Disposer = None }
        //
        //let useG (v: System.IDisposable) f = 
        //    { new Generator<_> with 
        //           member x.Apply = (fun () -> 
        //               let g = f v in 
        //               // We're leaving this generator but want to maintain the disposal on the target.
        //               // Hence chain it into the disposer of the target
        //               Goto(chainDisposeG v.Dispose g))
        //           member x.Disposer = Some (fun () -> v.Dispose()) }
        //
        //let yieldG (v:'T) = 
        //    let yielded = ref false
        //    { new Generator<_> with 
        //           member x.Apply = fun () -> if !yielded then Stop else (yielded := true; Yield(v))
        //           member x.Disposer = None }
        //
        //let rec whileG gd b = if gd() then bindG (b()) (fun () -> whileG gd b) else emptyG()
        //
        //let yieldThenG x b = bindG (yieldG x) b
        //
        //let forG (v: seq<'T>) f = 
        //    let e = v.GetEnumerator() in 
        //    whileG e.MoveNext (fun () -> f e.Current)

        // Internal type. Drive an underlying generator. Crucially when the generator returns
        // a new generator we simply update our current generator and continue. Thus the enumerator
        // effectively acts as a reference cell holding the current generator. This means that
        // infinite or large generation chains (e.g. caused by long sequences of append's, including 
        // possible delay loops) can be referenced via a single enumerator.
        //
        // A classic case where this arises in this sort of sequence expression:
        //    let rec data s = { yield s; 
        //                       yield! data (s + random()) }
        //
        // This translates to 
        //    let rec data s = Seq.delay (fun () -> Seq.append (Seq.singleton s) (Seq.delay (fun () -> data (s+random()))))
        //
        // When you unwind through all the Seq, IEnumerator and Generator objects created, 
        // you get (data s).GetEnumerator being an "GenerateFromEnumerator(EnumeratorWrappingLazyGenerator(...))" for the append.
        // After one element is yielded, we move on to the generator for the inner delay, which in turn
        // comes back to be a "GenerateFromEnumerator(EnumeratorWrappingLazyGenerator(...))".
        //
        // Defined as a type so we can optimize Enumerator/Generator chains in enumerateFromLazyGenerator
        // and GenerateFromEnumerator.


        [<Sealed>]
        type EnumeratorWrappingLazyGenerator<'T>(g:Generator<'T>) =
            let mutable g = g
            let mutable curr = None
            let mutable finished = false
            member e.Generator = g
            interface IEnumerator<'T> with
                member x.Current= match curr with Some(v) -> v | None -> failwith "MoveNext not called, or finished"
            interface System.Collections.IEnumerator with
                member x.Current = box (x :> IEnumerator<_>).Current
                member x.MoveNext() = 
                    not finished && 
                    (match appG g with 
                     | Stop -> 
                        curr <- None; 
                        finished <- true; 
                        false
                     | Yield(v) ->
                        curr <- Some(v); 
                        true
                     | Goto(next) ->
                        (g <- next);
                        (x :> IEnumerator).MoveNext())
                member x.Reset() = IEnumerator.noReset()
            interface System.IDisposable with
                member x.Dispose() =
                    if not finished then disposeG g

        // Internal type, used to optimize Enumerator/Generator chains
        type LazyGeneratorWrappingEnumerator<'T>(e:System.Collections.Generic.IEnumerator<'T>) =
            member g.Enumerator = e
            interface Generator<'T> with
                member g.Apply = (fun () -> 
                    if e.MoveNext() then 
                        Yield(e.Current) 
                    else 
                        Stop)
                member g.Disposer= Some(e.Dispose)

        let EnumerateFromGenerator(g:Generator<'T>) = 
            match g with 
            | :? LazyGeneratorWrappingEnumerator<'T> as g -> g.Enumerator
            | _ -> (new EnumeratorWrappingLazyGenerator<_>(g) :> System.Collections.Generic.IEnumerator<_>)

        let GenerateFromEnumerator (e:System.Collections.Generic.IEnumerator<'T>) =
            match e with 
            | :? EnumeratorWrappingLazyGenerator<'T> as e ->  e.Generator
            | _ -> (new LazyGeneratorWrappingEnumerator<'T>(e) :> Generator<'T>)
      

