Add a bunch of new Cardinal tests.

diff --git a/src/Tests/Cardinal.hs b/src/Tests/Cardinal.hs
index 907e3d9968ad8fbb838c922f24a6bccd201fe76f..0d8d592e7d37a75c233547421c404fa03a53d380 100644 (file)
--- a/src/Tests/Cardinal.hs
+++ b/src/Tests/Cardinal.hs
@@ -48,13 +48,24 @@ instance Arbitrary Cardinal where
           cquot = liftM2 Quotient arbitrary arbitrary
 
 
+-- | A list of all directions, sans the interior and composite types.
+all_directions :: [Cardinal]
+all_directions = [L, R, F, B, D, T, FL, FR, FD, FT,
+                  BL, BR, BD, BT, LD, LT, RD, RT, FLD,
+                  FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+
+
+-- | If we rotate a direction (other than front or back)
+--   counter-clockwise with respect to the x-axis, we should get a new
+--   direction.
 prop_ccwx_rotation_changes_direction :: Cardinal -> Property
 prop_ccwx_rotation_changes_direction c =
-    -- The front and back faces are unchanged by x-rotation.
     c `elem` [L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
           ==> ccwx c /= c
 
+-- | If we rotate a direction (other than front or back) clockwise
+--   with respect to the x-axis, we should get a new direction.
 prop_cwx_rotation_changes_direction :: Cardinal -> Property
 prop_cwx_rotation_changes_direction c =
     -- The front and back faces are unchanged by x-rotation.
@@ -62,6 +73,97 @@ prop_cwx_rotation_changes_direction c =
                RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
           ==> cwx c /= c
 
+-- | If we rotate a direction (other than left or right)
+--   counter-clockwise with respect to the y-axis, we should get a new
+--   direction.
+prop_ccwy_rotation_changes_direction :: Cardinal -> Property
+prop_ccwy_rotation_changes_direction c =
+    c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+               RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+          ==> ccwy c /= c
+
+
+-- | If we rotate a direction (other than left or right) clockwise
+--   with respect to the y-axis, we should get a new direction.
+prop_cwy_rotation_changes_direction :: Cardinal -> Property
+prop_cwy_rotation_changes_direction c =
+    c `elem` [F, B, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+               RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+          ==> cwy c /= c
+
+
+-- | If we rotate a direction (other than top or down)
+--   counter-clockwise with respect to the z-axis, we should get a new
+--   direction.
+prop_ccwz_rotation_changes_direction :: Cardinal -> Property
+prop_ccwz_rotation_changes_direction c =
+    c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+               RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+          ==> ccwz c /= c
+
+
+-- | If we rotate a direction (other than top or down) clockwise with
+--   respect to the z-axis, we should get a new direction.
+prop_cwz_rotation_changes_direction :: Cardinal -> Property
+prop_cwz_rotation_changes_direction c =
+    c `elem` [L, R, F, B, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT,
+               RD, RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT]
+          ==> cwz c /= c
+
+
+-- | If we are given a direction c, there should only be one direction
+--   d which, when rotated counter-clockwise with respect to the
+--   x-axis, produces c.
+prop_ccwx_rotation_result_unique :: Cardinal -> Property
+prop_ccwx_rotation_result_unique c =
+    c `elem` all_directions ==>
+          (length [ d | d <- all_directions, ccwx d == c ]) == 1
+
+-- | If we are given a direction c, there should only be one direction
+--   d which, when rotated clockwise with respect to the x-axis,
+--   produces c.
+prop_cwx_rotation_result_unique :: Cardinal -> Property
+prop_cwx_rotation_result_unique c =
+    c `elem` all_directions ==>
+          (length [ d | d <- all_directions, cwx d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+--   d which, when rotated counter-clockwise with respect to the
+--   y-axis, produces c.
+prop_ccwy_rotation_result_unique :: Cardinal -> Property
+prop_ccwy_rotation_result_unique c =
+    c `elem` all_directions ==>
+          (length [ d | d <- all_directions, ccwy d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+--   d which, when rotated clockwise with respect to the y-axis,
+--   produces c.
+prop_cwy_rotation_result_unique :: Cardinal -> Property
+prop_cwy_rotation_result_unique c =
+    c `elem` all_directions ==>
+          (length [ d | d <- all_directions, cwy d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+--   d which, when rotated counter-clockwise with respect to the
+--   z-axis, produces c.
+prop_ccwz_rotation_result_unique :: Cardinal -> Property
+prop_ccwz_rotation_result_unique c =
+    c `elem` all_directions ==>
+          (length [ d | d <- all_directions, ccwz d == c ]) == 1
+
+
+-- | If we are given a direction c, there should only be one direction
+--   d which, when rotated clockwise with respect to the z-axis,
+--   produces c.
+prop_cwz_rotation_result_unique :: Cardinal -> Property
+prop_cwz_rotation_result_unique c =
+    c `elem` all_directions ==>
+          (length [ d | d <- all_directions, cwz d == c ]) == 1
+
+
 -- | If you rotate a cardinal direction four times in the clockwise
 --   (with respect to x) direction, you should wind up with the same
 --   direction.