1 files changed, 68 insertions, 12 deletions
diff --git a/src/Expr.hs b/src/Expr.hs
index 4bf2c70..e427b65 100644
--- a/src/Expr.hs
+++ b/src/Expr.hs
@@ -18,19 +18,7 @@ data Expr
     | Function String Expr
     deriving (Eq)
 
-data Expr
-    = Atom
-    | BinOp
-    | Variable String
-    | Function String Expr
-
-
 instance Show Expr where
-    show (Rational r) = show r
-    show (Imaginary i) = show i ++ "i"
-    show (Complex a b) = show a ++ " + " ++ show b ++ "i"
-    show (Matrix m) = intercalate "\n" (map showRow m)
-        where showRow r = "[ " ++ intercalate ", " (map show r) ++ " ]"
     show (Add e1 e2) = show e1 ++ " + " ++ show e2
     show (Sub e1 e2) = show e1 ++ " - " ++ show e2
     show (Mul e1 e2) = show e1 ++ " * " ++ show e2
@@ -41,3 +29,71 @@ instance Show Expr where
     show (Variable name) = name
     show (Function name e) = name ++ "(" ++ show e ++ ")"
 
+
+-------------------------------------------------------------------------------
+-- Operators
+-------------------------------------------------------------------------------
+
+builtinAdd :: Expr -> Expr -> Maybe Expr
+
+builtinAdd (Rational a)    (Rational b)    = Just $ Rational (a + b)
+builtinAdd (Rational a)    (Imaginary b)   = Just $ Complex a b
+builtinAdd (Rational a)    (Complex br bi) = Just $ Complex (br + a) bi
+
+builtinAdd (Imaginary a)   (Imaginary b)   = Just $ Imaginary (a + b)
+builtinAdd (Imaginary a)   (Rational b)    = Just $ Complex b a
+builtinAdd (Imaginary a)   (Complex br bi) = Just $ Complex br (a + bi)
+
+builtinAdd (Complex ar ai) (Complex br bi) = Just $ Complex (ar + br) (ai + bi)
+builtinAdd (Complex ar ai) (Rational b)    = Just $ Complex (ar + b) ai
+builtinAdd (Complex ar ai) (Imaginary b)   = Just $ Complex ar (ai + b)
+
+builtinAdd _ _ = Nothing
+
+
+builtinSub :: Expr -> Expr -> Maybe Expr
+builtinSub a b = builtinAdd a =<< (Rational (-1) `builtinMul` b)
+
+
+-- could be derived from addition
+builtinMul :: Expr -> Expr -> Maybe Expr
+builtinMul (Rational a) (Rational b)    = Just $ Rational (a * b)
+builtinMul (Rational a) (Imaginary b)   = Just $ Imaginary (a * b)
+builtinMul (Rational a) (Complex br bi) = Just $ Complex (a * br) (a * bi)
+
+builtinMul (Imaginary a) (Imaginary b)   = Just $ Imaginary (a * b)
+builtinMul (Imaginary a) (Rational b)    = Just $ Complex b a
+builtinMul (Imaginary a) (Complex br bi) = Just $ Complex (a * br) (a * bi)
+
+builtinMul _ _ = Nothing
+
+
+builtinDiv :: Expr -> Expr -> Maybe Expr
+builtinDiv _ (Rational 0)  = Nothing
+builtinDiv _ (Imaginary 0) = Nothing
+builtinDiv _ (Complex 0 0) = Nothing
+builtinDiv a b = builtinMul a =<< (b `builtinExp` Rational (-1))
+
+
+builtinMod :: Expr -> Expr -> Maybe Expr
+builtinMod _ _ = Nothing
+
+
+-- could be derived from multiplication
+builtinExp :: Expr -> Expr -> Maybe Expr
+builtinExp (Rational a)  (Rational b) = Just $ Rational (a ** b)
+
+builtinExp (Imaginary a) (Rational b)
+  | b < 0     =  builtinDiv (Rational 1) =<< ((Imaginary a) `builtinExp` (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 `builtinExp` (Rational (b - 4))
+
+builtinExp _ _ = Nothing
+
+
+builtinDot :: Expr -> Expr -> Maybe Expr
+builtinDot (Matrix a) (Matrix b) = undefined
+builtinDot _ _ = Nothing