{-# LANGUAGE FlexibleContexts #-} {-| Parsing and pretty printing of Roman numerals. This module provides functions for parsing and pretty printing Roman numerals. Because the notation of Roman numerals has varied through the centuries this package allows for some customisation using a configuration that is passed to the conversion functions. Exceptions are dealt with by wrapping the results of conversions in the error monad. -} module Text.RomanNumerals ( -- * Types NumeralConfig(..) -- * Sample configurations , modernRoman , simpleRoman -- * Pretty printing , convertTo , unsafeConvertTo , toRoman , unsafeToRoman -- * Parsing , convertFrom , fromRoman , unsafeConvertFrom , unsafeFromRoman ) where import Control.Monad.Error import qualified Data.List as L ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- -- |A configuration with which the 'convertTo' and 'convertFrom' -- functions can be parameterized. data (Ord n, Num n) => NumeralConfig n = NC { -- |The largest value that can be -- represented using this configuration. ncMax :: n -- |Symbol to represent the value 0. The -- Romans did not have a symbol for -- zero. If set to Nothing a -- 'convertFrom' 0 will throw an error. , ncZero :: Maybe String -- |A table of symbols and their numerical -- values. The table must be ordered with -- the largest symbols appearing -- first. If any symbol is the empty -- string then 'convertFrom' will be -- undefined. If any symbol in this table -- is associated with the value 0 both -- the convertTo and 'convertFrom' -- function will be undefined. , ncTable :: [(String, n)] } ------------------------------------------------------------------------------- -- Default tables ------------------------------------------------------------------------------- -- |Configuration for Roman numerals as they are commenly used -- today. The value 0 is represented by the empty string. It can be -- interpreted as not writing down a number. This configuration is -- limited to the range [1..3999]. Larger numbers can be represented -- using Roman numerals but you will need notations that are hard or -- impossible to express using strings. modernRoman :: (Ord n, Num n) => NumeralConfig n modernRoman = NC { ncMax = 3999 , ncZero = Just "" , ncTable = [ ("M", 1000) , ("CM", 900) , ("D", 500) , ("CD", 400) , ("C", 100) , ("XC", 90) , ("L", 50) , ("XL", 40) , ("X", 10) , ("IX", 9) , ("V", 5) , ("IV", 4) , ("I", 1) ] } -- |Configuration for Roman numerals that do not use the rule that a -- lower rank symbol can be placed before a higher rank symbol to -- denote the difference between them. Thus a numeral like "IV" will -- not be accepted or generated by this configuration. simpleRoman :: (Ord n, Num n) => NumeralConfig n simpleRoman = NC { ncMax = 3999 , ncZero = Just "" , ncTable = [ ("M", 1000) , ("D", 500) , ("C", 100) , ("L", 50) , ("X", 10) , ("V", 5) , ("I", 1) ] } ------------------------------------------------------------------------------- -- Pretty printing ------------------------------------------------------------------------------- -- |Converts a number to a Roman numeral according to the given -- configuration. Numbers which are out of bounds will cause -- exceptions to be thrown. An exception will also be raised if no -- representation is possible with the given configuration. If the -- value of any symbol in the configuration is equal to 0 or a symbol -- is the empty string this function is undefined. convertTo :: (Ord n, Num n, MonadError String m) => NumeralConfig n -> n -> m String convertTo nc n | n < 0 = throwError "Roman.convertTo: can't represent negative numbers" | n > maxN = throwError $ "Roman.convertTo: too large (max = " ++ (show maxN) ++ ")" | n == 0 = maybe (throwError "Roman.convertTo: no symbol for zero") return $ ncZero nc | otherwise = go n $ ncTable nc where maxN = ncMax nc go 0 _ = return "" go _ [] = throwError "Roman.convertTo: out of symbols" go n tab@(~(sym, val) : ts) | n >= val = liftM2 (++) (return sym) $ go (n - val) tab | otherwise = go n ts -- |Like 'convertTo', but exceptions are promoted to errors. unsafeConvertTo :: (Ord n, Num n) => NumeralConfig n -> n -> String unsafeConvertTo nc = either error id . convertTo nc -- |Converts a number to a modern Roman numeral. See 'convertTo' for -- possible exceptions. toRoman :: (Ord n, Num n, MonadError String m) => n -> m String toRoman = convertTo modernRoman -- |Like 'toRoman', but exceptions are promoted to errors. unsafeToRoman :: (Ord n, Num n) => n -> String unsafeToRoman = unsafeConvertTo modernRoman ------------------------------------------------------------------------------- -- Parsing ------------------------------------------------------------------------------- -- convertFrom nc xs == undefined when any symbol in the NumeralConfig -- nc is associated with the value 0. -- |Parses a string as a Roman numeral according to the given -- configuration. An exception will be raised if the input is not a -- valid numeral. convertFrom :: (Ord n, Num n, MonadError String m) => NumeralConfig n -> String -> m n convertFrom nc xs | maybe False (== xs) (ncZero nc) = return 0 | otherwise = do n <- (go 0 (ncTable nc) xs) xs' <- convertTo nc n if xs == xs' then return n else throwError "Roman.convertFrom: invalid Roman numeral" where go n _ [] = return n go _ [] xs = throwError $ "Roman.convertFrom: can't parse: '" ++ (take 5 xs) ++ "'" go n tab@((sym, val) : ts) xs = maybe (go n ts xs) (go (n + val) tab) $ L.stripPrefix sym xs -- |Like 'convertFrom', but exceptions are promoted to errors. unsafeConvertFrom :: (Ord n, Num n) => NumeralConfig n -> String -> n unsafeConvertFrom nc = either error id . convertFrom nc -- |Parses a string as a modern Roman numeral. See 'convertFrom' for -- possible exceptions. fromRoman :: (Ord n, Num n, MonadError String m) => String -> m n fromRoman = convertFrom modernRoman -- |Like 'fromRoman', but exceptions are promoted to errors. unsafeFromRoman :: (Ord n, Num n) => String -> n unsafeFromRoman = unsafeConvertFrom modernRoman ------------------------------------------------------------------------------- -- Properties ------------------------------------------------------------------------------- printParseIsId :: (Ord n, Num n) => NumeralConfig n -> String -> Bool printParseIsId nc xs = either (const True) id $ do n <- convertFrom nc xs xs' <- convertTo nc n return $ xs' == xs parsePrintIsId :: (Ord n, Num n) => NumeralConfig n -> n -> Bool parsePrintIsId nc n = either (const True) id $ do xs <- convertTo nc n n' <- convertFrom nc xs return $ n' == n