naive_set_theoretic_functions.hs

{-# LANGUAGE OverloadedStrings #-}
module Data.Set.Naive
  ( empty
  , member
  , subset
  , properSubset
  , superset
  , properSuperset
  , powerset
  , showSet
  ) where

import Data.List (elem, foldl', subsequences)
import qualified Data.Text as T (pack, replace)

empty :: Eq a => [a] -> Bool
empty = (==[])

member :: Eq a => a -> [a] -> Bool
member = elem

subset :: Eq a => [a] -> [a] -> Bool
subset x y = x `member` powerset y

properSubset :: Eq a => [a] -> [a] -> Bool
properSubset x y = x `subset` y && x /= y

superset :: Eq a => [a] -> [a] -> Bool
superset x y = y `subset` x

properSuperset :: Eq a => [a] -> [a] -> Bool
properSuperset x y = x `superset` y && x /= y

powerset :: [a] -> [[a]]
powerset = subsequences

showSet = T.replace "]" "}"  .
          T.replace "[" "{"  .
          T.replace "[]" "0" .
          T.pack . show