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.QuickCheck
   7
   8 import Cardinal
   9
  10
  11
  12 instance Arbitrary Cardinal where
  13     arbitrary = oneof [f,b,l,r,d,t,fl,fr,fd,ft,bl,br,bd,bt,ld,lt,
  14                        rd,rt,fld,flt,frd,frt,bld,blt,brd,brt,i,
  15                        scalar,csum,cdiff,cprod,cquot]
  16         where
  17           f = return F
  18           b = return B
  19           l = return L
  20           r = return R
  21           d = return D
  22           t = return T
  23           fl = return FL
  24           fr = return FR
  25           fd = return FD
  26           ft = return FT
  27           bl = return BL
  28           br = return BR
  29           bd = return BD
  30           bt = return BT
  31           ld = return LD
  32           lt = return LT
  33           rd = return RD
  34           rt = return RT
  35           fld = return FLD
  36           flt = return FLT
  37           frd = return FRD
  38           frt = return FRT
  39           bld = return BLD
  40           blt = return BLT
  41           brd = return BRD
  42           brt = return BRT
  43           i = return I
  44           scalar = liftM Scalar arbitrary
  45           csum = liftM2 Sum arbitrary arbitrary
  46           cdiff = liftM2 Difference arbitrary arbitrary
  47           cprod = liftM2 Product arbitrary arbitrary
  48           cquot = liftM2 Quotient arbitrary arbitrary
  49
  50
  51 -- | A list of all directions, sans the interior and composite types.
  52 all_directions :: [Cardinal]
  53 all_directions = [L, R, F, B, D, T, FL, FR, FD, FT,
  54                   BL, BR, BD, BT, LD, LT, RD, RT, FLD,
  55                   FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  56
  57
  58 -- | If we rotate a direction (other than front or back)
  59 --   counter-clockwise with respect to the x-axis, we should get a new
  60 --   direction.
  61 prop_ccwx_rotation_changes_direction :: Cardinal -> Property
  62 prop_ccwx_rotation_changes_direction c =
  63     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  64                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  65           ==> ccwx c /= c
  66
  67 -- | If we rotate a direction (other than front or back) clockwise
  68 --   with respect to the x-axis, we should get a new direction.
  69 prop_cwx_rotation_changes_direction :: Cardinal -> Property
  70 prop_cwx_rotation_changes_direction c =
  71     -- The front and back faces are unchanged by x-rotation.
  72     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  73                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  74           ==> cwx c /= c
  75
  76 -- | If we rotate a direction (other than left or right)
  77 --   counter-clockwise with respect to the y-axis, we should get a new
  78 --   direction.
  79 prop_ccwy_rotation_changes_direction :: Cardinal -> Property
  80 prop_ccwy_rotation_changes_direction c =
  81     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  82                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  83           ==> ccwy c /= c
  84
  85
  86 -- | If we rotate a direction (other than left or right) clockwise
  87 --   with respect to the y-axis, we should get a new direction.
  88 prop_cwy_rotation_changes_direction :: Cardinal -> Property
  89 prop_cwy_rotation_changes_direction c =
  90     c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  91                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  92           ==> cwy c /= c
  93
  94
  95 -- | If we rotate a direction (other than top or down)
  96 --   counter-clockwise with respect to the z-axis, we should get a new
  97 --   direction.
  98 prop_ccwz_rotation_changes_direction :: Cardinal -> Property
  99 prop_ccwz_rotation_changes_direction c =
 100     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 101                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 102           ==> ccwz c /= c
 103
 104
 105 -- | If we rotate a direction (other than top or down) clockwise with
 106 --   respect to the z-axis, we should get a new direction.
 107 prop_cwz_rotation_changes_direction :: Cardinal -> Property
 108 prop_cwz_rotation_changes_direction c =
 109     c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
 110                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
 111           ==> cwz c /= c
 112
 113
 114 -- | If we are given a direction c, there should only be one direction
 115 --   d which, when rotated counter-clockwise with respect to the
 116 --   x-axis, produces c.
 117 prop_ccwx_rotation_result_unique :: Cardinal -> Property
 118 prop_ccwx_rotation_result_unique c =
 119     c `elem` all_directions ==>
 120           (length [ d | d <- all_directions, ccwx d == c ]) == 1
 121
 122 -- | If we are given a direction c, there should only be one direction
 123 --   d which, when rotated clockwise with respect to the x-axis,
 124 --   produces c.
