{-# LANGUAGE AllowAmbiguousTypes #-} {-# LANGUAGE DeriveLift #-} {-# LANGUAGE InstanceSigs #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeApplications #-} -- | Defines a 'D10' type as a newtype for any type with an -- instance of the 'Num' class, where the values are restricted -- to numbers between @'fromInteger' 0@ and @'fromInteger' 9@. module Data.D10.Num ( -- * Type D10 (..) -- $bounded -- $enum -- * Quasi-quoters , d10 , d10list -- * Splice expressions , d10Exp , d10ListExp -- * Converting between D10 and Char , d10Char , charD10Maybe , charD10Either , charD10Fail -- * Converting between D10 and String , d10Str , strD10Maybe , strD10Either , strD10Fail , isD10Str -- * Converting between [D10] and String , strD10ListMaybe , strD10ListEither , strD10ListFail -- * Converting between D10 and Natural , d10Nat , natD10Maybe , natD10Either , natD10Fail , natMod10 -- * Converting between D10 and Integer , d10Integer , integerD10Maybe , integerD10Either , integerD10Fail , integerMod10 -- * Converting between D10 and Int , d10Int , intD10Maybe , intD10Either , intD10Fail , intMod10 -- * Converting between D10 and general numeric types , d10Num , integralD10Maybe , integralD10Either , integralD10Fail , integralMod10 ) where import Data.D10.Predicate -- base import Control.Monad ((>=>)) import Control.Monad.Fail (MonadFail (fail)) import Data.Char (chr, ord) import Data.Monoid (Endo (..)) import GHC.Generics (Generic) import Numeric.Natural (Natural) import Prelude hiding (fail) -- template-haskell import Language.Haskell.TH (Exp, Q) import Language.Haskell.TH.Quote (QuasiQuoter (..)) import Language.Haskell.TH.Syntax (Lift (lift)) -- $setup -- >>> :set -XQuasiQuotes -- >>> :set -XTemplateHaskell --------------------------------------------------- -- | A value of some numeric type @a@ between -- @'fromInteger' 0@ and @'fromInteger' 9@. -- -- The "Data.D10.Num" module provides many functions for -- constructing 'D10' values, including: -- -- * @'integerD10Maybe' :: 'Integer' -> 'Maybe' 'D10'@ -- * @'integerMod10' :: 'Integer' -> 'D10'@ -- -- There are also several ways to safely write 'D10' literals -- using Template Haskell: -- -- * With the @QuasiQuotes@ GHC extension enabled, you can write -- use the quasi-quoters 'd10' and 'd10list'. -- * With the @TemplateHaskell@ GHC extension enabled, you can -- splice expressions produced by 'd10Exp' and 'd10ListExp'. newtype D10 a = D10_Unsafe a -- ^ The constructor's name include the word "unsafe" as a reminder -- that you should generally avoid using it directly, because it -- allows constructing invalid 'D10' values. deriving (Eq, Ord, Lift) -- $bounded -- ==== Bounded -- -- >>> minBound :: D10 Integer -- [d10|0|] -- -- >>> maxBound :: D10 Integer -- [d10|9|] instance Num a => Bounded (D10 a) where minBound = D10_Unsafe 0 maxBound = D10_Unsafe 9 -- $enum -- ==== Enum -- -- >>> [ [d10|5|] .. ] -- [d10list|56789|] -- -- >>> [ [d10|4|] .. [d10|7|] ] -- [d10list|4567|] -- -- >>> [ [d10|5|], [d10|4|] .. ] -- [d10list|543210|] -- -- >>> [ [d10|1|], [d10|3|] .. ] -- [d10list|13579|] -- -- >>> [ minBound .. maxBound ] :: [D10 Integer] -- [d10list|0123456789|] instance Integral a => Enum (D10 a) where fromEnum :: D10 a -> Int fromEnum = d10Int toEnum :: Int -> D10 a toEnum = either error id . intD10Either enumFrom :: D10 a -> [D10 a] enumFrom x = enumFromTo x maxBound enumFromThen :: D10 a -> D10 a -> [D10 a] enumFromThen