Lisp in Huskell - Speaker Deck

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Lisp in Huskell

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Huskelldoge

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By an 100% Haskell dummy

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What is Lisp, really?

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(def b 100) ;; defining vars! (def a (fn [c] (+ b c))) ;; defining functions! (a 5 7) ;; executing functions

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Easy!

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How do we express it?

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Parsing

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Come on bro, really?

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Reserved keywords (if, def, fn) parseReserved :: Parser LispExpression! parseReserved = do! res <- try (string "def") <|>! try (string "if") <|>! try (string "fn")! return $ toSexp res

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Numbers parseNumber :: Parser LispExpression! parseNumber = do! _ <- try (many (string "#d"))! sign <- many (oneOf "-")! num <- many1 (digit)! if (length sign) > 1! then pzero! else return $ (LispNumber . read) $ sign ++ num

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Booleans parseTrue :: Parser LispExpression! parseTrue = do! res <- try (string "true")! return $ LispBool True! ! parseFalse :: Parser LispExpression! parseFalse = do! res <- try (string "false")! return $ LispBool False

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Booleans parseReserved :: Parser LispExpression! parseReserved = do! res <- try (string "def") <|>! try (string "if") <|>! try (string "fn")! return $ toSexp res! ! parseTrue :: Parser LispExpression! parseTrue = do! res <- try (string "true")! return $ LispBool True

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Symbols parseSymbol :: Parser LispExpression! parseSymbol = do! first <- letter <|> symbols! rest <- many (letter <|> digit <|> symbols)! let symbol = first:rest! return $ LispSymbol symbol

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Lists parens parseList <|>! ! ! ! parseList :: Parser LispExpression! parseList = liftM LispList $ sepBy parseLispExpression whiteSpace

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Lists parseString :: Parser LispExpression! parseString = do _ <- char '"'! x <- many (noneOf "\"")! _ <- char '"'! return $ LispString x

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So, let’s see how it werkz

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(+ 1 1) LispList [LispSymbol "plus", ! LispNumber 1, ! LispNumber 1]

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Evaluation process

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Easy-peasy

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Literals evaluate to their values

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Numbers - to numbers

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Strings - to strings

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Lists - recursively evaluate their values left to right

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Symbols - to…

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(def a 1)! (def b 2)! (+ a b)

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(def a 1)! (def b 2)! (+ a b) What is `a`?

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Let’s check the Environment

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Ah ok, a is 1

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(def a 1)! (def b 2)! (+ a b) What is `b`?

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Ah ok, b is 1

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Substitution β-reduction

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(+ a b)! ! ! ! ! ! (+ 1 1) Becomes

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(def a 1)! (def b 2)! (def c 3)! (def d 4)! ! (+ a b (* c d))

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(def a 1)! (def b 2)! (def c 3)! (def d 4)! ! (+ a b (* 4 3))

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(def a 1)! (def b 2)! (def c 3)! (def d 4)! ! (+ a b 12)

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(def a 1)! (def b 2)! (def c 3)! (def d 4)! ! (+ 1 2 12)

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When you see the symbol, look for it in Environment

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Environment

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Monad is just a box, right?

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type Environment k v = H.BasicHashTable k v! type LispEnvironment = (Environment LispExpression LispExpression)!

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findVar :: LispEnvironment -> LispExpression -> ! ! ! ! ! ! IO (Maybe LispExpression)! ! findVar env symbol = H.lookup env symbol!

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Closures and polluting Environment

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I’m not polluting, I just don’t need it anymore

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(def sum ! (fn [a b] ! (fn [c] (+ c a b))))! ! (+ a b) ;; Shouldn't work Creates Closure

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Closure is a temporary Environment

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Passed only to recursive calls

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(def sum ! (fn [a b] ! (fn [c] (+ c a b))))! ! (+ a b) ;; Shouldn't work Limited Visibility

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That leads us to two-step lookup (shines in Haskell)

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Look up var value in Closure

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If there’s no Closure, look up Environment

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If there’s Closure, look up in Closure first (shadowing)

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If all fails, error

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lookup_ <- (liftM2 mplus) ! (findVarMaybe closure func_) ! (findVar envRef func_)

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(def sum ! (fn [a b] ! (fn [c] (+ c a b))))! ! (+ a b) ;; Shouldn't work Limited Visibility

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That makes me dance!

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Built-in Functions

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Problem: `+` symbol is a “native” function

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2 function types

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data LispFunk = UserFunction [LispExpression] LispExpression |! LibraryFunction String ([LispExpression] -> LispExpression)! deriving (Generic)

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“User” - is just a lisp expression (list)

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“Library” - is a Haskell (“native”) function

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numericOp :: (Integer -> Integer -> Integer) -> ! [LispExpression] -> LispExpression! ! numericOp op args = LispNumber $ foldl1 op $ ! ! ! ! ! ! ! ! ! map unpackNum args! ! builtInOp :: String -> [LispExpression] -> ! LispExpression! builtInOp "+" args = numericOp (+) args

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If statement

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Consists of 3 blocks: Test expression Truthy expression Faulty expression

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Test Expression: True is True (optimisation) Nil is False False is False Anything else is True

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eval env closure (LispList[(ReservedKeyword IfKeyword), ! ! ! ! ! ! ! ! ! testExpression,! truthyExpression, falsyExpression]) = do! test <- (eval env closure testExpression)! res <- if (isTrue test)! then (eval env closure truthyExpression)! else (eval env closure falsyExpression)! return res

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Map/reduce

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Primitives

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(def empty?! (fn [a] (= a (quote ()))))

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(def map! (fn [f coll]! (if (empty? coll)! (quote ())! (cons (f (first coll))! (map f (next coll)))))) Recur here

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(def reduce! (fn [f coll acc]! (if (empty? coll)! acc! (reduce f (next coll) (f acc (first coll)))))) Recur here

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Bottomline

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Definition is adding an evaluated expression to hash map

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Function (fn) captures an enclosed environment and evaluates to internal function primitive

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If Evaluates only test expression and one of given blocks, skipping the other one

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Recursion Is given basically for free, since it’s just a var lookup and a function call

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Evaluation Evaluate left from right, recursively

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Closures Capture the current environment, dismiss when reaching end of lexical scope