Disjoint

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{-# LANGUAGE NoImplicitPrelude #-}
module Disjoint (
  disjoint, _test_disjoint, main_disjoint
) where

import Testing
import Booleans
import And
import NaturalNumbers
import Lists
import HeadAndTail
import Reverse
import Cat
import Dedupe
import Common

disjoint :: (List t, Equal a) => t a -> t a -> Bool
disjoint x y = isNil (common x y)

_test_disjoint_nil :: (List t, Equal a, Equal (t a))
  => t a -> Test (t a -> Bool)
_test_disjoint_nil _ =
  testName "disjoint(nil,x) == true" $
  \x -> eq (disjoint nil x) true

_test_disjoint_dedupeL_right :: (List t, Equal a, Equal (t a))
  => t a -> Test (t a -> t a -> Bool)
_test_disjoint_dedupeL_right _ =
  testName "disjoint(x,dedupeL(y)) == disjoint(x,y)" $
  \x y -> eq
    (disjoint x (dedupeL y))
    (disjoint x y)

_test_disjoint_cat_left :: (List t, Equal a, Equal (t a))
  => t a -> Test (t a -> t a -> t a -> Bool)
_test_disjoint_cat_left _ =
  testName "disjoint(cat(x,y),z) == and(disjoint(x,z),disjoint(y,z))" $
  \x y z -> eq
    (disjoint (cat x y) z)
    (and (disjoint x z) (disjoint y z))

_test_disjoint_rev_right :: (List t, Equal a, Equal (t a))
  => t a -> Test (t a -> t a -> Bool)
_test_disjoint_rev_right _ =
  testName "disjoint(x,rev(y)) == disjoint(x,y)" $
  \x y -> eq
    (disjoint x (rev y))
    (disjoint x y)

_test_disjoint ::
  ( TypeName a, Equal a, Show a, Arbitrary a, CoArbitrary a
  , TypeName (t a), List t
  , Equal (t a), Show (t a), Arbitrary (t a), Equal (t (t a))
  ) => Int -> Int -> t a -> IO ()
_test_disjoint size cases t = do
  testLabel1 "disjoint" t

  let args = testArgs size cases

  runTest args (_test_disjoint_nil t)
  runTest args (_test_disjoint_dedupeL_right t)
  runTest args (_test_disjoint_cat_left t)
  runTest args (_test_disjoint_rev_right t)

main_disjoint :: IO ()
main_disjoint = do
  _test_disjoint 20 100 (nil :: ConsList Bool)
  _test_disjoint 20 100 (nil :: ConsList Unary)