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Mere interaction with a user through +a computer network, with no transfer of a copy, diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/mathexpr.cabal b/mathexpr.cabal new file mode 100644 --- /dev/null +++ b/mathexpr.cabal @@ -0,0 +1,25 @@ +name: mathexpr +version: 0.1.0.0 +synopsis: Parse and evaluate math expressions with variables and functions +description: A simple tool to evaluate math expressions as strings with support for custom functions and operators +homepage: https://github.com/mdibaiee/mathexpr +license: GPL-3 +license-file: LICENSE +author: Mahdi Dibaiee +maintainer: mdibaiee@aol.com +copyright: 2016 Mahdi Dibaiee +category: Math +build-type: Simple +-- extra-source-files: +cabal-version: >=1.10 + +library + hs-source-dirs: src + exposed-modules: Data.MathExpr + build-depends: base >= 4.7 && < 5, + data-default-class + default-language: Haskell2010 + +source-repository head + type: git + location: https://github.com/mdibaiee/mathexpr diff --git a/src/Data/MathExpr.hs b/src/Data/MathExpr.hs new file mode 100644 --- /dev/null +++ b/src/Data/MathExpr.hs @@ -0,0 +1,108 @@ +module Data.MathExpr + ( evaluate + , Settings (..) + , defaultFunctions + , defaultOperators + ) where + import Data.Default.Class + import Data.Maybe (isJust, fromJust) + import Debug.Trace + import Data.List (find) + + data Settings = Settings { operators :: [(Char, Int, Double -> Double -> Double)] + , functions :: [(String, Double -> Double)] + } + + defaultOperators = [ + ('+', 0, (+)), ('-', 0, (-)), + ('*', 1, (*)), ('/', 1, (/)), + ('^', 2, (**)) + ] + defaultFunctions = [("ln", log), ("sin", sin), ("cos", cos)] + + instance Default Settings where + def = Settings { operators = defaultOperators + , functions = defaultFunctions + } + toPostfix :: Settings -> String -> String + toPostfix settings s = helper (tokenize s) [] [] + where + ops = operators settings + fns = functions settings + + helper :: [String] -> [String] -> String -> String + helper [] os out = out ++ concat os + helper (c:cs) os out + | head c == '(' = helper cs (c:os) out + | head c == ')' && head os == "(" = helper cs (tail os) out + | head c == ')' = helper (c:cs) (tail os) (out ++ pad (head os)) + | isOperator c && (null os || precedence c > precedence (head os)) = helper cs (c:os) out + | isOperator c = helper (c:cs) (tail os) (out ++ pad (head os)) + | otherwise = helper cs os (out ++ pad c) + + isOperator cs = isOp cs || isFunction cs + isOp cs = isJust $ (head cs) `triLookup` ops + isFunction cs = isJust $ cs `lookup` fns + precedence cs + | isFunction cs = Just 999 + | otherwise = (head cs) `triLookup` ops + + tokenize :: String -> [String] + tokenize str = words $ helper str + where + helper :: String -> String + helper [] = [] + helper (c:cs) + | isAlphanumeric c = c : helper cs + | isSymbol c = pad [c] ++ helper cs + + replaceVariables :: String -> [(String, Double)] -> String + replaceVariables str [] = str + replaceVariables str vars = concatMap replace (tokenize str) + where + replace c + | isVariable c = pad $ show $ fromJust $ c `lookup` vars + | otherwise = c + + isVariable c = isJust $ c `lookup` vars + + -- | Evaluate an expression + -- Example: `evaluate def "x + y ^ 2" [("x", 1), ("y", 2)] + evaluate :: Settings -> String -> [(String, Double)] -> Double + evaluate settings expr vars = + let postfix = toPostfix settings expr + replaced = replaceVariables postfix vars + in helper (tokenize replaced) [] + where + ops = operators settings + fns = functions settings + + helper :: [String] -> [String] -> Double + helper [] [o] = read o + helper (c:cs) os + | isOperator c = + let result = (operatorFunction c) (read . head . tail $ os) (read . head $ os) + in helper cs $ (show result) : drop 2 os + | isFunction c = + let result = (function c) (read . head $ os) + in helper cs $ (show result) : tail os + | otherwise = helper cs (c:os) + + isOperator cs = isJust $ (head cs) `triLookup` ops + isFunction cs = isJust $ cs `lookup` fns + + function cs = fromJust $ cs `lookup` fns + operatorFunction cs = case find (\(a, _, _) -> a == head cs) ops of + Just (_, _, c) -> c + Nothing -> const (const 0) + isParen cs = head cs `elem` ['(', ')'] + + alphanumeric = '.' : ['a'..'z'] ++ ['0'..'9'] + isAlphanumeric = (`elem` alphanumeric) + isSymbol = not . (`elem` alphanumeric) + + triLookup :: (Eq a) => a -> [(a, b, c)] -> Maybe b + triLookup a x = lookup a $ map (\(a, b, _) -> (a, b)) x + + pad :: String -> String + pad x = ' ' : x ++ [' ']