Head and Tail

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{-# LANGUAGE NoImplicitPrelude #-}
module HeadAndTail (
  head, tail, isNil, _test_head_tail, main_head_tail
) where

import Testing
import Functions
import Booleans
import Not
import Tuples
import DisjointUnions
import NaturalNumbers
import Lists

isNil :: (List t) => t a -> Bool
isNil = (either (const true) (const false)) . uncons


head :: (List t) => t a -> Union () a
head = (upair id fst) . uncons


tail :: (List t) => t a -> t a
tail = (either (const nil) snd) . uncons

_test_isNil_nil :: (List t, Equal (t a))
  => t a -> Test Bool
_test_isNil_nil z =
  testName "isNil(nil) == true" $
  let nil' = nil `withTypeOf` z in
  isNil nil'


_test_isNil_cons :: (List t, Equal (t a))
  => t a -> Test (a -> t a -> Bool)
_test_isNil_cons _ =
  testName "isNil(cons(a,x)) == false" $
  \a x -> eq (isNil (cons a x)) false

_test_head_nil :: (List t, Equal (t a), Equal a)
  => t a -> Test Bool
_test_head_nil z =
  testName "head(nil) == lft(*)" $
  let nil' = nil `withTypeOf` z in
  eq (head nil') (lft ())


_test_head_cons :: (List t, Equal (t a), Equal a)
  => t a -> Test (a -> t a -> Bool)
_test_head_cons _ =
  testName "head(cons(a,x)) == rgt(a)" $
  \a x -> eq (head (cons a x)) (rgt a)

_test_tail_nil :: (List t, Equal (t a))
  => t a -> Test Bool
_test_tail_nil z =
  testName "tail(nil) == tail" $
  let nil' = nil `withTypeOf` z in
  eq (tail nil') nil'


_test_tail_cons :: (List t, Equal (t a))
  => t a -> Test (a -> t a -> Bool)
_test_tail_cons _ =
  testName "tail(cons(a,x)) == x" $
  \a x -> eq (tail (cons a x)) x

_test_cons_self :: (List t, Equal (t a))
  => t a -> Test (a -> t a -> Bool)
_test_cons_self _ =
  testName "x /= cons(a,x)" $
  \a x -> not (eq (cons a x) x)

_test_head_tail ::
  ( TypeName a, Equal a, Show a, Arbitrary a
  , TypeName (t a), List t, Equal (t a), Arbitrary (t a), Show (t a)
  ) => Int -> Int -> t a -> IO ()
_test_head_tail size cases t = do
  testLabel1 "head and tail" t

  let args = testArgs size cases

  runTest args (_test_isNil_nil t)
  runTest args (_test_isNil_cons t)
  runTest args (_test_head_nil t)
  runTest args (_test_head_cons t)
  runTest args (_test_tail_nil t)
  runTest args (_test_tail_cons t)
  runTest args (_test_cons_self t)

main_head_tail :: IO ()
main_head_tail = do
  _test_head_tail 20 100 (nil :: ConsList Bool)
  _test_head_tail 20 100 (nil :: ConsList Unary)