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module Expr where
import Control.Monad
import Data.List
import qualified Data.Map as M
data Expr
= Rational Float -- values
| Complex Float Float
| Matrix [[Expr]]
| Add Expr Expr --- ops
| Sub Expr Expr
| Mul Expr Expr
| Div Expr Expr
| Mod Expr Expr
| Exp Expr Expr
| Dot Expr Expr
| Variable String -- lables
| Function String Expr
deriving (Eq)
instance Show Expr where
show (Rational a) = show a
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
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 (Complex _ _) = True
isLitteral _ = False
isIgnored :: Expr -> Bool
isIgnored (Variable _) = True
-- isIgnored (Function _ _) = True
isIgnored (Add _ _) = True
isIgnored (Sub _ _) = True
isIgnored (Mul _ _) = True
isIgnored (Div _ _) = True
isIgnored (Mod _ _) = True
isIgnored (Exp _ _) = True
isIgnored (Dot _ _) = True
isIgnored _ = False
-------------------------------------------------------------------------------
-- Operators
-------------------------------------------------------------------------------
add :: Expr -> Expr -> Maybe Expr
add (Rational a) (Rational b) = Just $ Rational (a + b)
add (Rational 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 a b = ignoreCheck a b Add
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) (Complex br bi) = Just $ Complex (a * br) (a * bi)
mul a b = ignoreCheck a b Mul
div :: Expr -> Expr -> Maybe Expr
div _ (Rational 0) = Nothing
div _ (Complex 0 0) = Nothing
div a b = mul a =<< b `Expr.exp` Rational (-1)
mod :: Expr -> Expr -> Maybe Expr
mod a b = ignoreCheck a b Mod
exp :: Expr -> Expr -> Maybe Expr
exp (Rational a) (Rational b) = Just $ Rational (a ** b)
exp a b = ignoreCheck a b Exp
dot :: Expr -> Expr -> Maybe Expr
dot (Matrix a) (Matrix b)
| 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)]
dotProd :: [Expr] -> [Expr] -> Maybe Expr
dotProd r c = foldM add (Rational 0) =<< zipWithM mul r c
dot a b = ignoreCheck a b Dot
ignoreCheck :: Expr -> Expr -> (Expr -> Expr -> Expr) -> Maybe Expr
ignoreCheck a b constructor
| isIgnored a || isIgnored b = Just $ constructor a b
| otherwise = Nothing
-------------------------------------------------------------------------------
-- Evaluation
-------------------------------------------------------------------------------
type LabelMap a = M.Map String a
data Context = Context { variables :: LabelMap Expr
, functions :: LabelMap (String, Expr)
}
evalIgnored :: Expr -> Context -> String -> Maybe Expr
evalIgnored (Variable name) c i
| name == i = Just $ Variable name
| otherwise = name `M.lookup` (variables c) >>= (\e -> evalIgnored e c i)
evalIgnored (Function name e) (Context vars funcs) i =
do arg <- evalIgnored e (Context vars funcs) i
(argName, functionExpr) <- name `M.lookup` funcs
let localVars = M.insert argName arg vars
evalIgnored functionExpr (Context localVars funcs) i
evalIgnored (Matrix m) c i = Matrix <$> mapM (mapM (\e -> evalIgnored e c i)) m
evalIgnored (Add e1 e2) c i = evalIgnoredInfix e1 e2 Add add c i
evalIgnored (Sub e1 e2) c i = evalIgnoredInfix e1 e2 Sub sub c i
evalIgnored (Mul e1 e2) c i = evalIgnoredInfix e1 e2 Mul mul c i
evalIgnored (Div e1 e2) c i = evalIgnoredInfix e1 e2 Div Expr.div c i
evalIgnored (Mod e1 e2) c i = evalIgnoredInfix e1 e2 Mod Expr.mod c i
evalIgnored (Exp e1 e2) c i = evalIgnoredInfix e1 e2 Exp Expr.exp c i
evalIgnored (Dot e1 e2) c i = evalIgnoredInfix e1 e2 Dot dot c i
evalIgnored x _ _
| isLitteral x = Just x
| otherwise = Nothing
evalIgnoredInfix :: Expr -> Expr ->
(Expr -> Expr -> Expr) ->
(Expr -> Expr -> Maybe Expr) ->
Context -> String -> Maybe Expr
evalIgnoredInfix e1 e2 cons f c i
| isVariable e1 && varName e1 == i && isVariable e2 && varName e2 == i = Just $ cons e1 e2
| isVariable e1 && varName e1 == i = evalIgnored e2 c i >>= (\x -> Just $ cons e1 x)
| isVariable e2 && varName e2 == i = evalIgnored e1 c i >>= (\x -> Just $ cons x e2)
| otherwise = do a <- evalIgnored e1 c i
b <- evalIgnored e2 c i
f a b
where varName (Variable name) = name
varName _ = ""
isVariable (Variable _) = True
isVariable _ = False
-- bubbleVariable :: String -> Expr -> Expr -- with tree rotation
-- bubbleVariable i (Add l r)
eval :: Expr -> Context -> Maybe Expr
eval e c = evalIgnored e c ""
|
