TMPA-2017: Functional Parser of Markdown Language Based on Monad Combining and Monoidal Source...

functional parser of markdownlanguage based on monad combiningand monoidal source streamrepresentation.

Georgiy Lukjanov ([email protected])Assistant professor Artem Pelenitsin ([email protected])

TMPA conference, 3 Feb 2017

Southern Federal University, Rostov-on-Don, Russia

Goals.

∙ Explore approaches to structuring of computation withmultiple side-effects provided by modern Haskelllibraries

∙ Monad Transformers∙ Algebraic effects and effects handlers (specificallyExtensible Effects)

∙ As a case study, build parsers combinators librariesand restricted Markdown parsers using theseapproaches

∙ Compare these approaches in terms of expressibilityand performance

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Goals.

∙ Explore approaches to structuring of computation withmultiple side-effects provided by modern Haskelllibraries∙ Monad Transformers

∙ Algebraic effects and effects handlers (specificallyExtensible Effects)



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Goals.

∙ Explore approaches to structuring of computation withmultiple side-effects provided by modern Haskelllibraries∙ Monad Transformers∙ Algebraic effects and effects handlers (specificallyExtensible Effects)



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Parsers.

Informal definition

A parser is a program that converts text into some kind ofAST (abstract syntax tree)

∙ Auto-generated, by bottom-up parser generators (YACC)∙ Manually-written (e.g. top-down recursive descent)

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Parsers.

Informal definition


∙ Auto-generated, by bottom-up parser generators (YACC)

∙ Manually-written (e.g. top-down recursive descent)

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Parsers.

Informal definition


∙ Auto-generated, by bottom-up parser generators (YACC)∙ Manually-written (e.g. top-down recursive descent)

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Parser Combinators.

∙ Model parsers as higher-order functions

map :: (a→ b)→ [a]→ [b]map [ ] = [ ]

map f (x : xs) = f x :map f xs

∙ Construct complex parsers from small set of basic ones

alphanum :: Parser r Charalphanum = letter <|> digit

∙ Mirror grammar rules in source code of the parser

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Parser as a Monad.

Parser data type

newtype Parser a = Parser {parse :: String→ Maybe (a, String)}

Monad instance for Parserinstance Monad Parser where

return t = Parser $ λs→ Just (t, s)m>>= k = Parser $ λs→

do (u, v)← parse m s(x, y) ← parse (k u) vreturn (x, y)

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Parser as a Monad.

Parser data type

newtype Parser a = Parser {parse :: String→ Maybe (a, String)}

Monad instance for Parserinstance Monad Parser where

return t = Parser $ λs→ Just (t, s)m>>= k = Parser $ λs→

do (u, v)← parse m s(x, y) ← parse (k u) vreturn (x, y) 5 / 22

Types and Effects: main notions.

∙ Pure/Impure functions and referential transparency

Pure function

show :: (Show a)⇒ a→ String

IO action

putStrLn :: String→ IO ()

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Types and Effects: main notions.

∙ Static guarantees on computations permissions

Computation with static environment

readUser :: (MonadReader Database m)⇒UserID→ m UserData

∙ Combining multiple effects

Static environment and ‘mutable’ state

handler :: (MonadReader Config m,MonadState Database m)⇒ m a

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Haskell frameworks for effects typing.

Monad Transformers — type class based

class (Monad m)⇒ MonadState m whereget ::m (StateType m)

put :: StateType m→ m ()

newtype StateT s m a = StateT {runStateT :: s→ m (a, s)}instance (Monad m)⇒ MonadState (StateT s m) whereget = StateT $ λs→ return (s, s)put s = StateT $ \_→ return ((), s)

instance MonadTrans (StateT s) where ...instance (MonadIO m)⇒ MonadIO (StateT s m) where ...

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Haskell frameworks for effects typing.

Extensible Effects — free monad based

data Free f a wherePure :: a→ Free f aImpure :: f (Free f a)→ Free f a

data State s v whereGet :: State s sPut :: !s→ State s ()

instance Functor (State s)

type FState s = Free (State s)

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Parser as a monadic stack.

Parser

newtype Parser a = Parser (StateT String Maybe a)

Running a parser

parse :: Parser a→ String→ Maybe (a, String t)parse (Parser p) s = runStateT p s

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Parser as a Union of Effects.

type Parsable r = (Member Fail r,Member (State String) r)

type Parser r a = Parsable r⇒ Eff r a

Running a parser (handling effects)

parse :: Eff (Fail ’: State String ’ : [ ]) a→String→ (Either () a, String)

parse p inp = run $ runState (runError p) inp

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Basic parsers.