x y = enumFromThenTo x y bound where bound | fromEnum y >= fromEnum x = maxBound | otherwise = minBound succ (D10_Unsafe 9) = error "D10 overflow" succ (D10_Unsafe x) = D10_Unsafe (succ x) pred (D10_Unsafe 0) = error "D10 underflow" pred (D10_Unsafe x) = D10_Unsafe (pred x) --------------------------------------------------- -- | Shows base-10 digits using the quasiquoters defined in -- "Data.D10.Char". A single digit is displayed using 'd10'. -- A list of digits is displayed using 'd10list'. instance Integral a => Show (D10 a) where showsPrec _ x = showString "[d10|" . showsChar x . showString "|]" showList xs = showString "[d10list|" . showsStr xs . showString "|]" showsChar :: Integral a => D10 a -> ShowS showsChar = showChar . d10Char showsStr :: Integral a => [D10 a] -> ShowS showsStr = appEndo . foldMap (Endo . showsChar) --------------------------------------------------- -- | Convert a 'D10' to its underlying 'Char' representation. -- -- >>> d10Char [d10|7|] -- '7' d10Char :: Integral a => D10 a -> Char d10Char (D10_Unsafe x) = chr (ord '0' + fromIntegral x) -- | Convert a 'D10' to a 'String'. -- -- @'d10Str' x = ['d10Char' x]@ -- -- >>> d10Str [d10|7|] -- "7" d10Str :: Integral a => D10 a -> String d10Str x = [d10Char x] -- | Convert a 'D10' to a 'Natural'. -- -- 'd10Num' is a more general version of this function. -- -- >>> d10Nat [d10|7|] -- 7 d10Nat :: Integral a => D10 a -> Natural d10Nat = d10Num -- | Convert a 'D10' to an 'Integer'. -- -- 'd10Num' is a more general version of this function. -- -- >>> d10Integer [d10|7|] -- 7 d10Integer :: Integral a => D10 a -> Integer d10Integer = d10Num -- | Convert a 'D10' to an 'Int'. -- -- 'd10Num' is a more general version of this function. -- -- >>> d10Int [d10|7|] -- 7 d10Int :: Integral a => D10 a -> Int d10Int = d10Num -- | Convert a 'D10' to any kind of number with a 'Num' instance. -- -- Specialized versions of this function include 'd10Nat', -- 'd10Integer', and 'd10Int'. -- -- >>> d10Num [d10|7|] :: Integer -- 7 d10Num :: (Integral b, Num a) => D10 b -> a d10Num (D10_Unsafe x) = fromIntegral x --------------------------------------------------- -- | The 'D10' which is uniquely congruent modulo 10 to the given 'Natural'. -- -- 'integralMod10' is a more general version of this function. -- -- >>> natMod10 56 :: D10 Int -- [d10|6|] natMod10 :: Num a => Natural -> D10 a natMod10 = integralMod10 -- | The 'D10' which is uniquely congruent modulo 10 to the given 'Integer'. -- -- 'integralMod10' is a more general version of this function. -- -- >>> integerMod10 56 :: D10 Int -- [d10|6|] -- -- >>> integerMod10 (-56) :: D10 Int -- [d10|4|] integerMod10 :: Num a => Integer -> D10 a integerMod10 = integralMod10 -- | The 'D10' which is uniquely congruent modulo 10 to the given 'Int'. -- -- 'integralMod10' is a more general version of this function. -- -- >>> intMod10 56 :: D10 Int -- [d10|6|] -- -- >>> intMod10 (-56) :: D10 Int -- [d10|4|] intMod10 :: Num a => Int -> D10 a intMod10 = integralMod10 -- | The 'D10' which is uniquely congruent modulo 10 to the given number -- (whose type must have an instance of the 'Integral' class). -- -- Specialized versions of this function include 'natMod10', -- 'integerMod10', and 'intMod10'. -- -- >>> integralMod10 (56 :: Integer) :: D10 Int -- [d10|6|] -- -- >>> integralMod10 ((-56) :: Integer) :: D10 Int -- [d10|4|] integralMod10 :: (Num b, Integral a) => a -> D10 b