type ChurchList<'a> = ('a -> 'b -> 'b) -> 'b -> 'b

let nil : ChurchList<'a> = fun _ z -> z

let cons (x: 'a) (xs: ChurchList<'a>) : ChurchList<'a> = 
    fun f z -> f x (xs f z)

let toList (churchList: ChurchList<'a>) : 'a list =
    churchList (fun x acc -> x :: acc) []
    |> List.rev

let ofList (lst: 'a list) : ChurchList<'a> =
    List.foldBack cons lst nil

let foldWithPredicate (f: 'a -> 'b -> 'b) (p: 'a -> bool) (acc: 'b) (churchList: ChurchList<'a>) : 'b =
    let rec foldTailRec lst currentAcc =
        match lst with
        | [] -> currentAcc
        | x :: xs -> 
            if p x then
                foldTailRec xs (f x currentAcc)
            else
                foldTailRec xs currentAcc
    
    let regularList = toList churchList
    foldTailRec regularList acc

let findMin (churchList: ChurchList<int>) : int option =
    let regularList = toList churchList
    match regularList with
    | [] -> None
    | x :: xs -> 
        let minValue = foldWithPredicate (fun x acc -> min x acc) (fun _ -> true) x churchList
        Some minValue

let sumEven (churchList: ChurchList<int>) : int =
    foldWithPredicate (+) (fun x -> x % 2 = 0) 0 churchList

let countOdd (churchList: ChurchList<int>) : int =
    foldWithPredicate (fun _ acc -> acc + 1) (fun x -> x % 2 <> 0) 0 churchList

[<EntryPoint>]
let main argv =
    let testList = ofList [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
    let emptyList = nil
    
    printfn "Тестовый список: [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]"
    
    match findMin testList with
    | Some min -> printfn "Минимальный элемент: %d" min
    | None -> printfn "Список пуст"
    
    printfn "Сумма четных чисел: %d" (sumEven testList)
    printfn "Количество нечетных чисел: %d" (countOdd testList)
    
    printfn "\nТест с пустым списком:"
    match findMin emptyList with
    | Some min -> printfn "Минимальный элемент: %d" min
    | None -> printfn "Список пуст"
    
    printfn "Сумма четных чисел в пустом списке: %d" (sumEven emptyList)
    printfn "Количество нечетных чисел в пустом списке: %d" (countOdd emptyList)
    
    0