    module SequenceExpressionHelpers =
        
        let mkSeq f = 
            { new IEnumerable<'b> with 
                member x.GetEnumerator() = f()
              interface IEnumerable with 
                member x.GetEnumerator() = (f() :> IEnumerator) }

        type EmptyEnumerable<'T> = 
            | EmptyEnumerable
            interface IEnumerable<'T> with 
                member x.GetEnumerator() = IEnumerator.Empty<'T>()
            interface IEnumerable with 
                member x.GetEnumerator() = (IEnumerator.Empty<'T>() :> IEnumerator) 

        let Generate openf compute closef = 
            mkSeq (fun () -> IEnumerator.generateWhileSome openf compute closef) 
        
        let GenerateUsing (openf : unit -> ('b :> System.IDisposable)) compute = 
            Generate openf compute (fun (s:'b) -> s.Dispose())

        let EnumerateFromFunctions opener moveNext current = 
            Generate 
                opener 
                (fun x -> if moveNext x then Some(current x) else None) 
                (fun x -> match box(x) with :? System.IDisposable as id -> id.Dispose() | _ -> ())

        // A family of enumerators that can have additional 'finally' actions added to the enumerator through
        // the use of mutation. This is used to 'push' the disposal action for a 'use' into the next enumerator.
        // For example,
        //    seq { use x = ...
        //          while ... }
        // results in the 'while' loop giving an adjustable enumerator. This is then adjusted by adding the disposal action
        // from the 'use' into the enumerator. This means that we avoid constructing a two-deep enumerator chain in this
        // common case.
        type IFinallyEnumerator = 
            abstract AppendFinallyAction : (unit -> unit) -> unit

        /// A concrete implementation of IEnumerable that adds the given compensation to the "Dispose" chain of any
        /// enumerators returned by the enumerable.
        [<Sealed>]
        type FinallyEnumerable<'T>(compensation: unit -> unit, restf: unit -> seq<'T>) = 
            interface IEnumerable<'T> with 
                member x.GetEnumerator() = 
                    try 
                        let ie = restf().GetEnumerator()
                        match ie with 
                        | :? IFinallyEnumerator as a -> 
                            a.AppendFinallyAction(compensation); 
                            ie
                        | _ -> 
                            IEnumerator.EnumerateThenFinally compensation ie 
                    with e -> 
                        compensation(); 
                        rethrow() 
            interface IEnumerable with 
                member x.GetEnumerator() = ((x :> IEnumerable<'T>).GetEnumerator() :> IEnumerator) 
              
        /// An optimized object for concatenating a sequence of enumerables
        [<Sealed>]
        type ConcatEnumerator<'T,'b when 'b :> seq<'T>>(ies: seq<'b>) = 
            let mutable outerEnum = ies.GetEnumerator()
            let mutable currInnerEnum = IEnumerator.Empty()

            let mutable started = false 
            let mutable finished = false 
            let mutable compensations = []
            
            [<DefaultValue(false)>] // false = unchecked
            val mutable currElement : 'T

            member x.Finish() = 
                finished <- true
                match currInnerEnum with 
                | null -> ()
                | _ -> 
                    currInnerEnum.Dispose()
                    currInnerEnum <- null
                match outerEnum with 
                | null -> ()
                | _ -> 
                    outerEnum.Dispose()
                    outerEnum <- null
                for f in compensations do
                   f()
                compensations <- []
                
            member x.GetCurrent() = 
                IEnumerator.check started;
                if finished then IEnumerator.alreadyFinished() else x.currElement
            
            interface IFinallyEnumerator with 
                member x.AppendFinallyAction(f) = 
                    compensations <- f :: compensations
                    
            interface IEnumerator<'T> with 
                member x.Current = x.GetCurrent()

            interface IEnumerator with 
                member x.Current = box (x.GetCurrent())
                   
                member x.MoveNext() = 
                   if not started then (started <- true) 
                   if finished then false
                   else 
                      let rec takeInner () = 
                        // check the inner list
                        if currInnerEnum.MoveNext() then 
                            x.currElement <- currInnerEnum.Current; 
                            true
                        else
                            // check the outer list
                            let rec takeOuter() = 
                                if outerEnum.MoveNext() then 
                                    let ie = outerEnum.Current 
                                    // Optimization to detect the statically-allocated empty IEnumerables
                                    match box ie with
                                    | :? EmptyEnumerable<'T> -> 
                                         // This one is empty, just skip, don't call GetEnumerator, try again
                                         takeOuter()
                                    | _ -> 
                                         // OK, this one may not be empty.
                                         // Don't forget to dispose of the enumerator for the inner list now we're done with it
                                         currInnerEnum.Dispose(); 
                                         currInnerEnum <- ie.GetEnumerator(); 
                                         takeInner ()
                                else 
                                    // We're done
                                    x.Finish()
                                    false
                            takeOuter()
                      takeInner () 

