Parsing floating point numbers

The first task is extending the LispVal type to grok floats.

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type LispInt = Integer type LispFloat = Float -- numeric data types data LispNum = Integer LispInt | Float LispFloat -- data types data LispVal = Atom String | List [LispVal] | DottedList [LispVal] LispVal | Number LispNum | Char Char | String String | ...

The reason for using the new LispNum type and not just throwing a new Float Float constructor in there is so that functions can accept and operate on parameters of any supported numeric type. First the floating point numbers need to be parsed. For now I only parse floating point numbers in decimal because the effort to parse other bases is too great for the benefits gained (none, for me).

ElSchemo now parses negative numbers so I'll start with 2 helper functions that are used when parsing both integers and floats:

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parseSign :: Parser Char parseSign = do try (char '-') <|> do optional (char '+') return '+' applySign :: Char -> LispNum -> LispNum applySign sign n = if sign == '-' then negate n else n

parseSign

is straightforward as it follows the convention that a literal number is positive unless explicitly marked as negative with a leading minus sign. A leading plus sign is allowed but not required.

applySign

takes a sign character and a LispNum and negates it if necessary, returning a LispNum .

Armed with these 2 functions we can now parse floating point numbers in decimal. Conforming to R5RS an optional #d prefix is allowed.

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parseFloat :: Parser LispVal parseFloat = do optional (string "#d") sign <- parseSign whole <- many1 digit char '.' fract <- many1 digit return . Number $ applySign sign (makeFloat whole fract) where makeFloat whole fract = Float . fst . head . readFloat $ whole ++ "." ++ fract

The first 6 lines should be clear. Line 7 simply applies the parsed sign to the parsed number and returns it, delegating most of the work to makeFloat . makeFloat in turn delegates the work to the readFloat library function, extracts the result and constructs a LispNum for it.

The last step for parsing is to modify parseExpr to try and parse floats.

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-- Integers, floats, characters and atoms can all start with a # so wrap those with try. -- (Left factor the grammar in the future) parseExpr :: Parser LispVal parseExpr = (try parseFloat) <|> (try parseInteger) <|> (try parseChar) <|> parseAtom <|> parseString <|> parseQuoted <|> do char '(' x <- (try parseList) <|> parseDottedList char ')' return x <|> parseComment

Displaying the floats

That's it for parsing, now let's provide a way to display these suckers. LispVal is an instance of show, where show = showVal so showVal is our first stop. Remembering that LispVal now has a single Number constructor we modify it accordingly:

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showVal (Number n) = showNum n showNum :: LispNum -> String showNum (Integer contents) = show contents showNum (Float contents) = show contents instance Show LispNum where show = showNum

One last, and certainly not least, step is to modify eval so that numbers evaluate to themselves.

eval env val@(Number _) = return val

There's a little more housekeeping to be done such as fixing integer? , number? , implementing float? but I will leave those as an exercise to the reader, or just wait until I share the full code. As it stands now floating point numbers can be parsed and displayed. If you fire up the interpreter and type 2.5 or -10.88 they will be understood. Now try adding them:

(+ 2.5 1.1) Invalid type: expected integer, found 2.5

Oops, we don't know how to operate on floats yet!

Operating on floats

Parsing was the easy part. Operating on the new floats is not necessarily difficult, but it was more work than I realized it would be. I don't claim that this is the best or the only way to operate on any LispNum , it's just the way I did it and it seems to work. There's a bunch of boilerplate necessary to make LispNum an instance of the required classes, Eq, Num, Real, and Ord. I don't think I have done this properly but for now it works. What is clearly necessary is the code that operates on different types of numbers. I think I've specified sane semantics for coercion. This will be very handy shortly.

