Multiplicative Partitions in Purescript (Purescript by Example, Chapter 4.11 Exercise 4)

Factorizations.purs

module Factorizations where

import Prelude

import Control.MonadZero (guard)
import Data.Array ((..), sort, nub, snoc)

factorizations :: Int -> Array (Array Int)
factorizations = nub <<< map sort <<< factors
  where
    factors :: Int -> Array (Array Int)
    factors 1 = [[1]]
    factors i = do
      j <- 1 .. (i - 1)
      guard (i `mod` j == 0)
      k <- factors j
      pure $ snoc k $ i / j

-- factorizations 10
-- [[1,10],[1,2,5]]

-- factorizations 12
-- [[1,12],[1,2,6],[1,2,2,3],[1,3,4]]