src/Tests/Cardinal.hs

   1 module Tests.Cardinal
   2 where
   3
   4 import Prelude hiding (LT)
   5 import Test.HUnit
   6 import Test.QuickCheck (Property, (==>))
   7
   8 import Cardinal
   9
  10 -- | We know what (c t6 2 1 0 0) should be from Sorokina and
  11 --   Zeilfelder, p. 87.  This test checks that the directions are
  12 --   rotated properly.  The order of the letters has to be just right
  13 --   since I haven't defined a proper Eq instance for Cardinals.
  14 test_c_tilde_2100_rotation_correct :: Assertion
  15 test_c_tilde_2100_rotation_correct =
  16     assertEqual "auto-rotate equals manual rotate" ((ccwz . ccwz . cwy) expr1) expr2
  17     where
  18       expr1 =
  19           (3/8)*I +
  20           (1/12)*(T + R + L + D) +
  21           (1/64)*(FT + FR + FL + FD) +
  22           (7/48)*F +
  23           (1/48)*B +
  24           (1/96)*(RT + LD + LT + RD) +
  25           (1/192)*(BT + BR + BL + BD)
  26
  27       expr2 =
  28           (3/8)*I +
  29           (1/12)*(F + L + R + B) +
  30           (1/64)*(FT + LT + RT + BT) +
  31           (7/48)*T +
  32           (1/48)*D +
  33           (1/96)*(FL + BR + FR + BL) +
  34           (1/192)*(FD + LD + RD + BD)
  35
  36 -- | A list of all directions, sans the interior and composite types.
  37 all_directions :: [Cardinal]
  38 all_directions = [L, R, F, B, D, T, FL, FR, FD, FT,
  39                   BL, BR, BD, BT, LD, LT, RD, RT, FLD,
  40                   FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  41
  42
  43 -- | If we rotate a direction (other than front or back)
  44 --   counter-clockwise with respect to the x-axis, we should get a new
  45 --   direction.
  46 prop_ccwx_rotation_changes_direction :: Cardinal -> Property
  47 prop_ccwx_rotation_changes_direction c =
  48     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  49                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  50           ==> ccwx c /= c
  51
  52 -- | If we rotate a direction (other than front or back) clockwise
  53 --   with respect to the x-axis, we should get a new direction.
  54 prop_cwx_rotation_changes_direction :: Cardinal -> Property
  55 prop_cwx_rotation_changes_direction c =
  56     -- The front and back faces are unchanged by x-rotation.
  57     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  58                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  59           ==> cwx c /= c
  60
  61 -- | If we rotate a direction (other than left or right)
  62 --   counter-clockwise with respect to the y-axis, we should get a new
  63 --   direction.
  64 prop_ccwy_rotation_changes_direction :: Cardinal -> Property
  65 prop_ccwy_rotation_changes_direction c =
  66     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  67                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  68           ==> ccwy c /= c
  69
  70
  71 -- | If we rotate a direction (other than left or right) clockwise
  72 --   with respect to the y-axis, we should get a new direction.
  73 prop_cwy_rotation_changes_direction :: Cardinal -> Property
  74 prop_cwy_rotation_changes_direction c =
  75     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  76                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  77           ==> cwy c /= c
  78
  79
  80 -- | If we rotate a direction (other than top or down)
  81 --   counter-clockwise with respect to the z-axis, we should get a new
  82 --   direction.
  83 prop_ccwz_rotation_changes_direction :: Cardinal -> Property
  84 prop_ccwz_rotation_changes_direction c =
  85     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  86                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  87           ==> ccwz c /= c
  88
  89
  90 -- | If we rotate a direction (other than top or down) clockwise with
  91 --   respect to the z-axis, we should get a new direction.
  92 prop_cwz_rotation_changes_direction :: Cardinal -> Property
  93 prop_cwz_rotation_changes_direction c =
  94     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  95                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  96           ==> cwz c /= c
  97
  98
  99 -- | If we are given a direction c, there should only be one direction
 100 --   d which, when rotated counter-clockwise with respect to the
 101 --   x-axis, produces c.