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lispNumEq :: LispNum -> LispNum -> Bool lispNumEq (Integer arg1) (Integer arg2) = arg1 == arg2 lispNumEq (Integer arg1) (Float arg2) = (fromInteger arg1) == arg2 lispNumEq (Float arg1) (Float arg2) = arg1 == arg2 lispNumEq (Float arg1) (Integer arg2) = arg1 == (fromInteger arg2) instance Eq LispNum where (==) = lispNumEq lispNumPlus :: LispNum -> LispNum -> LispNum lispNumPlus (Integer x) (Integer y) = Integer $ x + y lispNumPlus (Integer x) (Float y) = Float $ (fromInteger x) + y lispNumPlus (Float x) (Float y) = Float $ x + y lispNumPlus (Float x) (Integer y) = Float $ x + (fromInteger y) lispNumMinus :: LispNum -> LispNum -> LispNum lispNumMinus (Integer x) (Integer y) = Integer $ x - y lispNumMinus (Integer x) (Float y) = Float $ (fromInteger x) - y lispNumMinus (Float x) (Float y) = Float $ x - y lispNumMinus (Float x) (Integer y) = Float $ x - (fromInteger y) lispNumMult :: LispNum -> LispNum -> LispNum lispNumMult (Integer x) (Integer y) = Integer $ x * y lispNumMult (Integer x) (Float y) = Float $ (fromInteger x) * y lispNumMult (Float x) (Float y) = Float $ x * y lispNumMult (Float x) (Integer y) = Float $ x * (fromInteger y) lispNumDiv :: LispNum -> LispNum -> LispNum lispNumDiv (Integer x) (Integer y) = Integer $ x `div` y lispNumDiv (Integer x) (Float y) = Float $ (fromInteger x) / y lispNumDiv (Float x) (Float y) = Float $ x / y lispNumDiv (Float x) (Integer y) = Float $ x / (fromInteger y) lispNumAbs :: LispNum -> LispNum lispNumAbs (Integer x) = Integer (abs x) lispNumAbs (Float x) = Float (abs x) lispNumSignum :: LispNum -> LispNum lispNumSignum (Integer x) = Integer (signum x) lispNumSignum (Float x) = Float (signum x) instance Num LispNum where (+) = lispNumPlus (-) = lispNumMinus (*) = lispNumMult abs = lispNumAbs signum = lispNumSignum fromInteger x = Integer x lispNumToRational :: LispNum -> Rational lispNumToRational (Integer x) = toRational x lispNumToRational (Float x) = toRational x instance Real LispNum where toRational = lispNumToRational lispIntQuotRem :: LispInt -> LispInt -> (LispInt, LispInt) lispIntQuotRem n d = quotRem n d lispIntToInteger :: LispInt -> Integer lispIntToInteger x = x lispNumLessThanEq :: LispNum -> LispNum -> Bool lispNumLessThanEq (Integer x) (Integer y) = x <= y lispNumLessThanEq (Integer x) (Float y) = (fromInteger x) <= y lispNumLessThanEq (Float x) (Integer y) = x <= (fromInteger y) lispNumLessThanEq (Float x) (Float y) = x <= y instance Ord LispNum where (<=) = lispNumLessThanEq

Phew, ok with that out of the way now we can actually extend our operators to work with any type of LispNum . Our Scheme operators are defined using the functions numericBinop and numBoolBinop . First we'll slightly modify our definition of primitives :

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primitives :: [(String, [LispVal] -> ThrowsError LispVal)] primitives = [("+", numericBinop (+)), ("-", subtractOp), ("*", numericBinop (*)), ("/", floatBinop (/)), ("mod", integralBinop mod), ("quotient", integralBinop quot), ("remainder", integralBinop rem), ("=", numBoolBinop (==)), ("<", numBoolBinop (<)), (">", numBoolBinop (>)), ("/=", numBoolBinop (/=)), (">=", numBoolBinop (>=)), ("<=", numBoolBinop (<=)), ...]

Note that mod , quotient , and remainder are only defined for integers and as such use integralBinop , while division (/) is only defined for floating point numbers using floatBinop . subtractOp is different to support unary usage, e.g. (- 4) => -4 , but it uses numericBinop internally when more than 1 argument is given. On to the implementation! First extend unpackNum to work with any LispNum , and provide separate unpackInt and unpackFloat functions to handle both kinds of LispNum .

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unpackNum :: LispVal -> ThrowsError LispNum unpackNum (Number (Integer n)) = return $ Integer n unpackNum (Number (Float n)) = return $ Float n unpackNum notNum = throwError $ TypeMismatch "number" notNum unpackInt :: LispVal -> ThrowsError Integer unpackInt (Number (Integer n)) = return n unpackInt (List [n]) = unpackInt n unpackInt notInt = throwError $ TypeMismatch "integer" notInt unpackFloat :: LispVal -> ThrowsError Float unpackFloat (Number (Float f)) = return f unpackFloat (Number (Integer f)) = return $ fromInteger f unpackFloat (List [f]) = unpackFloat f unpackFloat notFloat = throwError $ TypeMismatch "float" notFloat

The initial work of separating integers and floats into the LispNum abstraction, and the code I said would be handy shortly, are going to be really handy here. There's relatively no change in numericBinop except for the type signature. integralBinop and floatBinop are just specific versions of the same function. I'm sure there's a nice Haskelly way of doing this with less repetition, and I welcome such corrections.

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numericBinop :: (LispNum -> LispNum -> LispNum) -> [LispVal] -> ThrowsError LispVal numericBinop op singleVal@[_] = throwError $ NumArgs 2 singleVal numericBinop op params = mapM unpackNum params >>= return . Number . foldl1 op integralBinop :: (LispInt -> LispInt -> LispInt) -> [LispVal] -> ThrowsError LispVal integralBinop op singleVal@[_] = throwError $ NumArgs 2 singleVal integralBinop op params = mapM unpackInt params >>= return . Number . Integer . foldl1 op floatBinop :: (LispFloat -> LispFloat -> LispFloat) -> [LispVal] -> ThrowsError LispVal floatBinop op singleVal@[_] = throwError $ NumArgs 2 singleVal floatBinop op params = mapM unpackFloat params >>= return . Number . Float . foldl1 op subtractOp :: [LispVal] -> ThrowsError LispVal subtractOp num@[_] = unpackNum (head num) >>= return . Number . negate subtractOp params = numericBinop (-) params numBoolBinop :: (LispNum -> LispNum -> Bool) -> [LispVal] -> ThrowsError LispVal numBoolBinop op params = boolBinop unpackNum op params

That was a bit of work but now ElSchemo supports floating point numbers, and if you're following along then your Scheme might too if I haven't missed any important details!