 125 prop_cwx_rotation_result_unique :: Cardinal -> Property
 126 prop_cwx_rotation_result_unique c =
 127     c `elem` all_directions ==>
 128           (length [ d | d <- all_directions, cwx d == c ]) == 1
 129
 130
 131 -- | If we are given a direction c, there should only be one direction
 132 --   d which, when rotated counter-clockwise with respect to the
 133 --   y-axis, produces c.
 134 prop_ccwy_rotation_result_unique :: Cardinal -> Property
 135 prop_ccwy_rotation_result_unique c =
 136     c `elem` all_directions ==>
 137           (length [ d | d <- all_directions, ccwy d == c ]) == 1
 138
 139
 140 -- | If we are given a direction c, there should only be one direction
 141 --   d which, when rotated clockwise with respect to the y-axis,
 142 --   produces c.
 143 prop_cwy_rotation_result_unique :: Cardinal -> Property
 144 prop_cwy_rotation_result_unique c =
 145     c `elem` all_directions ==>
 146           (length [ d | d <- all_directions, cwy d == c ]) == 1
 147
 148
 149 -- | If we are given a direction c, there should only be one direction
 150 --   d which, when rotated counter-clockwise with respect to the
 151 --   z-axis, produces c.
 152 prop_ccwz_rotation_result_unique :: Cardinal -> Property
 153 prop_ccwz_rotation_result_unique c =
 154     c `elem` all_directions ==>
 155           (length [ d | d <- all_directions, ccwz d == c ]) == 1
 156
 157
 158 -- | If we are given a direction c, there should only be one direction
 159 --   d which, when rotated clockwise with respect to the z-axis,
 160 --   produces c.
 161 prop_cwz_rotation_result_unique :: Cardinal -> Property
 162 prop_cwz_rotation_result_unique c =
 163     c `elem` all_directions ==>
 164           (length [ d | d <- all_directions, cwz d == c ]) == 1
 165
 166
 167 -- | If you rotate a cardinal direction four times in the clockwise
 168 --   (with respect to x) direction, you should wind up with the same
 169 --   direction.
 170 prop_four_cwx_is_identity :: Cardinal -> Bool
 171 prop_four_cwx_is_identity c =
 172     (cwx . cwx . cwx . cwx) c == c
 173
 174 -- | If you rotate a cardinal direction four times in the
 175 --   counter-clockwise (with respect to x) direction, you should wind up
 176 --   with the same direction.
 177 prop_four_ccwx_is_identity :: Cardinal -> Bool
 178 prop_four_ccwx_is_identity c =
 179     (ccwx . ccwx . ccwx . ccwx) c == c
 180
 181 -- | If you rotate a cardinal direction four times in the clockwise
 182 --   (with respect to y) direction, you should wind up with the same
 183 --   direction.
 184 prop_four_cwy_is_identity :: Cardinal -> Bool
 185 prop_four_cwy_is_identity c =
 186     (cwy . cwy . cwy . cwy) c == c
 187
 188 -- | If you rotate a cardinal direction four times in the counter-clockwise
 189 --   (with respect to y) direction, you should wind up with the same
 190 --   direction.
 191 prop_four_ccwy_is_identity :: Cardinal -> Bool
 192 prop_four_ccwy_is_identity c =
 193     (ccwy . ccwy . ccwy . ccwy) c == c
 194
 195 -- | If you rotate a cardinal direction four times in the clockwise
 196 --   (with respect to z) direction, you should wind up with the same
 197 --   direction.
 198 prop_four_cwz_is_identity :: Cardinal -> Bool
 199 prop_four_cwz_is_identity c =
 200     (cwz . cwz . cwz . cwz) c == c
 201
 202 -- | If you rotate a cardinal direction four times in the
 203 --   counter-clockwise (with respect to z) direction, you should wind up
 204 --   with the same direction.
 205 prop_four_ccwz_is_identity :: Cardinal -> Bool
 206 prop_four_ccwz_is_identity c =
 207     (ccwz . ccwz . ccwz . ccwz) c == c