integralMod10 x = D10_Unsafe (fromIntegral (x `mod` 10)) --------------------------------------------------- -- | Convert a 'Char' to a 'D10' if it is within the range -- @'0'@ to @'9'@, or produce 'Nothing' otherwise. -- -- @'Data.D10.Predicate.isD10Char' x = 'Data.Maybe.isJust' ('charD10Maybe' x)@ -- -- 'charD10Fail' is a more general version of this function. -- -- >>> charD10Maybe '5' -- Just [d10|5|] -- -- >>> charD10Maybe 'a' -- Nothing charD10Maybe :: Num a => Char -> Maybe (D10 a) charD10Maybe x | isD10Char x = Just (D10_Unsafe (fromIntegral (ord x - ord '0'))) | otherwise = Nothing -- | Convert a 'String' to a 'D10' if it consists of exactly one -- character and that character is within the range @'0'@ to @'9'@, -- or produce 'Nothing' otherwise. -- -- @'Data.D10.Predicate.isD10Str' x = 'Data.Maybe.isJust' ('strD10Maybe' x)@ -- -- 'strD10Fail' is a more general version of this function. -- -- >>> strD10Maybe "5" -- Just [d10|5|] -- -- >>> strD10Maybe "a" -- Nothing -- -- >>> strD10Maybe "58" -- Nothing strD10Maybe :: Num a => String -> Maybe (D10 a) strD10Maybe [x] = charD10Maybe x strD10Maybe _ = Nothing -- | Convert a 'String' to a list of 'D10' if all of the characters -- in the string are within the range @'0'@ to @'9'@, or produce -- 'Nothing' otherwise. -- -- @'Data.D10.Predicate.isD10Str' x = 'Data.Maybe.isJust' ('strD10ListMaybe' x)@ -- -- 'strD10ListFail' is a more general version of this function. -- -- >>> strD10ListMaybe "5" -- Just [d10list|5|] -- -- >>> strD10ListMaybe "a" -- Nothing -- -- >>> strD10ListMaybe "58" -- Just [d10list|58|] strD10ListMaybe :: Num a => String -> Maybe [D10 a] strD10ListMaybe = traverse charD10Maybe -- | Convert a 'Natural' to a 'D10' if it is less than 10, -- or produce 'Nothing' otherwise. -- -- @'Data.D10.Predicate.isD10Nat' x = 'Data.Maybe.isJust' ('natD10Maybe' x)@ -- -- 'integralD10Maybe', 'natD10Fail', and 'integralD10Fail' -- are more general versions of this function. -- -- >>> natD10Maybe 5 -- Just [d10|5|] -- -- >>> natD10Maybe 12 -- Nothing natD10Maybe :: Num a => Natural -> Maybe (D10 a) natD10Maybe x | isD10Nat x = Just (D10_Unsafe (fromIntegral x)) | otherwise = Nothing -- | Convert an 'Integer' to a 'D10' if it is within the range 0 to 9, -- or produce 'Nothing' otherwise. -- -- @'Data.D10.Predicate.isD10Integer' x = 'Data.Maybe.isJust' ('integerD10Maybe' x)@ -- -- 'integralD10Maybe', 'integerD10Fail', and 'integralD10Fail' -- are more general versions of this function. -- -- >>> integerD10Maybe 5 -- Just [d10|5|] -- -- >>> integerD10Maybe 12 -- Nothing -- -- >>> integerD10Maybe (-5) -- Nothing integerD10Maybe :: Num a => Integer -> Maybe (D10 a) integerD10Maybe x | isD10Integer x = Just (D10_Unsafe (fromIntegral x)) | otherwise = Nothing -- | Convert an 'Int' to a 'D10' if it is within the range 0 to 9, -- or produce 'Nothing' otherwise. -- -- @'Data.D10.Predicate.isD10Int' x = 'Data.Maybe.isJust' ('intD10Maybe' x)@ -- -- 'integralD10Maybe', 'intD10Fail', and 'integralD10Fail' -- are more general versions of this function. -- -- >>> intD10Maybe 5 -- Just [d10|5|] -- -- >>> intD10Maybe 12 -- Nothing -- -- >>> intD10Maybe (-5) -- Nothing intD10Maybe :: Num a => Int -> Maybe (D10 a) intD10Maybe x | isD10Int x = Just (D10_Unsafe (fromIntegral x)) | otherwise = Nothing -- | Construct a 'D10' from any kind of number with an 'Integral' -- instance, or produce 'Nothing' if the number falls outside the -- range 0 to 9. -- -- @'Data.D10.Predicate.isD10Integral' x = 'Data.Maybe.isJust' ('integralD10Maybe' x)@ -- -- Specialized versions of this function include 'natD10Maybe', -- 'integerD10Maybe', and 'intD10Maybe'. -- -- 'integralD10Fail' is a more general version of this function. -- -- >>> integralD10Maybe (5 :: Integer) -- Just [d10|5|] -- -- >>> integralD10Maybe (12 :: Integer) -- Nothing -- -- >>> integralD10Maybe ((-5) :: Integer) -- Nothing integralD10Maybe :: (Num b, Integral a) => a -> Maybe (D10 b) integralD10Maybe x = integerD10Maybe (toInteger x) --------------------------------------------------- -- | Convert a 'Char' to a 'D10' if it is within the range -- @'0'@ to @'9'@, or 'Left' with an error message otherwise. -- -- >>> charD10Either '5' -- Right [d10|5|] -- -- >>> charD10Either 'a' -- Left "d10 must be between 0 and 9" charD10Either :: Num a => Char -> Either String (D10 a) charD10Either x | isD10Char x = Right (D10_Unsafe (fromIntegral (ord x - ord '0'))) | otherwise = Left "d10 must be between 0 and 9" -- | Convert a 'String' to a 'D10' if it consists of a single -- character and that character is within the range @'0'@ to -- @'9'@, or 'Left' with an error message otherwise. -- -- >>> strD10Either "5" -- Right [d10|5|] -- -- >>> strD10Either "a" -- Left "d10 must be between 0 and 9" -- -- >>> strD10Either "58" -- Left "d10 must be a single character" strD10Either :: Num a => String -> Either String (D10 a) strD10Either [x] = charD10Either x strD10Either _ = Left "d10 must be a single character" -- | Convert a 'String' to a 'D10' if all of the characters in -- the string fall within the range @'0'@ to @'9'@, or 'Left' -- with an error message otherwise. -- -- >>> strD10ListEither "5" -- Right [d10list|5|] -- -- >>> strD10ListEither "a" -- Left "d10 must be between 0 and 9" -- -- >>> strD10ListEither "58" -- Right [d10list|58|] strD10ListEither :: Num a => String -> Either String [D10 a] strD10ListEither = traverse charD10Either -- | Convert a 'Natural' to a 'D10' if it is less than 10, -- or 'Left' with an error message otherwise. -- -- >>> natD10Either 5 -- Right [d10|5|] -- -- >>> natD10Either 12 -- Left "d10 must be less than 10" natD10Either :: Num a => Natural -> Either String (D10 a) natD10Either x = case (natD10Maybe x) of Just y -> Right y Nothing -> Left "d10 must be less than 10" -- | Convert an 'Integer' to a 'D10' if it is within the -- range 0 to 9, or 'Left' with an error message otherwise. -- -- >>> integerD10Either 5 -- Right [d10|5|] -- -- >>> integerD10Either 12 -- Left "d10 must be between 0 and 9" -- -- >>> integerD10Either (-5) -- Left "d10 must be between 0 and 9" integerD10Either :: Num a => Integer -> Either String (D10 a) integerD10Either x = case (integerD10Maybe x) of Just y -> Right y Nothing -> Left "d10 must be between 0 and 9" -- | Convert an 'Int' to a 'D10' if it is within the range -- 0 to 9, or 'Left' with an error message otherwise. -- -- >>> intD10Either 5 -- Right [d10|5|] -- -- >>> intD10Either 12 -- Left "d10 must be between 0 and 9" -- -- >>> intD10Either (-5) -- Left "d10 must be between 0 and 9" intD10Either :: Num a => Int -> Either String (D10 a) intD10Either x = case (intD10Maybe x) of Just y -> Right y Nothing -> Left "d10 must be between 0 and 9" -- | Convert a number of a type that has an 'Integral' instance -- to a 'D10' if it falls within the range 0 to 9, or 'Left' -- with an error message