Functional way to add to Lists that are Class-Members - f#

Question

I want to sort items of a class and collect them in Collection-Classes that beside a List-Member also contain further information that are necessary for the sorting process.
The following example is a a very simplified example for my problem. Although it doesn't make sense, I hope it still can help to understand my Question.
type ItemType = Odd|Even //realworld: more than two types possible
type Item(number) =
member this.number = number
member this.Type = if (this.number % 2) = 0 then Even else Odd
type NumberTypeCollection(numberType:ItemType , ?items:List<Item>) =
member this.ItemType = numberType
member val items:List<Item> = defaultArg items List.empty<Item> with get,set
member this.append(item:Item) = this.items <- item::this.items
let addToCollection (collections:List<NumberTypeCollection>) (item:Item) =
let possibleItem =
collections
|> Seq.where (fun c -> c.ItemType = item.Type) //in my realworld code, several groups may be returned
|> Seq.tryFind(fun _ -> true)
match possibleItem with
|Some(f) -> f.append item
collections
|None -> NumberTypeCollection(item.Type, [item]) :: collections
let rec findTypes (collections:List<NumberTypeCollection>) (items:List<Item>) =
match items with
| [] -> collections
| h::t -> let newCollections = ( h|> addToCollection collections)
findTypes newCollections t
let items = [Item(1);Item(2);Item(3);Item(4)]
let finalCollections = findTypes List.empty<NumberTypeCollection> items
I'm unsatisfied with the addToCollection method, since it requires the items in NumberTypeCollection to be mutual. Maybe there are further issues.
What can be a proper functional solution to solve this issue?
Edit: I'm sorry. May code was too simplified. Here is a little more complex example that should hopefully illustrate why I chose the mutual class-member (although this could still be the wrong decision):
open System
type Origin = Afrika|Asia|Australia|Europa|NorthAmerika|SouthAmerica
type Person(income, taxrate, origin:Origin) =
member this.income = income
member this.taxrate = taxrate
member this.origin = origin
type PersonGroup(origin:Origin , ?persons:List<Person>) =
member this.origin = origin
member val persons:List<Person> = defaultArg persons List.empty<Person> with get,set
member this.append(person:Person) = this.persons <- person::this.persons
//just some calculations to group people into some subgroups
let isInGroup (person:Person) (personGroup:PersonGroup) =
let avgIncome =
personGroup.persons
|> Seq.map (fun p -> float(p.income * p.taxrate) / 100.0)
|> Seq.average
Math.Abs ( (avgIncome / float person.income) - 1.0 ) < 0.5
let addToGroup (personGroups:List<PersonGroup>) (person:Person) =
let possibleItem =
personGroups
|> Seq.where (fun p -> p.origin = person.origin)
|> Seq.where (isInGroup person)
|> Seq.tryFind(fun _ -> true)
match possibleItem with
|Some(f) -> f.append person
personGroups
|None -> PersonGroup(person.origin, [person]) :: personGroups
let rec findPersonGroups (persons:List<Person>) (personGroups:List<PersonGroup>) =
match persons with
| [] -> personGroups
| h::t -> let newGroup = ( h|> addToGroup personGroups)
findPersonGroups t newGroup
let persons = [Person(1000,20, Afrika);Person(1300,22,Afrika);Person(500,21,Afrika);Person(400,20,Afrika)]
let c = findPersonGroups persons List.empty<PersonGroup>
What I may need to emphasize: There can be several different groups with the same origin.

Answer 1

Tomas' solution using groupby is the optimal approach if you want to generate your collections only once, it's a simple and concise.
If you want to be able to add/remove items in a functional, referentially transparent style for this type of problem, I suggest you move away from seq and start using Map.
You have a setup which is fundamentally dictionary-like. You have a unique key and a value. The functional F# equivalent to a dictionary is a Map, it is an immutable data structure based on an AVL tree. You can insert, remove and search in O(log n) time. When you append/remove from the Map, the old Map is maintained and you receive a new Map.
Here is your code expressed in this style
type ItemType =
|Odd
|Even
type Item (number) =
member this.Number = number
member this.Type = if (this.Number % 2) = 0 then Even else Odd
type NumTypeCollection = {Items : Map<ItemType, Item list>}
/// Functions on NumTypeCollection
module NumberTypeCollection =
/// Create empty collection
let empty = {Items = Map.empty}
/// Append one item to the collection
let append (item : Item) numTypeCollection =
let key = item.Type
match Map.containsKey key numTypeCollection.Items with
|true ->
let value = numTypeCollection.Items |> Map.find key
let newItems =
numTypeCollection.Items
|> Map.remove key
|> Map.add key (item :: value) // append item
{Items = newItems }
|false -> {Items = numTypeCollection.Items |> Map.add key [item]}
/// Append a list of items to the collections
let appendList (item : Item list) numTypeCollection =
item |> List.fold (fun acc it -> append it acc) numTypeCollection
Then call it using:
let items = [Item(1);Item(2);Item(3);Item(4)]
let finalCollections = NumberTypeCollection.appendList items (NumberTypeCollection.empty)

Answer 2

If I understand your problem correctly, you're trying to group the items by their type. The easiest way to do that is to use the standard library function Seq.groupBy. The following should implement the same logic as your code:
items
|> Seq.groupBy (fun item -> item.Type)
|> Seq.map (fun (key, values) ->
NumberTypeCollection(key, List.ofSeq values))

Answer 3

Maybe there are further issues.
Probably. It's difficult to tell, since it's hard to detect the purpose of the OP code... still:
Why do you even need an Item class? Instead, you could simply have a itemType function:
let itemType i = if i % 2 = 0 then Even else Odd
This function is referentially transparent, which means that you can replace it with its value if you wish. That makes it as good as a property getter method, but now you've already saved yourself from introducing a new type.
Why define a NumberTypeCollection class? Why not a simple record?
type NumberTypeList = { ItemType : ItemType; Numbers : int list }
You can implement addToCollection like something like this:
let addToCollection collections i =
let candidate =
collections
|> Seq.filter (fun c -> c.ItemType = (itemType i))
|> Seq.tryHead
match candidate with
| Some x ->
let x' = { x with Numbers = i :: x.Numbers }
collections |> Seq.filter ((<>) x) |> Seq.append [x']
| None ->
collections |> Seq.append [{ ItemType = (itemType i); Numbers = [i] }]
Being immutable, it doesn't mutate the input collections, but instead returns a new sequence of NumberTypeList.
Also notice the use of Seq.tryHead instead of Seq.tryFind(fun _ -> true).
Still, if you're attempting to group items, then Tomas' suggestion of using Seq.groupBy is more appropriate.