                member x.Reset() = IEnumerator.noReset()

            interface System.IDisposable with 
                member x.Dispose() = 
                    if not finished then 
                        x.Finish() 
          
        let EnumerateUsing (resource : 'T :> System.IDisposable) (rest: 'T -> #seq<'b>) = 
            (FinallyEnumerable((fun () -> match box resource with null -> () | _ -> resource.Dispose()), 
                               (fun () -> rest resource :> seq<_>)) :> seq<_>)

        let mkConcatEnumerable (ies: seq<'b :> seq<'T>>) = 
            mkSeq (fun () -> new ConcatEnumerator<_,_>(ies) :> IEnumerator<'T>)

        let EnumerateWhile (g : unit -> bool) (b: seq<'T>) : seq<'T> = 
            let started = ref false 
            let curr = ref None
            let getCurr() = 
                IEnumerator.check !started;
                match !curr with None -> IEnumerator.alreadyFinished() | Some x -> x 
            let start() = if not !started then (started := true) 

            let finish() = (curr := None) 
            mkConcatEnumerable 
               (mkSeq (fun () -> 
                    { new IEnumerator<_> with 
                          member x.Current = getCurr()
                       interface IEnumerator with 
                          member x.Current = box (getCurr())
                          member x.MoveNext() = 
                               start();
                               let keepGoing = (try g() with e -> finish(); rethrow ()) in
                               if keepGoing then 
                                   curr := Some(b); true
                               else 
                                   finish(); false
                          member x.Reset() = IEnumerator.noReset()
                       interface System.IDisposable with 
                          member x.Dispose() = () }))

        let EnumerateThenFinally (rest : seq<'T>) (compensation : unit -> unit)  =
            (FinallyEnumerable(compensation, (fun () -> rest)) :> seq<_>)

        [<AbstractClass>]
        type GeneratedSequenceBase<'T>() as this =
            let mutable redirectTo : GeneratedSequenceBase<'T> = Unchecked.defaultof<_>
            let mutable redirect : bool = false
            
            abstract GetFreshEnumerator : unit -> IEnumerator<'T>
            abstract GenerateNext : next:byref<IEnumerable<'T>> -> int // 0 = Stop, 1 = Yield, 2 = Goto
            abstract Close: unit -> unit
            abstract CheckClose: bool
            abstract LastGenerated : 'T
            
            member x.MoveNextImpl() = 
                 let active = 
                     if redirect then redirectTo
                     else this
                 let mutable target = null
                 match active.GenerateNext(&target) with 
                 | 1 -> 
                     true
                 | 2 -> 
                     match target.GetEnumerator() with 
                     | :? GeneratedSequenceBase<'T> as g when not active.CheckClose -> 
                         redirectTo <- g
                     | e -> 
                         redirectTo <- 
                               { new GeneratedSequenceBase<'T>() with 
                                     member x.GetFreshEnumerator() = e
                                     member x.GenerateNext(_) = if e.MoveNext() then 1 else 0 
                                     member x.Close() = e.Dispose(); active.Close()
                                     member x.CheckClose = true
                                     member x.LastGenerated = e.Current }
                     redirect <- true
                     x.MoveNextImpl()
                 | _ (* 0 *)  -> 
                     false
            
            interface IEnumerable<'T> with 
                member x.GetEnumerator() = x.GetFreshEnumerator()
            interface IEnumerable with
                member x.GetEnumerator() = (x.GetFreshEnumerator() :> IEnumerator);
            interface IEnumerator<'T> with 
                member x.Current = if redirect then redirectTo.LastGenerated else x.LastGenerated
                member x.Dispose() = if redirect then redirectTo.Close() else x.Close()
            interface IEnumerator with
                member x.Current = box (if redirect then redirectTo.LastGenerated else x.LastGenerated)
                member x.MoveNext() = x.MoveNextImpl() 
                   
                member x.Reset() = raise <| new System.NotSupportedException();


