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Monday, 10. November 2008

A immutable sorted list in F# – part I

Filed under: .NET 3.0,English posts,F#,Informatik,Theoretische — Steffen Forkmann at 12:06 Uhr

F# supports a powerful implementation of immutable lists (see Dustin’s introduction). But for my current work I needed a sorted list and of course I wanted it the F#-way, which means immutable. I didn’t want to reinvent the wheel so I asked my question in the hubFS forum.

It turned out (thanks to Robert) that F# uses red-black trees to give a fast implementation for the immutable set. This means that a set in F# stores all elements in a balanced binary tree and searching for an element costs only O(log n). As a side effect all elements can be visited in the underlying order, which means the set implementation gives a possibility for implementing a sorted list. The only limitation is that a set usually don’t store objects more than once.

The next problem I got, was that my sorted list needs a specific ordering function. The standard F# set implementation uses structural comparison to give an order, which is not the order I need. But Laurent mentioned the Set.Make function in the F# PowerPack. This function creates a new set type for the given ordering function. The only problem with Set.Make is that it was only designed for OCaml compatibility. But with this hint I was able to put all information together and got a nice immutable sorted list implementation for F#:

// wrap orderingFunction as Collections.Generic.IComparer
type 'a FComparer =
  {compareF: 'a -> 'a -> int}
  static member Create(compareF) =
    {new 'a FComparer with compareF = compareF}
  interface Collections.Generic.IComparer<'a> with
    member x.Compare(a, b) = x.compareF a b    
// a immutable sorted list - based on F# set
type 'a SortedFList =
 {items: Tagged.Set<'a,Collections.Generic.IComparer<'a>> }
  member x.Min = x.items.MinimumElement
  member x.Items = seq {for item in x.items do yield item}
  member x.Length = x.items.Count
  member x.IsEmpty = x.items.IsEmpty
  static member FromList(list, sortFunction) = 
    let comparer = FComparer<'a>.Create(sortFunction)
    {new 'a SortedFList with 
      items = Tagged.Set<'a>.Create(comparer,list)}
  static member FromListWithDefaultComparer(list) = 
  static member Empty(sortFunction) = 
  static member EmptyWithDefaultComparer() = 
  member x.Add(y) =     
    {x with items = x.items.Add(y)}    
  member x.Remove(y) =     
    {x with items = x.items.Remove(y)}    

Please note that this implementation stores every item only once. Next time I will show a version which allows to store repeated items.

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