F#: Project Euler Library for Problem 1 to 10

projectEulerLibFor1_10.fs

module ProjectEulerLib

open System
open System.IO
open System.Collections.Generic
open System.Linq

//let ( ** )(x:int64) n =
//  let mutable r,n = 1L,n
//  while n>0 do
//    r<-r*x
//    n<-n-1
//  r

let factorize (x:int64) =
  let rec f (x:int64) m i= seq {
    if x%m=0L then yield! f (x/m) m (i+1)
    else
      if i<>0 then yield (m,i)
      if x<>1L then yield! f x (m+1L) 0 }
  f x 2L 0 |> Seq.toList
let factorize32 = int64>>factorize>>Seq.map(fun(p,n)->(int p,n))

/// nested while loop
let factorize2 (x:int64) =
  seq{
  let x,m,i=ref x,ref 2L,ref 0
  while !x<>1L do
    while !x % !m=0L do
      x:= !x / !m
      i:= !i+1
    if !i<>0 then yield(!m,!i)
    m:=!m+1L
    i:=0
  } |> List.ofSeq

/// reverse digits
let reverseDigit =
  Seq.unfold(fun x->if x=0 then None else Some(x%10,x/10))
  >> Seq.toList 
  >> List.reduce(fun a b ->a*10+b)

let reverseDigit2 x=
  let mutable x,acc=x,0
  while x<>0 do 
    acc<-acc*10+x%10
    x<-x/10
  acc

/// prime generators
let primes() =
  let primes = new List<int>()
  primes.Add 2
  seq {
    yield 2
    for n in 3.. Int32.MaxValue do
      if primes|> Seq.takeWhile(fun p->p*p<=n)|> Seq.forall (fun p->n%p<>0) then
        yield n
        primes.Add n }

let problem8str = @"73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450"

let maybe predicate value = if predicate then Some value else None