    [<Sealed>]
    [<CodeAnalysis.SuppressMessage("Microsoft.Naming", "CA1710:IdentifiersShouldHaveCorrectSuffix")>]
    type CachedSeq<'T>(cleanup,res:seq<'T>) =
        interface System.IDisposable with 
            member x.Dispose() = cleanup()
        interface System.Collections.Generic.IEnumerable<'T> with 
            member x.GetEnumerator() = res.GetEnumerator()
        interface System.Collections.IEnumerable with 
            member x.GetEnumerator() = (res :> System.Collections.IEnumerable).GetEnumerator()
        member obj.Clear() = cleanup()
           

    [<RequireQualifiedAccess>]
    [<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]
    module Seq = 

        open SequenceExpressionHelpers
        
        let mkDelayedSeq (f: unit -> IEnumerable<'T>) = mkSeq (fun () -> f().GetEnumerator())
        let mkUnfoldSeq f x = mkSeq (fun () -> IEnumerator.unfold f x) 
        
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let delay f = mkDelayedSeq f

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let unfold f x = mkUnfoldSeq f x
        
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let empty<'T> = (EmptyEnumerable :> seq<'T>)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let initInfinite f = mkSeq (fun () -> IEnumerator.upto None f)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let init_infinite f = initInfinite f

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let init count f =
            if count < 0 then invalidArg "count" "the number of elements was negative"
            mkSeq (fun () -> IEnumerator.upto (Some (count-1)) f)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let init_finite count f = init count f

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let iter f (ie : seq<'T>) = 
            use e = ie.GetEnumerator()
            while e.MoveNext() do
                f e.Current;

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let nth     i (ie : seq<'T>) = 
            use e = ie.GetEnumerator()
            IEnumerator.nth i e

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let iteri f (ie : seq<'T>) = 
            use e = ie.GetEnumerator()
            let mutable i = 0 
            while e.MoveNext() do
                f i e.Current;
                i <- i + 1;

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let exists f (ie : seq<'T>) = 
            use e = ie.GetEnumerator()
            let mutable state = false
            while (not state && e.MoveNext()) do
                state <- f e.Current
            state
            
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let for_all f (ie : seq<'T>) = 
            use e = ie.GetEnumerator()
            let mutable state = true 
            while (state && e.MoveNext()) do
                state <- f e.Current
            state
            
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let forall f ie = for_all f ie
            
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let iter2 f (ie1 : seq<_>) (ie2 : seq<_>)    = 
            use e1 = ie1.GetEnumerator()
            use e2 = ie2.GetEnumerator()
            while (e1.MoveNext() && e2.MoveNext()) do
                f e1.Current e2.Current;


        // Build an IEnumerble by wrapping/transforming iterators as they get generated.
        let revamp f (ie : seq<_>) = mkSeq (fun () -> f (ie.GetEnumerator()))
        let revamp2 f (ie1 : seq<_>) (ie2 : seq<_>) = mkSeq (fun () -> f (ie1.GetEnumerator()) (ie2.GetEnumerator()))
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let filter f ie      = revamp  (IEnumerator.filter f) ie
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let map    f ie      = revamp  (IEnumerator.map    f) ie
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let mapi f ie      = revamp  (IEnumerator.mapi   f) ie
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let map2 f ie1 ie2 = revamp2 (IEnumerator.map2    f) ie1 ie2
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let choose f ie      = revamp  (IEnumerator.choose f) ie
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let zip     ie1 ie2  = map2    (fun x y -> x,y) ie1 ie2
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let zip3 ie1 ie2  ie3 = map2 (fun x (y,z) -> x,y,z) ie1 (zip ie2 ie3)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let cast (seq: IEnumerable) = mkSeq (fun () -> IEnumerator.cast (seq.GetEnumerator()))

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let tryPick f (ie : seq<'T>)  = 
            use e = ie.GetEnumerator()
            let mutable res = None 
            while (Option.isNone res && e.MoveNext()) do
                res <-  f e.Current;
            res
        let first f ie  = tryPick f ie
        let pick f ie  = match tryPick f ie with None -> raise (System.Collections.Generic.KeyNotFoundException()) | Some x -> x
          
