src/Misc.hs

   1 -- | The Misc module contains helper functions that seem out of place
   2 --   anywhere else.
   3 module Misc
   4 where
   5
   6 import qualified Data.Vector as V (Vector, elem, empty, filter)
   7 import Test.Framework (Test, testGroup)
   8 import Test.Framework.Providers.HUnit (testCase)
   9 import Test.Framework.Providers.QuickCheck2 (testProperty)
  10 import Test.HUnit (Assertion, assertEqual)
  11 import Test.QuickCheck
  12
  13
  14 -- | The standard factorial function. See
  15 --   <http://www.willamette.edu/~fruehr/haskell/evolution.html> for
  16 --   possible improvements.
  17 --
  18 --   Examples:
  19 --
  20 --   >>> factorial 0
  21 --   1
  22 --
  23 --   >>> factorial 4
  24 --   24
  25 --
  26 factorial :: Int -> Int
  27 factorial n
  28     | n <= 1 = 1
  29     | n > 20 = error "integer overflow in factorial function"
  30     | otherwise = product [1..n]
  31
  32
  33 -- | Takes a three-dimensional list, and flattens it into a
  34 --   one-dimensional one.
  35 --
  36 --  Examples:
  37 --
  38 --  >>> flatten [ [[1,2], [3,4]], [[5,6], [7,8]] ]
  39 --  [1,2,3,4,5,6,7,8]
  40 --
  41 flatten :: [[[a]]] -> [a]
  42 flatten xs = concat $ concat xs
  43
  44
  45 -- | Switch the x and z dimensions of a three-dimensional list.
  46 transpose_xz :: [[[a]]] -> [[[a]]]
  47 transpose_xz [] = []
  48 transpose_xz [[]] = [[]]
  49 transpose_xz [[[]]] = [[[]]]
  50 transpose_xz m =
  51     [[[ m !! x !! y !! z | x <- [0..xsize]]
  52                       | y <- [0..ysize]]
  53                       | z <- [0..zsize]]
  54     where
  55       zsize = (length m) - 1
  56       ysize = length (head m) - 1
  57       xsize = length (head $ head m) - 1
  58
  59 -- | Takes a list, and returns True if its elements are pairwise
  60 --   equal. Returns False otherwise.
  61 all_equal :: (Eq a) => [a] -> Bool
  62 all_equal xs =
  63     all (== first_element) other_elements
  64     where
  65       first_element  = head xs
  66       other_elements = tail xs
  67
  68
  69 -- | Returns 'True' if the vectors xs and ys are disjoint, 'False'
  70 --   otherwise.
  71 --
  72 --   Examples:
  73 --
  74 --   >>> let xs = Data.Vector.fromList [1,2,3]
  75 --   >>> let ys = Data.Vector.fromList [4,5,6]
  76 --   >>> disjoint xs ys
  77 --   True
  78 --
  79 --   >>> let ys = Data.Vector.fromList [3,4,5]
  80 --   >>> disjoint xs ys
  81 --   False
  82 --
  83 disjoint :: (Eq a) => V.Vector a -> V.Vector a -> Bool
  84 disjoint xs ys =
  85   intersect xs ys == V.empty
  86   where
  87     intersect :: (Eq a) => V.Vector a -> V.Vector a -> V.Vector a
  88     intersect ws zs =
  89       V.filter (`V.elem` zs) ws
  90
  91 prop_factorial_greater :: Int -> Property
  92 prop_factorial_greater n =
  93     n <= 20 ==> factorial n >= n
  94
  95
  96 test_flatten1 :: Assertion
  97 test_flatten1 =
  98     assertEqual "flatten actually works" expected_list actual_list
  99     where
 100       target = [[[1::Int]], [[2, 3]]]
 101       expected_list = [1, 2, 3]
 102       actual_list = flatten target
 103
 104
 105 misc_tests :: Test.Framework.Test
 106 misc_tests =
 107     testGroup "Misc Tests" [
 108       testCase "flatten (1)" test_flatten1 ]
 109
 110
 111 misc_properties :: Test.Framework.Test
 112 misc_properties =
 113     testGroup "Misc Properties" [
 114       testProperty "factorial greater" prop_factorial_greater ]