src/Tests/Cardinal.hs

   1 module Tests.Cardinal
   2 where
   3
   4 import Control.Monad (liftM, liftM2)
   5 import Prelude hiding (LT)
   6 import Test.HUnit
   7 import Test.QuickCheck
   8
   9 import Cardinal
  10
  11
  12
  13 instance Arbitrary Cardinal where
  14     arbitrary = oneof [f,b,l,r,d,t,fl,fr,fd,ft,bl,br,bd,bt,ld,lt,
  15                        rd,rt,fld,flt,frd,frt,bld,blt,brd,brt,i,
  16                        scalar,csum,cdiff,cprod,cquot]
  17         where
  18           f = return F
  19           b = return B
  20           l = return L
  21           r = return R
  22           d = return D
  23           t = return T
  24           fl = return FL
  25           fr = return FR
  26           fd = return FD
  27           ft = return FT
  28           bl = return BL
  29           br = return BR
  30           bd = return BD
  31           bt = return BT
  32           ld = return LD
  33           lt = return LT
  34           rd = return RD
  35           rt = return RT
  36           fld = return FLD
  37           flt = return FLT
  38           frd = return FRD
  39           frt = return FRT
  40           bld = return BLD
  41           blt = return BLT
  42           brd = return BRD
  43           brt = return BRT
  44           i = return I
  45           scalar = liftM Scalar arbitrary
  46           csum = liftM2 Sum arbitrary arbitrary
  47           cdiff = liftM2 Difference arbitrary arbitrary
  48           cprod = liftM2 Product arbitrary arbitrary
  49           cquot = liftM2 Quotient arbitrary arbitrary
  50
  51
  52 -- | We know what (c t6 2 1 0 0) should be from Sorokina and
  53 --   Zeilfelder, p. 87.  This test checks that the directions are
  54 --   rotated properly.  The order of the letters has to be just right
  55 --   since I haven't defined a proper Eq instance for Cardinals.
  56 test_c_tilde_2100_rotation_correct :: Test
  57 test_c_tilde_2100_rotation_correct =
  58     TestCase $ assertEqual "auto-rotate equals manual rotate" ((ccwz . ccwz . cwy) expr1) expr2
  59     where
  60       expr1 =
  61           (3/8)*I +
  62           (1/12)*(T + R + L + D) +
  63           (1/64)*(FT + FR + FL + FD) +
  64           (7/48)*F +
  65           (1/48)*B +
  66           (1/96)*(RT + LD + LT + RD) +
  67           (1/192)*(BT + BR + BL + BD)
  68
  69       expr2 =
  70           (3/8)*I +
  71           (1/12)*(F + L + R + B) +
  72           (1/64)*(FT + LT + RT + BT) +
  73           (7/48)*T +
  74           (1/48)*D +
  75           (1/96)*(FL + BR + FR + BL) +
  76           (1/192)*(FD + LD + RD + BD)
  77
  78 cardinal_tests = [test_c_tilde_2100_rotation_correct]
  79
  80 -- | A list of all directions, sans the interior and composite types.
  81 all_directions :: [Cardinal]
  82 all_directions = [L, R, F, B, D, T, FL, FR, FD, FT,
  83                   BL, BR, BD, BT, LD, LT, RD, RT, FLD,
  84                   FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  85
  86
  87 -- | If we rotate a direction (other than front or back)
  88 --   counter-clockwise with respect to the x-axis, we should get a new
  89 --   direction.
  90 prop_ccwx_rotation_changes_direction :: Cardinal -> Property
  91 prop_ccwx_rotation_changes_direction c =
  92     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  93                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  94           ==> ccwx c /= c
  95
  96 -- | If we rotate a direction (other than front or back) clockwise
  97 --   with respect to the x-axis, we should get a new direction.
  98 prop_cwx_rotation_changes_direction :: Cardinal -> Property
  99 prop_cwx_rotation_changes_direction c =
 100     -- The front and back faces are unchanged by x-rotation.
 101     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 102                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 103           ==> cwx c /= c
 104
 105 -- | If we rotate a direction (other than left or right)
 106 --   counter-clockwise with respect to the y-axis, we should get a new
 107 --   direction.
 108 prop_ccwy_rotation_changes_direction :: Cardinal -> Property
 109 prop_ccwy_rotation_changes_direction c =
 110     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 111                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 112           ==> ccwy c /= c
 113
 114
 115 -- | If we rotate a direction (other than left or right) clockwise
 116 --   with respect to the y-axis, we should get a new direction.
 117 prop_cwy_rotation_changes_direction :: Cardinal -> Property
 118 prop_cwy_rotation_changes_direction c =
 119     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 120                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 121           ==> cwy c /= c
 122
 123
 124 -- | If we rotate a direction (other than top or down)
 125 --   counter-clockwise with respect to the z-axis, we should get a new
 126 --   direction.