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let tryFind f (ie : seq<'T>)  = 
            use e = ie.GetEnumerator()
            let mutable res = None 
            while (Option.isNone res && e.MoveNext()) do
                let c = e.Current 
                if f c then res <- Some(c)
            res

        let tryfind f ie = tryFind f ie

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let find f ie = match tryfind f ie with None -> raise (System.Collections.Generic.KeyNotFoundException()) | Some x -> x

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let take count (sequence : seq<'T>)    = 
            if count < 0 then invalidArg "count" "the number of elements to take may not be negative"
            (* Note: don't create or dispose any IEnumerable if n = 0 *)
            if count = 0 then empty else  
            { use e = sequence.GetEnumerator() 
              for i in 0 .. count - 1 do
                  if not (e.MoveNext()) then
                      raise <| System.InvalidOperationException "the input sequence had insufficient elements" 
                  yield e.Current }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let isEmpty (ie : seq<'T>)  = 
            use ie = ie.GetEnumerator()
            not (ie.MoveNext())

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let is_empty ie = isEmpty ie

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let concat ies = SequenceExpressionHelpers.mkConcatEnumerable ies

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let length (ie : seq<'T>)    = 
            match ie with 
            | :? array<'T> as a -> a.Length
            | :? list<'T> as a -> a.Length
            | :? ResizeArray<'T> as a -> a.Count
            | _ -> 
                use e = ie.GetEnumerator() 
                let mutable state = 0 
                while e.MoveNext() do
                    state <-  state + 1;
                state

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let fold f x (ie : seq<'T>)  = 
            use e = ie.GetEnumerator() 
            let mutable state = x 
            while e.MoveNext() do
                state <- f state  e.Current;
            state

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let reduce f (sequence : seq<'T>)  = 
            use e = sequence.GetEnumerator() 
            if not (e.MoveNext()) then invalidArg "sequence" "the input sequence was empty";
            let mutable state = e.Current 
            while e.MoveNext() do
                state <- f state  e.Current;
            state

        let fromGenerator f = mkSeq(fun () -> Generator.EnumerateFromGenerator (f()))
        let toGenerator (ie : seq<_>) = Generator.GenerateFromEnumerator (ie.GetEnumerator())


        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let append (ie1: seq<'T>) (ie2: seq<'T>) = 
            fromGenerator(fun () -> Generator.bindG (toGenerator ie1) (fun () -> toGenerator ie2))

        
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let collect f ies = map f ies |> concat

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let map_concat f ies = collect f ies

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let compareWith (f:'T -> 'T -> int) (s1 : seq<'T>) (s2: seq<'T>) = 
            use e1 = s1.GetEnumerator()
            use e2 = s2.GetEnumerator()
            let rec go () = 
                let e1ok = e1.MoveNext() 
                let e2ok = e2.MoveNext() 
                let c = (if e1ok = e2ok then 0 else if e1ok then 1 else -1) 
                if c <> 0 then c else
                if not e1ok || not e2ok then 0 
                else
                    let c = f e1.Current e2.Current 
                    if c <> 0 then c else
                    go () 
            go()

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let compare f s1 s2  = compareWith f s1 s2

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let of_list (l : 'T list) = 
            (l :> seq<'T>)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let to_list (ie : seq<'T>) = 
            match ie with 
            | :? list<'T> as res -> res
            | :? array<'T> as res -> List.of_array res
            | _ -> 
                use e = ie.GetEnumerator()
                let mutable res = [] 
                while e.MoveNext() do
                    res <- e.Current :: res
                List.rev res

        // Create a new object to ensure underlying array may not be mutated by a backdoor cast 
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let of_array (a : 'T array) = 
            mkSeq (fun () -> IEnumerator.of_array a)        
            
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let to_array (ie : seq<'T>)  = 
            match ie with 
            | :? ('T[]) as res -> res
            | :? list<'T> as res -> List.to_array res
            | _ -> 
                use e = ie.GetEnumerator()
                let res = new System.Collections.Generic.List<_>()
                while e.MoveNext() do
                    res.Add(e.Current)
                res.ToArray()

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let singleton x = mkSeq (fun () -> IEnumerator.Singleton x)


