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module Expr where
import Data.List
import qualified Data.Map as M
import Control.Monad
data Expr
= Rational Float
| Imaginary Float
| Complex Float Float
| Matrix [[Expr]]
| Add Expr Expr
| Sub Expr Expr
| Mul Expr Expr
| Div Expr Expr
| Mod Expr Expr
| Exp Expr Expr
| Dot Expr Expr
| Variable String
| Function String Expr
deriving (Eq)
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 (Add e1 e2) = show e1 ++ " + " ++ show e2
show (Sub e1 e2) = show e1 ++ " - " ++ show e2
show (Mul e1 e2) = show e1 ++ " * " ++ show e2
show (Div e1 e2) = show e1 ++ " / " ++ show e2
show (Mod e1 e2) = show e1 ++ " % " ++ show e2
show (Exp e1 e2) = show e1 ++ " ^ " ++ show e2
show (Dot e1 e2) = show e1 ++ " ** " ++ show e2
show (Variable name) = name
show (Function name e) = name ++ "(" ++ show e ++ ")"
show (Matrix rows) = intercalate "\n" $ map showRow rows
where showRow r = "[ " ++ (intercalate ", " $ map show r) ++ " ]"
isLitteral :: Expr -> Bool
isLitteral (Rational _) = True
isLitteral (Imaginary _) = True
isLitteral (Complex _ _) = True
isLitteral _ = False
-------------------------------------------------------------------------------
-- Operators
-------------------------------------------------------------------------------
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
sub :: Expr -> Expr -> Maybe Expr
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)
mod :: Expr -> Expr -> Maybe Expr
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 <$> mapM (\ai -> mapM (dotProd ai) bT) a
| otherwise = Nothing
where bT = transpose b
shape m = [length m, length (head m)]
dotProd :: [Expr] -> [Expr] -> Maybe Expr
dotProd r c = foldM add (Rational 0) =<< zipWithM mul r c
dot _ _ = Nothing
-------------------------------------------------------------------------------
-- Evaluation
-------------------------------------------------------------------------------
type LabelMap a = M.Map String a
data Context = Context { variables :: LabelMap Expr
, functions :: LabelMap (String, Expr)
}
eval :: Expr -> Context -> Maybe Expr
eval (Add e1 e2) c = evalInfix e1 e2 add c
eval (Sub e1 e2) c = evalInfix e1 e2 sub c
eval (Mul e1 e2) c = evalInfix e1 e2 mul c
eval (Div e1 e2) c = evalInfix e1 e2 Expr.div c
eval (Mod e1 e2) c = evalInfix e1 e2 Expr.mod c
eval (Exp e1 e2) c = evalInfix e1 e2 Expr.exp c
eval (Dot e1 e2) c = evalInfix e1 e2 dot c
eval (Variable name) c = name `M.lookup` (variables c) >>= (\e -> eval e c)
eval (Function name e) (Context vars funcs) =
do arg <- eval e (Context vars funcs)
(argName, functionExpr) <- name `M.lookup` funcs
let localVars = M.insert argName arg vars
eval functionExpr (Context localVars funcs)
eval (Matrix m) c = Matrix <$> mapM (mapM (\e -> eval e c)) m
eval x _
| isLitteral x = Just x
| otherwise = Nothing
evalInfix :: Expr -> Expr -> (Expr -> Expr -> Maybe Expr) -> Context -> Maybe Expr
evalInfix e1 e2 f c = do a <- eval e1 c
b <- eval e2 c
f a b
|