 127 prop_ccwz_rotation_changes_direction :: Cardinal -> Property
 128 prop_ccwz_rotation_changes_direction c =
 129     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 130                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 131           ==> ccwz c /= c
 132
 133
 134 -- | If we rotate a direction (other than top or down) clockwise with
 135 --   respect to the z-axis, we should get a new direction.
 136 prop_cwz_rotation_changes_direction :: Cardinal -> Property
 137 prop_cwz_rotation_changes_direction c =
 138     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 139                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 140           ==> cwz c /= c
 141
 142
 143 -- | If we are given a direction c, there should only be one direction
 144 --   d which, when rotated counter-clockwise with respect to the
 145 --   x-axis, produces c.
 146 prop_ccwx_rotation_result_unique :: Cardinal -> Property
 147 prop_ccwx_rotation_result_unique c =
 148     c `elem` all_directions ==>
 149           (length [ d | d <- all_directions, ccwx d == c ]) == 1
 150
 151 -- | If we are given a direction c, there should only be one direction
 152 --   d which, when rotated clockwise with respect to the x-axis,
 153 --   produces c.
 154 prop_cwx_rotation_result_unique :: Cardinal -> Property
 155 prop_cwx_rotation_result_unique c =
 156     c `elem` all_directions ==>
 157           (length [ d | d <- all_directions, cwx d == c ]) == 1
 158
 159
 160 -- | If we are given a direction c, there should only be one direction
 161 --   d which, when rotated counter-clockwise with respect to the
 162 --   y-axis, produces c.
 163 prop_ccwy_rotation_result_unique :: Cardinal -> Property
 164 prop_ccwy_rotation_result_unique c =
 165     c `elem` all_directions ==>
 166           (length [ d | d <- all_directions, ccwy d == c ]) == 1
 167
 168
 169 -- | If we are given a direction c, there should only be one direction
 170 --   d which, when rotated clockwise with respect to the y-axis,
 171 --   produces c.
 172 prop_cwy_rotation_result_unique :: Cardinal -> Property
 173 prop_cwy_rotation_result_unique c =
 174     c `elem` all_directions ==>
 175           (length [ d | d <- all_directions, cwy d == c ]) == 1
 176
 177
 178 -- | If we are given a direction c, there should only be one direction
 179 --   d which, when rotated counter-clockwise with respect to the
 180 --   z-axis, produces c.
 181 prop_ccwz_rotation_result_unique :: Cardinal -> Property
 182 prop_ccwz_rotation_result_unique c =
 183     c `elem` all_directions ==>
 184           (length [ d | d <- all_directions, ccwz d == c ]) == 1
 185
 186
 187 -- | If we are given a direction c, there should only be one direction
 188 --   d which, when rotated clockwise with respect to the z-axis,
 189 --   produces c.
 190 prop_cwz_rotation_result_unique :: Cardinal -> Property
 191 prop_cwz_rotation_result_unique c =
 192     c `elem` all_directions ==>
 193           (length [ d | d <- all_directions, cwz d == c ]) == 1
 194
 195
 196 -- | If you rotate a cardinal direction four times in the clockwise
 197 --   (with respect to x) direction, you should wind up with the same
 198 --   direction.
 199 prop_four_cwx_is_identity :: Cardinal -> Bool
 200 prop_four_cwx_is_identity c =
 201     (cwx . cwx . cwx . cwx) c == c
 202
 203 -- | If you rotate a cardinal direction four times in the
 204 --   counter-clockwise (with respect to x) direction, you should wind up
 205 --   with the same direction.
 206 prop_four_ccwx_is_identity :: Cardinal -> Bool
 207 prop_four_ccwx_is_identity c =
 208     (ccwx . ccwx . ccwx . ccwx) c == c
 209
 210 -- | If you rotate a cardinal direction four times in the clockwise
 211 --   (with respect to y) direction, you should wind up with the same
 212 --   direction.
 213 prop_four_cwy_is_identity :: Cardinal -> Bool
 214 prop_four_cwy_is_identity c =
 215     (cwy . cwy . cwy . cwy) c == c
 216
 217 -- | If you rotate a cardinal direction four times in the counter-clockwise
 218 --   (with respect to y) direction, you should wind up with the same
 219 --   direction.
 220 prop_four_ccwy_is_identity :: Cardinal -> Bool
 221 prop_four_ccwy_is_identity c =
 222     (ccwy . ccwy . ccwy . ccwy) c == c
 223
 224 -- | If you rotate a cardinal direction four times in the clockwise
 225 --   (with respect to z) direction, you should wind up with the same
 226 --   direction.
 227 prop_four_cwz_is_identity :: Cardinal -> Bool
 228 prop_four_cwz_is_identity c =
 229     (cwz . cwz . cwz . cwz) c == c
 230
 231 -- | If you rotate a cardinal direction four times in the
 232 --   counter-clockwise (with respect to z) direction, you should wind up
 233 --   with the same direction.
 234 prop_four_ccwz_is_identity :: Cardinal -> Bool
 235 prop_four_ccwz_is_identity c =
 236     (ccwz . ccwz . ccwz . ccwz) c == c