        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let truncate n (x: seq<'T>) =
            { let i = ref 0
              use ie = x.GetEnumerator() 
              while !i < n && ie.MoveNext() do
                 i := !i + 1
                 yield ie.Current }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let pairwise (x: seq<'T>) =
            {   use ie = x.GetEnumerator() 
                if ie.MoveNext() then
                    let iref = ref ie.Current
                    while ie.MoveNext() do
                        let j = ie.Current 
                        yield (!iref, j)
                        iref := j }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let scan f z (seq : seq<_>) = 
            { let zref = ref z
              yield !zref
              use ie = seq.GetEnumerator() 
              while ie.MoveNext() do
                  zref := f !zref ie.Current 
                  yield !zref }

(*
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let scan1 f (sequence : seq<'T>) = 
            { use ie = sequence.GetEnumerator() 
              if ie.MoveNext() then 
                  let zref = ref ie.Current
                  while ie.MoveNext() do
                      zref := f !zref ie.Current 
                      yield !zref 
              else
                  raise <| System.InvalidOperationException "the input sequence was empty"  }
*)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let find_index p s = s |> find (snd >> p) |> fst

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let findIndex p (s:seq<_>) = 
            use ie = s.GetEnumerator() 
            let rec loop i = 
                if ie.MoveNext() then 
                    if p ie.Current then
                        i
                    else loop (i+1)
                else
                    raise (System.Collections.Generic.KeyNotFoundException())
            loop 0

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let tryFindIndex p (s:seq<_>) = 
            use ie = s.GetEnumerator() 
            let rec loop i = 
                if ie.MoveNext() then 
                    if p ie.Current then
                        Some i
                    else loop (i+1)
                else
                    None
            loop 0

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let tryfind_index p s = s |> tryfind (snd >> p) |> Option.map fst
        

        // windowed : int -> seq<'T> -> seq<array<'T>>
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let windowed windowSize (s: seq<_>) =    
            if windowSize <= 0 then invalidArg "windowSize" "the window size must be positive"
            { let arr = Array.zeroCreate windowSize 
              let r = ref (windowSize-1)
              let i = ref 0 
              use e = s.GetEnumerator() 
              while e.MoveNext() do 
                  arr.[!i] <- e.Current
                  i := (!i + 1) % windowSize
                  if !r = 0 then 
                      yield Array.init windowSize (fun j -> arr.[(!i+j) % windowSize])
                  else 
                      r := (!r - 1) }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let cache (seq : seq<'T>) = 
            // Wrap a seq to ensure that it is enumerated just once and only as far as is necessary.
            //
            // This code is required to be thread safe.
            // The necessary calls should be called at most once (include .MoveNext() = false).
            // The enumerator should be disposed (and dropped) when no longer required.
            //------
            // The state is (prefix,enumerator) with invariants:
            //   * the prefix followed by elts from the enumerator are the initial sequence.
            //   * the prefix contains only as many elements as the longest enumeration so far.
            let prefix      = System.Collections.Generic.List<_>()
            let enumeratorR = ref None : IEnumerator<'T> option option ref // nested options rather than new type...
                               // None          = Unstarted.
                               // Some(Some e)  = Started.
                               // Some None     = Finished.
            let oneStepTo i = 
              // If possible, step the enumeration to prefix length i (at most one step).
              // Be speculative, since this could have already happened via another thread.
              lock enumeratorR (fun () ->
                                    if not (i < prefix.Count) then // is a step still required?
                                        // If not yet started, start it (create enumerator).
                                        if !enumeratorR = None then enumeratorR := Some (Some (seq.GetEnumerator()))
                                        match (!enumeratorR).Value with
                                        | Some enumerator -> if enumerator.MoveNext() then
                                                                prefix.Add(enumerator.Current)
                                                             else
                                                                enumerator.Dispose()     // Move failed, dispose enumerator,
                                                                enumeratorR := Some None // drop it and record finished.
                                        | None -> ())
            let result = 
                unfold (fun i -> // i being the next position to be returned
                              if i < prefix.Count then
                                Some (prefix.[i],i+1)
                              else
                                oneStepTo i
                                if i < prefix.Count then
                                  Some (prefix.[i],i+1)
                                else
                                  None) 0
            let cleanup() = 
               lock enumeratorR (fun () -> 
                   prefix.Clear()
                   begin match !enumeratorR with 
                   | Some (Some e) -> IEnumerator.dispose e; 
                   | _ -> ()
                   end;
                   enumeratorR := None)
            (new CachedSeq<_>(cleanup, result) :> seq<_>)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let readonly (s:seq<_>) = mkSeq (fun () -> s.GetEnumerator())