 102 prop_ccwx_rotation_result_unique :: Cardinal -> Property
 103 prop_ccwx_rotation_result_unique c =
 104     c `elem` all_directions ==>
 105           (length [ d | d <- all_directions, ccwx d == c ]) == 1
 106
 107 -- | If we are given a direction c, there should only be one direction
 108 --   d which, when rotated clockwise with respect to the x-axis,
 109 --   produces c.
 110 prop_cwx_rotation_result_unique :: Cardinal -> Property
 111 prop_cwx_rotation_result_unique c =
 112     c `elem` all_directions ==>
 113           (length [ d | d <- all_directions, cwx d == c ]) == 1
 114
 115
 116 -- | If we are given a direction c, there should only be one direction
 117 --   d which, when rotated counter-clockwise with respect to the
 118 --   y-axis, produces c.
 119 prop_ccwy_rotation_result_unique :: Cardinal -> Property
 120 prop_ccwy_rotation_result_unique c =
 121     c `elem` all_directions ==>
 122           (length [ d | d <- all_directions, ccwy d == c ]) == 1
 123
 124
 125 -- | If we are given a direction c, there should only be one direction
 126 --   d which, when rotated clockwise with respect to the y-axis,
 127 --   produces c.
 128 prop_cwy_rotation_result_unique :: Cardinal -> Property
 129 prop_cwy_rotation_result_unique c =
 130     c `elem` all_directions ==>
 131           (length [ d | d <- all_directions, cwy d == c ]) == 1
 132
 133
 134 -- | If we are given a direction c, there should only be one direction
 135 --   d which, when rotated counter-clockwise with respect to the
 136 --   z-axis, produces c.
 137 prop_ccwz_rotation_result_unique :: Cardinal -> Property
 138 prop_ccwz_rotation_result_unique c =
 139     c `elem` all_directions ==>
 140           (length [ d | d <- all_directions, ccwz d == c ]) == 1
 141
 142
 143 -- | If we are given a direction c, there should only be one direction
 144 --   d which, when rotated clockwise with respect to the z-axis,
 145 --   produces c.
 146 prop_cwz_rotation_result_unique :: Cardinal -> Property
 147 prop_cwz_rotation_result_unique c =
 148     c `elem` all_directions ==>
 149           (length [ d | d <- all_directions, cwz d == c ]) == 1
 150
 151
 152 -- | If you rotate a cardinal direction four times in the clockwise
 153 --   (with respect to x) direction, you should wind up with the same
 154 --   direction.
 155 prop_four_cwx_is_identity :: Cardinal -> Bool
 156 prop_four_cwx_is_identity c =
 157     (cwx . cwx . cwx . cwx) c == c
 158
 159 -- | If you rotate a cardinal direction four times in the
 160 --   counter-clockwise (with respect to x) direction, you should wind up
 161 --   with the same direction.
 162 prop_four_ccwx_is_identity :: Cardinal -> Bool
 163 prop_four_ccwx_is_identity c =
 164     (ccwx . ccwx . ccwx . ccwx) c == c
 165
 166 -- | If you rotate a cardinal direction four times in the clockwise
 167 --   (with respect to y) direction, you should wind up with the same
 168 --   direction.
 169 prop_four_cwy_is_identity :: Cardinal -> Bool
 170 prop_four_cwy_is_identity c =
 171     (cwy . cwy . cwy . cwy) c == c
 172
 173 -- | If you rotate a cardinal direction four times in the counter-clockwise
 174 --   (with respect to y) direction, you should wind up with the same
 175 --   direction.
 176 prop_four_ccwy_is_identity :: Cardinal -> Bool
 177 prop_four_ccwy_is_identity c =
 178     (ccwy . ccwy . ccwy . ccwy) c == c
 179
 180 -- | If you rotate a cardinal direction four times in the clockwise
 181 --   (with respect to z) direction, you should wind up with the same
 182 --   direction.
 183 prop_four_cwz_is_identity :: Cardinal -> Bool
 184 prop_four_cwz_is_identity c =
 185     (cwz . cwz . cwz . cwz) c == c
 186
 187 -- | If you rotate a cardinal direction four times in the
 188 --   counter-clockwise (with respect to z) direction, you should wind up
 189 --   with the same direction.
 190 prop_four_ccwz_is_identity :: Cardinal -> Bool
 191 prop_four_ccwz_is_identity c =
 192     (ccwz . ccwz . ccwz . ccwz) c == c