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 :: Assertion
  57 test_c_tilde_2100_rotation_correct =
  58     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 -- | A list of all directions, sans the interior and composite types.
  79 all_directions :: [Cardinal]
  80 all_directions = [L, R, F, B, D, T, FL, FR, FD, FT,
  81                   BL, BR, BD, BT, LD, LT, RD, RT, FLD,
  82                   FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  83
  84
  85 -- | If we rotate a direction (other than front or back)
  86 --   counter-clockwise with respect to the x-axis, we should get a new
  87 --   direction.
  88 prop_ccwx_rotation_changes_direction :: Cardinal -> Property
  89 prop_ccwx_rotation_changes_direction c =
  90     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  91                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  92           ==> ccwx c /= c
  93
  94 -- | If we rotate a direction (other than front or back) clockwise
  95 --   with respect to the x-axis, we should get a new direction.
  96 prop_cwx_rotation_changes_direction :: Cardinal -> Property
  97 prop_cwx_rotation_changes_direction c =
  98     -- The front and back faces are unchanged by x-rotation.
  99     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 100                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 101           ==> cwx c /= c
 102
 103 -- | If we rotate a direction (other than left or right)
 104 --   counter-clockwise with respect to the y-axis, we should get a new
 105 --   direction.
 106 prop_ccwy_rotation_changes_direction :: Cardinal -> Property
 107 prop_ccwy_rotation_changes_direction c =
 108     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 109                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 110           ==> ccwy c /= c
 111
 112
 113 -- | If we rotate a direction (other than left or right) clockwise
 114 --   with respect to the y-axis, we should get a new direction.
 115 prop_cwy_rotation_changes_direction :: Cardinal -> Property
 116 prop_cwy_rotation_changes_direction c =
 117     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 118                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 119           ==> cwy c /= c
 120
 121
 122 -- | If we rotate a direction (other than top or down)
 123 --   counter-clockwise with respect to the z-axis, we should get a new
 124 --   direction.
 125 prop_ccwz_rotation_changes_direction :: Cardinal -> Property
 126 prop_ccwz_rotation_changes_direction c =
 127     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 128                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 129           ==> ccwz c /= c
 130
 131
 132 -- | If we rotate a direction (other than top or down) clockwise with
 133 --   respect to the z-axis, we should get a new direction.
 134 prop_cwz_rotation_changes_direction :: Cardinal -> Property
 135 prop_cwz_rotation_changes_direction c =
 136     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 137                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 138           ==> cwz c /= c
 139
 140
 141 -- | If we are given a direction c, there should only be one direction
 142 --   d which, when rotated counter-clockwise with respect to the
 143 --   x-axis, produces c.
 144 prop_ccwx_rotation_result_unique :: Cardinal -> Property
 145 prop_ccwx_rotation_result_unique c =
 146     c `elem` all_directions ==>
 147           (length [ d | d <- all_directions, ccwx d == c ]) == 1
 148
 149 -- | If we are given a direction c, there should only be one direction
 150 --   d which, when rotated clockwise with respect to the x-axis,
 151 --   produces c.
 152 prop_cwx_rotation_result_unique :: Cardinal -> Property
 153 prop_cwx_rotation_result_unique c =
 154     c `elem` all_directions ==>
 155           (length [ d | d <- all_directions, cwx d == c ]) == 1
 156
 157
 158 -- | If we are given a direction c, there should only be one direction
 159 --   d which, when rotated counter-clockwise with respect to the
 160 --   y-axis, produces c.
 161 prop_ccwy_rotation_result_unique :: Cardinal -> Property
 162 prop_ccwy_rotation_result_unique c =
 163     c `elem` all_directions ==>
 164           (length [ d | d <- all_directions, ccwy d == c ]) == 1
 165
 166
 167 -- | If we are given a direction c, there should only be one direction
 168 --   d which, when rotated clockwise with respect to the y-axis,
 169 --   produces c.
 170 prop_cwy_rotation_result_unique :: Cardinal -> Property
 171 prop_cwy_rotation_result_unique c =
 172     c `elem` all_directions ==>
 173           (length [ d | d <- all_directions, cwy d == c ]) == 1
 174
 175
 176 -- | If we are given a direction c, there should only be one direction
 177 --   d which, when rotated counter-clockwise with respect to the
 178 --   z-axis, produces c.
 179 prop_ccwz_rotation_result_unique :: Cardinal -> Property
 180 prop_ccwz_rotation_result_unique c =
 181     c `elem` all_directions ==>
 182           (length [ d | d <- all_directions, ccwz d == c ]) == 1
 183
 184
 185 -- | If we are given a direction c, there should only be one direction
 186 --   d which, when rotated clockwise with respect to the z-axis,
 187 --   produces c.
 188 prop_cwz_rotation_result_unique :: Cardinal -> Property
 189 prop_cwz_rotation_result_unique c =
 190     c `elem` all_directions ==>
 191           (length [ d | d <- all_directions, cwz d == c ]) == 1
 192
 193
 194 -- | If you rotate a cardinal direction four times in the clockwise
 195 --   (with respect to x) direction, you should wind up with the same
 196 --   direction.
 197 prop_four_cwx_is_identity :: Cardinal -> Bool
 198 prop_four_cwx_is_identity c =
 199     (cwx . cwx . cwx . cwx) c == c
 200
 201 -- | If you rotate a cardinal direction four times in the
 202 --   counter-clockwise (with respect to x) direction, you should wind up
 203 --   with the same direction.
 204 prop_four_ccwx_is_identity :: Cardinal -> Bool
 205 prop_four_ccwx_is_identity c =
 206     (ccwx . ccwx . ccwx . ccwx) c == c
 207
 208 -- | If you rotate a cardinal direction four times in the clockwise
 209 --   (with respect to y) direction, you should wind up with the same
 210 --   direction.
 211 prop_four_cwy_is_identity :: Cardinal -> Bool
 212 prop_four_cwy_is_identity c =
 213     (cwy . cwy . cwy . cwy) c == c
 214
 215 -- | If you rotate a cardinal direction four times in the counter-clockwise
 216 --   (with respect to y) direction, you should wind up with the same
 217 --   direction.
 218 prop_four_ccwy_is_identity :: Cardinal -> Bool
 219 prop_four_ccwy_is_identity c =
 220     (ccwy . ccwy . ccwy . ccwy) c == c
 221
 222 -- | If you rotate a cardinal direction four times in the clockwise
 223 --   (with respect to z) direction, you should wind up with the same
 224 --   direction.
 225 prop_four_cwz_is_identity :: Cardinal -> Bool
 226 prop_four_cwz_is_identity c =
 227     (cwz . cwz . cwz . cwz) c == c
 228
 229 -- | If you rotate a cardinal direction four times in the
 230 --   counter-clockwise (with respect to z) direction, you should wind up
 231 --   with the same direction.
 232 prop_four_ccwz_is_identity :: Cardinal -> Bool
 233 prop_four_ccwz_is_identity c =
 234     (ccwz . ccwz . ccwz . ccwz) c == c