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let groupBy keyf seq =

            mkDelayedSeq (fun () -> 
                // Wrap a Some(_) aroud all keys in case the key type is itself a type using null as a representation
                let dict = new Dictionary<'key option,System.Collections.Generic.List<'T>>(HashIdentity.Structural)

                // Build the groupings
                seq |> iter (fun v -> 
                    let key = Some (keyf v)
                    let ok,prev = dict.TryGetValue(key)
                    if ok then prev.Add(v)
                    else let prev = new List<'T>(1)
                         dict.[key] <- prev
                         prev.Add(v))

                // Trim the size of each result group.
                dict |> iter (fun group -> group.Value.TrimExcess())
                         
                // Return the sequence-of-sequences. Don't reveal the 
                // internal collections: just reveal them as sequences
                dict |> map (fun group -> (group.Key.Value, readonly group.Value)))


        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let distinct seq =
            {   // Wrap a Some(_) aroud all keys in case the key type is itself a type using null as a representation
                let dict = new Dictionary<'key option,obj>(HashIdentity.Structural)
                for v in seq do 
                    let key = Some v
                    if not (dict.ContainsKey(key)) then 
                        dict.[key] <- null; 
                        yield v }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let distinctBy f seq =
            {   // Wrap a Some(_) aroud all keys in case the key type is itself a type using null as a representation
                let dict = new Dictionary<'key option,obj>(HashIdentity.Structural)
                for v in seq do
                    let key = Some (f v)
                    if not (dict.ContainsKey(key)) then 
                        dict.[key] <- null; 
                        yield v }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let sortBy keyf seq =
            let comparer = ComparisonIdentity.Structural
            mkDelayedSeq (fun () -> 
                (seq |> to_list |> List.sortWith (fun x y -> comparer.Compare(keyf x,keyf y)) |> to_array) :> seq<_>)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let sort seq =
            mkDelayedSeq (fun () -> 
                (seq |> to_list |> List.sortWith Operators.compare |> to_array) :> seq<_>)

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let countBy keyf seq =
            mkDelayedSeq (fun () -> 
                let dict = new Dictionary<'key option,int>(HashIdentity.Structural)

                // Build the groupings
                seq |> iter (fun v -> 
                    let key = Some (keyf v )
                    let ok,prev = dict.TryGetValue(key)
                    if ok then dict.[key] <- dict.[key] + 1
                    else dict.[key] <- 1)

                dict |> map (fun group -> (group.Key.Value, group.Value)))

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let inline sum (seq: seq< (^a) >) : ^a = 
            use e = seq.GetEnumerator() 
            let mutable acc = LanguagePrimitives.GenericZero< (^a) >
            while e.MoveNext() do
                acc <- Checked.(+) acc e.Current
            acc

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let inline sumBy (f : 'T -> ^U) (seq: seq<'T>) : ^U = 
            use e = seq.GetEnumerator() 
            let mutable acc = LanguagePrimitives.GenericZero< (^U) >
            while e.MoveNext() do
                acc <- Checked.(+) acc (f e.Current)
            acc

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let inline average (sequence: seq< (^a) >) : ^a = 
            use e = sequence.GetEnumerator()     
            let mutable acc = LanguagePrimitives.GenericZero< (^a) >
            let mutable count = 0
            while e.MoveNext() do
                acc <- Checked.(+) acc e.Current
                count <- count + 1
            if count = 0 then 
                invalidArg "sequence" "the input sequence is empty";
            LanguagePrimitives.DivideByInt< (^a) > acc count

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let inline averageBy (f : 'T -> ^U) (sequence: seq< 'T >) : ^U = 
            use e = sequence.GetEnumerator() 
            let mutable acc = LanguagePrimitives.GenericZero< (^U) >
            let mutable count = 0
            while e.MoveNext() do
                acc <- Checked.(+) acc (f e.Current)
                count <- count + 1
            if count = 0 then 
                invalidArg "sequence" "the input sequence is empty";
            LanguagePrimitives.DivideByInt< (^U) > acc count
            
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let min (sequence: seq<_>) = 
            use e = sequence.GetEnumerator() 
            if not (e.MoveNext()) then 
                invalidArg "sequence" "the input sequence is empty";
            let mutable acc = e.Current
            while e.MoveNext() do
                acc <- Operators.min acc e.Current
            acc

