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 prop_ccwx_rotation_changes_direction :: Cardinal -> Property
  52 prop_ccwx_rotation_changes_direction c =
  53     -- The front and back faces are unchanged by x-rotation.
  54     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  55                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  56           ==> ccwx c /= c
  57
  58 prop_cwx_rotation_changes_direction :: Cardinal -> Property
  59 prop_cwx_rotation_changes_direction c =
  60     -- The front and back faces are unchanged by x-rotation.
  61     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
  62                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
  63           ==> cwx c /= c
  64
  65 -- | If you rotate a cardinal direction four times in the clockwise
  66 --   (with respect to x) direction, you should wind up with the same
  67 --   direction.
  68 prop_four_cwx_is_identity :: Cardinal -> Bool
  69 prop_four_cwx_is_identity c =
  70     (cwx . cwx . cwx . cwx) c == c
  71
  72 -- | If you rotate a cardinal direction four times in the
  73 --   counter-clockwise (with respect to x) direction, you should wind up
  74 --   with the same direction.
  75 prop_four_ccwx_is_identity :: Cardinal -> Bool
  76 prop_four_ccwx_is_identity c =
  77     (ccwx . ccwx . ccwx . ccwx) c == c
  78
  79 -- | If you rotate a cardinal direction four times in the clockwise
  80 --   (with respect to y) direction, you should wind up with the same
  81 --   direction.
  82 prop_four_cwy_is_identity :: Cardinal -> Bool
  83 prop_four_cwy_is_identity c =
  84     (cwy . cwy . cwy . cwy) c == c
  85
  86 -- | If you rotate a cardinal direction four times in the counter-clockwise
  87 --   (with respect to y) direction, you should wind up with the same
  88 --   direction.
  89 prop_four_ccwy_is_identity :: Cardinal -> Bool
  90 prop_four_ccwy_is_identity c =
  91     (ccwy . ccwy . ccwy . ccwy) c == c
  92
  93 -- | If you rotate a cardinal direction four times in the clockwise
  94 --   (with respect to z) direction, you should wind up with the same
  95 --   direction.
  96 prop_four_cwz_is_identity :: Cardinal -> Bool
  97 prop_four_cwz_is_identity c =
  98     (cwz . cwz . cwz . cwz) c == c
  99
 100 -- | If you rotate a cardinal direction four times in the
 101 --   counter-clockwise (with respect to z) direction, you should wind up
 102 --   with the same direction.
 103 prop_four_ccwz_is_identity :: Cardinal -> Bool
 104 prop_four_ccwz_is_identity c =
 105     (ccwz . ccwz . ccwz . ccwz) c == c