otherwise. -- -- >>> integralD10Either (5 :: Integer) -- Right [d10|5|] -- -- >>> integralD10Either (12 :: Integer) -- Left "d10 must be between 0 and 9" -- -- >>> integralD10Either ((-5) :: Integer) -- Left "d10 must be between 0 and 9" integralD10Either :: (Num b, Integral a) => a -> Either String (D10 b) integralD10Either x = integerD10Either (toInteger x) --------------------------------------------------- -- | Convert a 'Char' to a 'D10' if it is within the range -- @'0'@ to @'9'@, or 'fail' with an error message otherwise. -- -- 'charD10Maybe' is a specialized version of this function. -- -- >>> charD10Fail '5' :: IO (D10 Int) -- [d10|5|] -- -- >>> charD10Fail 'a' :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) charD10Fail :: (Num a, MonadFail m) => Char -> m (D10 a) charD10Fail x | isD10Char x = return (D10_Unsafe (fromIntegral (ord x - ord '0'))) | otherwise = fail "d10 must be between 0 and 9" -- | Convert a 'String' to a 'D10' if it consists of a single -- character and that character is within the range @'0'@ to -- @'9'@, or 'fail' with an error message otherwise. -- -- 'strD10Maybe' is a specialized version of this function. -- -- >>> strD10Fail "5" :: IO (D10 Int) -- [d10|5|] -- -- >>> strD10Fail "a" :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) -- -- >>> strD10Fail "58" :: IO (D10 Int) -- *** Exception: user error (d10 must be a single character) strD10Fail :: (Num a, MonadFail m) => String -> m (D10 a) strD10Fail [x] = charD10Fail x strD10Fail _ = fail "d10 must be a single character" -- | Convert a 'String' to a 'D10' if all of the characters in -- the string fall within the range @'0'@ to @'9'@, or 'fail' -- with an error message otherwise. -- -- 'strD10ListMaybe' is a specialized version of this function. -- -- >>> strD10ListFail "5" :: IO [D10 Int] -- [d10list|5|] -- -- >>> strD10ListFail "a" :: IO [D10 Int] -- *** Exception: user error (d10 must be between 0 and 9) -- -- >>> strD10ListFail "58" :: IO [D10 Int] -- [d10list|58|] strD10ListFail :: (Num a, MonadFail m) => String -> m [D10 a] strD10ListFail = traverse charD10Fail -- | Convert a 'Natural' to a 'D10' if it is less than 10, -- or 'fail' with an error message otherwise. -- -- 'natD10Maybe' is a specialized version of this function. -- -- 'integralD10Fail' is a more general version of this function. -- -- >>> natD10Fail 5 :: IO (D10 Int) -- [d10|5|] -- -- >>> natD10Fail 12 :: IO (D10 Int) -- *** Exception: user error (d10 must be less than 10) natD10Fail :: (Num a, MonadFail m) => Natural -> m (D10 a) natD10Fail x = case (natD10Maybe x) of Just y -> return y Nothing -> fail "d10 must be less than 10" -- | Convert an 'Integer' to a 'D10' if it is within the -- range 0 to 9, or 'fail' with an error message otherwise. -- -- 'integerD10Maybe' is a specialized version of this function. -- -- 'integralD10Fail' is a more general version of this function. -- -- >>> integerD10Fail 5 :: IO (D10 Int) -- [d10|5|] -- -- >>> integerD10Fail 12 :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) -- -- >>> integerD10Fail (-5) :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) integerD10Fail :: (Num a, MonadFail m) => Integer -> m (D10 a) integerD10Fail x = case (integerD10Maybe x) of Just y -> return y Nothing -> fail "d10 must be between 0 and 9" -- | Convert an 'Int' to a 'D10' if it is within the range -- 0 to 9, or 'fail' with an error message otherwise. -- -- 'intD10Maybe' is