Unconditional consumer

item :: Parser r Charitem = do s← get

case s of [ ]→ put s>> die(x : xs)→ put xs>> pure x

Conditional consumer

sat :: (Char→ Bool)→ Parser r Charsat p = do x← item

if p x then return x else die

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Basic parsers.

Unconditional consumer

item :: Parser r Charitem = do s← get

case s of [ ]→ put s>> die(x : xs)→ put xs>> pure x

Conditional consumer

sat :: (Char→ Bool)→ Parser r Charsat p = do x← item

if p x then return x else die12 / 22

Parsers combinators.

Determenistic alternative combinator

alt :: Parser r a→ Parser r a→ Parser r aalt ma mb = do s← get

catchExc ma $ λea→put s>> catchExc mb $ λeb→ die

Repetition combinator

many :: Parser r a→ Parser r [a]many v = many_vwhere many_v = some_v ‘alt‘ (pure [ ])

some_v = (fmap (:) v)< ∗ >many_v

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Parsers combinators.

Determenistic alternative combinator

alt :: Parser r a→ Parser r a→ Parser r aalt ma mb = do s← get

catchExc ma $ λea→put s>> catchExc mb $ λeb→ die

Repetition combinator

many :: Parser r a→ Parser r [a]many v = many_vwhere many_v = some_v ‘alt‘ (pure [ ])

some_v = (fmap (:) v)< ∗ >many_v 13 / 22

Restricted Markdown AST.

Document

type Document = [Block]

Block

data Block = Blank| Header (Int, Line)| Paragraph [Line]| UnorderedList [Line]| BlockQuote [Line]

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Constructing AST.

Parser for Documentdoc :: Parser Documentdoc = many block

where block = blank <|> header <|> paragraph<|> unorderdList <|> blockquote<|> blockMath

Parser for headersheader :: Parser Blockheader = do

hashes← token $ some $ char ’#’text ← nonEmptyLinereturn $ Header (length hashes, text) 15 / 22

Performance benchmarks. MTL.

Estimate Confidence intervalMean time 121 μs [119 μs, 126 μs]

σ 10.0 μs [20.2 μs, 3.84 μs]

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Performance benchmarks. Freer EE.

Estimate Confidence intervalMean time 7.53 ms [7.44 ms, 7.66 ms]

σ 289 μs [194 μs, 436 μs]

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String-like types in Haskell.

StringEssentially a [Char] — poor performance

ByteStringHigh performance, but low-level interface

TextUnicode-oriented high performance type

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Text-oriented Monoids.

Input-polymorphic base parser

item :: TextualMonoid t⇒ Parser t Charitem = dos← splitCharacterPrefix ◦ remainder< $ > getcase s of Nothing→ throwError

Just (c, rest)→ put rest ∗ > pure c

‘uncons’-like function

splitCharacterPrefix :: TextualMonoid t⇒t→ Maybe (Char, t)

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Conclusion and results.

1. Parsers combinators library and Markdown parserbased on Monad Transformers.∙ https://github.com/geo2a/markdown_monparsing

2. Parsers combinators library and Markdown parserbased on Extensible Effects.∙ https://github.com/geo2a/ext-effects-parsers∙ https://github.com/geo2a/ext-effects-markdown

3. Performance comparison of Monad Transformers andExtensible Effects based libraries.

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https://github.com/geo2a/markdown_monparsing

https://github.com/geo2a/ext-effects-parsers

https://github.com/geo2a/ext-effects-markdown

References.

∙ Monadic Parser Combinators // Graham Hutton, ErikMeijer – Department of Computer Science, University ofNottingham, 1996

∙ Adding Structure to Monoids // Mario Blaževic – StiloInternational plc

∙ Extensible Effects An Alternative to MonadTransformers // Oleg Kiselyov, Amr Sabry, CameronSwords – Indiana University, USA

∙ Freer monads and more extensible effects // OlegKiselyov, Hiromi Ishii

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Questions?.

Results outline

1. Parsers combinators library and Markdown parserbased on Monad Transformers.

2. Parsers combinators library and Markdown parserbased on Extensible Effects.

3. Performance comparison of Monad Transformers andExtensible Effects based libraries.

Georgiy Lukyanov [email protected] Pelenitsin [email protected]

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TMPA-2017: Functional Parser of Markdown Language Based on Monad Combining and Monoidal Source...

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