Removed Imaginary type, Added variable name check (/= i), Added Matrix check if rectangular

1 files changed, 20 insertions, 25 deletions

diff --git a/src/Expr.hs b/src/Expr.hs
index 852ee47..93828d9 100644
--- a/src/Expr.hs
+++ b/src/Expr.hs
@@ -4,10 +4,27 @@ import           Control.Monad
 import           Data.List
 import qualified Data.Map      as M
 
+-- data Operand
+--     = Rational Float
+--     | Complex Float Float
+--     | Matrix [[Operand]]
+--
+--
+-- data (Operable a, Operable b) => Operator a b
+--     = Add a b
+--     | Sub a b
+--     | Mul a b
+--     | Div a b
+--     | Mod a b
+--     | Exp a b
+--     | Dot a b
+--
+-- data Label
+--     = Variable String
+--     | Function String Expr
 
 data Expr
     = Rational Float  -- values
-    | Imaginary Float
     | Complex Float Float
     | Matrix [[Expr]]
 
@@ -25,8 +42,7 @@ data Expr
 
 instance Show Expr where
     show (Rational a)      = show a
-    show (Imaginary b)     = show b ++ "i"
-    show (Complex a b)     = show a ++ " + " ++ show (Imaginary b)
+    show (Complex a b)     = (if a /= 0 then show a ++ " + " else "") ++ show b ++ "i"
     show (Add e1 e2)       = show e1 ++ " + " ++ show e2
     show (Sub e1 e2)       = show e1 ++ " - " ++ show e2
     show (Mul e1 e2)       = show e1 ++ " * " ++ show e2
@@ -42,7 +58,6 @@ instance Show Expr where
 
 isLitteral :: Expr -> Bool
 isLitteral (Rational _)  = True
-isLitteral (Imaginary _) = True
 isLitteral (Complex _ _) = True
 isLitteral _             = False
 
@@ -53,16 +68,10 @@ isLitteral _             = False
 add :: Expr -> Expr -> Maybe Expr
 
 add (Rational a)    (Rational b)    = Just $ Rational (a + b)
-add (Rational a)    (Imaginary b)   = Just $ Complex a b
 add (Rational a)    (Complex br bi) = Just $ Complex (br + a) bi
 
-add (Imaginary a)   (Imaginary b)   = Just $ Imaginary (a + b)
-add (Imaginary a)   (Rational b)    = Just $ Complex b a
-add (Imaginary a)   (Complex br bi) = Just $ Complex br (a + bi)
-
 add (Complex ar ai) (Complex br bi) = Just $ Complex (ar + br) (ai + bi)
 add (Complex ar ai) (Rational b)    = Just $ Complex (ar + b) ai
-add (Complex ar ai) (Imaginary b)   = Just $ Complex ar (ai + b)
 
 add _ _                             = Nothing
 
@@ -73,19 +82,14 @@ sub a b = add a =<< Rational (-1) `mul` b
 
 mul :: Expr -> Expr -> Maybe Expr
 mul (Rational a) (Rational b)     = Just $ Rational (a * b)
-mul (Rational a) (Imaginary b)    = Just $ Imaginary (a * b)
 mul (Rational a) (Complex br bi)  = Just $ Complex (a * br) (a * bi)
 
-mul (Imaginary a) (Imaginary b)   = Just $ Imaginary (a * b)
-mul (Imaginary a) (Rational b)    = Just $ Complex b a
-mul (Imaginary a) (Complex br bi) = Just $ Complex (a * br) (a * bi)
 
 mul _ _                           = Nothing
 
 
 div :: Expr -> Expr -> Maybe Expr
 div _ (Rational 0)  = Nothing
-div _ (Imaginary 0) = Nothing
 div _ (Complex 0 0) = Nothing
 div a b             = mul a =<< b `Expr.exp` Rational (-1)
 
@@ -96,21 +100,12 @@ mod _ _ = Nothing
 
 exp :: Expr -> Expr -> Maybe Expr
 exp (Rational a)  (Rational b) = Just $ Rational (a ** b)
-
-exp (Imaginary a) (Rational b)
-  | b < 0     = Expr.div (Rational 1) =<< Imaginary a `Expr.exp` Rational b
-  | b == 0    = Just $ Rational a
-  | b == 1    = Just $ Imaginary a
-  | b == 2    = Just $ Rational (-a)
-  | b == 3    = Just $ Imaginary (-a)
-  | otherwise = Imaginary a `Expr.exp` Rational (b - 4)
-
 exp _ _ = Nothing
 
 
 dot :: Expr -> Expr -> Maybe Expr
 dot (Matrix a) (Matrix b)
-    | shape a == shape bT = Matrix <$> mapM (\ai -> mapM (dotProd ai) bT) a
+    | shape a == shape bT = Matrix <$> mapM (\aRow -> mapM (dotProd aRow) bT) a
     | otherwise           = Nothing
     where bT = transpose b
           shape m = [length m, length (head m)]