a specialized version of this function. -- -- 'integralD10Fail' is a more general version of this function. -- -- >>> intD10Fail 5 :: IO (D10 Int) -- [d10|5|] -- -- >>> intD10Fail 12 :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) -- -- >>> intD10Fail (-5) :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) intD10Fail :: (Num a, MonadFail m) => Int -> m (D10 a) intD10Fail x = case (intD10Maybe x) of Just y -> return y Nothing -> fail "d10 must be between 0 and 9" -- | Convert a number of a type that has an 'Integral' instance -- to a 'D10' if it falls within the range 0 to 9, or 'fail' -- with an error message otherwise. -- -- 'natD10Maybe', 'integerD10Maybe', 'intD10Maybe', -- 'integralD10Maybe', 'natD10Fail', 'integerD10Fail', and -- 'intD10Fail' are all specialized versions of this function. -- -- >>> integralD10Fail (5 :: Integer) :: IO (D10 Int) -- [d10|5|] -- -- >>> integralD10Fail (12 :: Integer) :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) -- -- >>> integralD10Fail ((-5) :: Integer) :: IO (D10 Int) -- *** Exception: user error (d10 must be between 0 and 9) integralD10Fail :: (Num b, Integral a, MonadFail m) => a -> m (D10 b) integralD10Fail x = integerD10Fail (toInteger x) --------------------------------------------------- -- | A single base-10 digit. -- -- Produces an expression of type @'D10' a@ that can be used -- in a Template Haskell splice. -- -- >>> d10Nat $(d10Exp 5) -- 5 -- -- >>> d10Nat $(d10Exp 12) -- ... -- ... d10 must be between 0 and 9 -- ... d10Exp :: forall a b. (Integral b, Lift a, Num a) => b -> Q Exp d10Exp = integralD10Fail >=> lift @(D10 a) -- | A list of base-10 digits. -- -- Produces an expression of type @['D10' a]@ that can be used -- in a Template Haskell splice. -- -- >>> d10Nat <$> $(d10ListExp "") -- [] -- -- >>> d10Nat <$> $(d10ListExp "5") -- [5] -- -- >>> d10Nat <$> $(d10ListExp "58") -- [5,8] -- -- >>> d10Nat <$> $(d10ListExp "a") -- ... -- ... d10 must be between 0 and 9 -- ... d10ListExp :: forall a. (Lift a, Num a) => String -> Q Exp d10ListExp = strD10ListFail >=> lift @[D10 a] --------------------------------------------------- -- | A single base-10 digit. -- -- This quasi-quoter, when used as an expression, produces a -- value of type @'D10' a@. -- -- >>> d10Nat [d10|5|] -- 5 -- -- >>> d10Nat [d10|a|] -- ... -- ... d10 must be between 0 and 9 -- ... -- -- >>> d10Nat [d10|58|] -- ... -- ... d10 must be a single character -- ... d10 :: forall a. (Lift a, Num a) => QuasiQuoter d10 = QuasiQuoter { quoteExp = strD10Fail >=> lift @(D10 a) , quotePat = \_ -> fail "d10 cannot be used in a pattern context" , quoteType = \_ -> fail "d10 cannot be used in a type context" , quoteDec = \_ -> fail "d10 cannot be used in a declaration context" } -- | A list of base-10 digits. -- -- This quasi-quoter, when used as an expression, produces a -- value of type @['D10' a]@. -- -- >>> d10Nat <$> [d10list||] -- [] -- -- >>> d10Nat <$> [d10list|5|] -- [5] -- -- >>> d10Nat <$> [d10list|58|] -- [5,8] -- -- >>> d10Nat <$> [d10list|a|] -- ... -- ... d10 must be between 0 and 9 -- ... d10list :: forall a. (Lift a, Num a) => QuasiQuoter d10list = QuasiQuoter { quoteExp = strD10ListFail >=> lift @[D10 a] , quotePat = \_ -> fail "d10list cannot be used in a pattern context" , quoteType = \_ -> fail "d10list cannot be used in a type context" , quoteDec = \_ -> fail "d10list cannot be used in a declaration context" }