Revert "Remove almost all 'type' usage to make types more transparent"

This reverts commit 5120a44d0f.

Conflicts:
	Parser/Meshparser.hs

Test/Vector.hs

@@ -82,40 +82,40 @@ instance Arbitrary P2 where
 
 -- the point describing the lower left corner of the square
 -- must be part of the square
-inRangeProp1 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp1 :: Square -> Bool
 inRangeProp1 sq@((x1, y1), _) =
   inRange sq (p2 (x1, y1))
 
 
 -- the point describing the upper right corner of the square
 -- must be part of the square
-inRangeProp2 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp2 :: Square -> Bool
 inRangeProp2 sq@(_, (x2, y2)) =
   inRange sq (p2 (x2, y2))
 
 
 -- the point describing the upper left corner of the square
 -- must be part of the square
-inRangeProp3 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp3 :: Square -> Bool
 inRangeProp3 sq@((x1, _), (_, y2)) =
   inRange sq (p2 (x1, y2))
 
 
 -- the point describing the lower right corner of the square
 -- must be part of the square
-inRangeProp4 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp4 :: Square -> Bool
 inRangeProp4 sq@((_, y1), (x2, _)) =
   inRange sq (p2 (x2, y1))
 
 
 -- generating random points within the square
-inRangeProp5 :: ((Double, Double), (Double, Double)) -> Positive Double -> Positive Double -> Bool
+inRangeProp5 :: Square -> Positive Double -> Positive Double -> Bool
 inRangeProp5 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
   inRange sq (p2 (x1 + ((x2 - x1) / (a + 1)), y1 + ((y2 - y1) / (b + 1))))
 
 
 -- generating random points outside of the square
-inRangeProp6 :: ((Double, Double), (Double, Double)) -> Positive Double -> Positive Double -> Bool
+inRangeProp6 :: Square -> Positive Double -> Positive Double -> Bool
 inRangeProp6 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
   (not . inRange sq $ p2 (max x1 x2 + (a + 1), max y1 y2 + (b + 1)))
   && (not . inRange sq $ p2 (max x1 x2 + (a + 1), max y1 y2 - (b + 1)))
@@ -126,51 +126,51 @@ inRangeProp6 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
 
 
 -- apply id function on the point
-onPTProp1 :: P2 -> Bool
+onPTProp1 :: PT -> Bool
 onPTProp1 pt = onPT id pt == pt
 
 
 -- add a random value to the point coordinates
-onPTProp2 :: P2 -> Positive R2 -> Bool
+onPTProp2 :: PT -> Positive R2 -> Bool
 onPTProp2 pt (Positive (R2 rx ry))
   = onPT (\(x, y) -> (x + rx, y + ry)) pt /= pt
 
 
 -- angle between two vectors both on the x-axis must be 0
-getAngleProp1 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp1 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp1 (Positive (R2 x1 _)) (Positive (R2 x2 _))
   = getAngle (R2 x1 0) (R2 x2 0) == 0
 
 
 -- angle between two vectors both on the y-axis must be 0
-getAngleProp2 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp2 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp2 (Positive (R2 _ y1)) (Positive (R2 _ y2))
   = getAngle (R2 0 y1) (R2 0 y2) == 0
 
 
 -- angle between two vectors both on the x-axis but with opposite direction
 -- must be pi
-getAngleProp3 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp3 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp3 (Positive (R2 x1 _)) (Positive (R2 x2 _))
   = getAngle (R2 (negate x1) 0) (R2 x2 0) == pi
 
 
 -- angle between two vectors both on the y-axis but with opposite direction
 -- must be pi
-getAngleProp4 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp4 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp4 (Positive (R2 _ y1)) (Positive (R2 _ y2))
   = getAngle (R2 0 (negate y1)) (R2 0 y2) == pi
 
 
 -- angle between vector in x-axis direction and y-axis direction must be
 -- p/2
-getAngleProp5 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp5 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
   = getAngle (R2 x1 0) (R2 0 y2) == pi / 2
 
 
 -- commutative
-getAngleProp6 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp6 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp6 (Positive v1) (Positive v2)
   = getAngle v1 v2 == getAngle v2 v1
 
@@ -183,7 +183,7 @@ getAngleProp7 (PosRoundR2 v)
 
 
 -- commutative
-scalarProdProp1 :: R2 -> R2 -> Bool
+scalarProdProp1 :: Vec -> Vec -> Bool
 scalarProdProp1 v1 v2 = v1 `scalarProd` v2 == v2 `scalarProd` v1
 
 
@@ -212,7 +212,7 @@ scalarProdProp4 (RoundDouble s1) (RoundDouble s2) (RoundR2 v1) (RoundR2 v2)
 
 
 -- orthogonal
-scalarProdProp5 :: Positive R2 -> Positive R2 -> Bool
+scalarProdProp5 :: Positive Vec -> Positive Vec -> Bool
 scalarProdProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
   = scalarProd (R2 x1 0) (R2 0 y2) == 0
 
@@ -226,40 +226,40 @@ dimToSquareProp1 (x1, x2) (y1, y2) =
 -- multiply scalar with result of vecLength or with the vector itself...
 -- both results must be the same. We can't check against 0
 -- because of sqrt in vecLength.
-vecLengthProp1 :: PosRoundDouble -> R2 -> Bool
+vecLengthProp1 :: PosRoundDouble -> Vec -> Bool
 vecLengthProp1 (PosRoundDouble r) v
   = abs (vecLength v * r - vecLength (scalarMul r v)) < 0.0001
 
 
 -- convert to vector and back again
-pt2VecProp1 :: P2 -> Bool
+pt2VecProp1 :: PT -> Bool
 pt2VecProp1 pt = (vec2Pt . pt2Vec $ pt) == pt
 
 
 -- unbox coordinates and check if equal
-pt2VecProp2 :: P2 -> Bool
+pt2VecProp2 :: PT -> Bool
 pt2VecProp2 pt = (unr2 . pt2Vec $ pt) == unp2 pt
 
 
 -- convert to point and back again
-vec2PtProp1 :: R2 -> Bool
+vec2PtProp1 :: Vec -> Bool
 vec2PtProp1 v = (pt2Vec . vec2Pt $ v) == v
 
 
 -- unbox coordinates and check if equal
-vec2PtProp2 :: R2 -> Bool
+vec2PtProp2 :: Vec -> Bool
 vec2PtProp2 v = (unp2 . vec2Pt $ v) == unr2 v
 
 
 -- vector from a to b must not be the same as b to a
-vp2Prop1 :: P2 -> P2 -> Bool
+vp2Prop1 :: PT -> PT -> Bool
 vp2Prop1 p1' p2'
   | p1' == origin && p2' == origin = True
   | otherwise = vp2 p1' p2' /= vp2 p2' p1'
 
 
 -- negating vector from a to be must be the same as vector b to a
-vp2Prop2 :: P2 -> P2 -> Bool
+vp2Prop2 :: PT -> PT -> Bool
 vp2Prop2 p1' p2'
   | p1' == origin && p2' == origin = True
   | otherwise = vp2 p1' p2' == (\(R2 x y) -> negate x ^& negate y)
@@ -270,5 +270,5 @@ vp2Prop2 p1' p2'
 
 
 -- determinant of the 3 same points is always 0
-detProp1 :: P2 -> Bool
+detProp1 :: PT -> Bool
 detProp1 pt' = det pt' pt' pt' == 0