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let minBy (f : 'T -> 'U) (sequence: seq<'T>) : 'T = 
            use e = sequence.GetEnumerator() 
            if not (e.MoveNext()) then 
                invalidArg "sequence" "the input sequence is empty";
            let mutable acc = f e.Current
            let mutable acc_v = e.Current
            while e.MoveNext() do
                let cur = f e.Current
                if cur < acc then
                    acc <- cur
                    acc_v <- e.Current
            acc_v

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let max (sequence: seq<_>) = 
            use e = sequence.GetEnumerator() 
            if not (e.MoveNext()) then 
                invalidArg "sequence" "the input sequence is empty";
            let mutable acc = e.Current
            while e.MoveNext() do
                acc <- Operators.max acc e.Current
            acc

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let maxBy (f : 'T -> 'U) (sequence: seq<'T>) : 'T = 
            use e = sequence.GetEnumerator() 
            if not (e.MoveNext()) then 
                invalidArg "sequence" "the input sequence is empty";
            let mutable acc = f e.Current
            let mutable acc_v = e.Current
            while e.MoveNext() do
                let cur = f e.Current
                if cur > acc then
                    acc <- cur
                    acc_v <- e.Current
            acc_v

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let group_by keyf seq = groupBy keyf seq
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let distinct_by f seq = distinctBy f seq
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let sort_by keyf seq = sortBy keyf seq
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let count_by keyf seq = countBy keyf seq
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let inline sum_by (f : 'T -> ^U) (seq: seq<'T>) : ^U =  sumBy f seq
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let inline average_by (f : 'T -> ^U) (sequence: seq< 'T >) : ^U =  averageBy f sequence 
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let min_by (f : 'T -> 'U) (sequence: seq<'T>) : 'T = minBy f sequence 
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let max_by (f : 'T -> 'U) (sequence: seq<'T>) : 'T = maxBy f sequence 
            
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let takeWhile p (sequence: seq<_>) = 
            { use e = sequence.GetEnumerator() 
              let latest = ref (Unchecked.defaultof<_>)
              while e.MoveNext() && (latest := e.Current; p !latest) do 
                  yield !latest }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let skip count (sequence: seq<_>) =
            { use e = sequence.GetEnumerator() 
              let latest = ref (Unchecked.defaultof<_>)
              let ok = ref false
              for i in 1 .. count do
                  if not (e.MoveNext()) then 
                      raise <| System.InvalidOperationException "the input sequence had insufficient elements" 
              while e.MoveNext() do
                  yield e.Current }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let skipWhile p (sequence: seq<_>) = 
            { use e = sequence.GetEnumerator() 
              let latest = ref (Unchecked.defaultof<_>)
              let ok = ref false
              while e.MoveNext() do
                  if (latest := e.Current; (!ok || not (p !latest))) then
                      ok := true
                      yield !latest }

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let skip_while p sequence = skipWhile  p sequence

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let take_while p sequence = takeWhile  p sequence

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let forall2 p (sequence1: seq<_>) (sequence2: seq<_>) = 
            use e1 = sequence1.GetEnumerator()
            use e2 = sequence2.GetEnumerator()
            let mutable ok = true
            while (ok && e1.MoveNext() && e2.MoveNext()) do
                ok <- p e1.Current e2.Current;
            ok

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let for_all2 p sequence1 sequence2 = forall2 p sequence1 sequence2
        
        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let exists2 p (sequence1: seq<_>) (sequence2: seq<_>) = 
            use e1 = sequence1.GetEnumerator()
            use e2 = sequence2.GetEnumerator()
            let mutable ok = false
            while (not ok && e1.MoveNext() && e2.MoveNext()) do
                ok <- p e1.Current e2.Current;
            ok

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let hd (sequence : seq<_>) =
          use e = sequence.GetEnumerator() 
          if (e.MoveNext()) then e.Current
          else invalidArg "sequence" "the input sequence was empty"


        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let find_indexi p s = s |> find (fun (x,y) -> p x y) |> fst

        [<CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1709:IdentifiersShouldBeCasedCorrectly"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1707:IdentifiersShouldNotContainUnderscores"); CodeAnalysis.SuppressMessage("Microsoft.Naming","CA1704:IdentifiersShouldBeSpelledCorrectly")>]             
        let tryfind_indexi p s = s |> tryFind (fun (x,y) -> p x y) |> Option.map fst