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Packrat Parsin g: Sim ple, Powerfu l, Lazy, Lin ear Tim e Bryan Ford Massachusetts Institute of Technology In tern ation al Con feren ce on Fu n ction al Program m in g, October 2002 Overview Wh at Is Packrat Parsin

  1. Packrat Parsin g: Sim ple, Powerfu l, Lazy, Lin ear Tim e Bryan Ford Massachusetts Institute of Technology In tern ation al Con feren ce on Fu n ction al Program m in g, October 2002

  2. � � � � � Overview Wh at Is Packrat Parsin g? Wh at is it Good (an d n ot good) For? Practical Experien ce Related Work Con clu sion

  3. Wh at is Packrat Parsin g? Answe r: Top-down parsin g with backtrackin g – except: Uses m em oization to ach ieve lin ear parse tim e

  4. Example Grammar → Additive Multitive '+' Additive | Multitive Multitive → Primary '*' Multitive | Primary → Primary '(' Additive ')' | Decimal → Decimal '0' | ... | '9'

  5. Recu rsive Descen t Parser

  6. Recu rsive Descen t Parser data Result v = Parsed v String | NoParse

  7. Recu rsive Descen t Parser data Result v = Parsed v String | NoParse

  8. Recu rsive Descen t Parser data Result v = Parsed v String | NoParse Semantic Value

  9. Recu rsive Descen t Parser data Result v = Parsed v String | NoParse Remainder String

  10. Recu rsive Descen t Parser data Result v = Parsed v String | NoParse

  11. Recu rsive Descen t Parser data Result v = Parsed v String | NoParse pAdditive :: String -> Result Int pMultitive:: String -> Result Int pPrimary :: String -> Result Int pDecimal :: String -> Result Int

  12. Recu rsive Descen t Parser pAdditive :: String -> Result Int

  13. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int

  14. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int pAdditive = (do l <- pMultitive char '+' r <- pAdditive return (l + r)) <|> (do pMultitive)

  15. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int pAdditive = (do l <- pMultitive char '+' r <- pAdditive return (l + r)) <|> (do pMultitive)

  16. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int pAdditive = (do l <- pMultitive char '+' r <- pAdditive return (l + r)) <|> (do pMultitive)

  17. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int pAdditive = (do l <- pMultitive char '+' r <- pAdditive return (l + r)) <|> (do pMultitive)

  18. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int pAdditive = (do l <- pMultitive char '+' r <- pAdditive return (l + r)) <|> (do pMultitive)

  19. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int pAdditive = (do l <- pMultitive char '+' r <- pAdditive return (l + r)) <|> (do pMultitive)

  20. Recu rsive Descen t Parser -- Additive → Multitive '+' Additive | Multitive -- pAdditive :: String -> Result Int pAdditive = (do l <- pMultitive char '+' r <- pAdditive return (l + r)) <|> (do pMultitive)

  21. Parsin g Exam ple pAdditive “2*(3+4)”

  22. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)”

  23. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” pMu ltitive “2*(3+4)”

  24. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)”

  25. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” pPrim ary “2*(3+4)”

  26. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” P → '(' A ')' pPrim ary “2*(3+4)”

  27. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” P → '(' A ')' pPrim ary “2*(3+4)”

  28. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” P → D pPrim ary “2*(3+4)”

  29. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” P → D pPrim ary “2*(3+4)” pDecim al “2*(3+4)”

  30. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” P → D pPrim ary “2*(3+4)” ⇒ Parsed 2 “*(3+4)” pDecim al “2*(3+4)”

  31. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” ⇒ Parsed 2 “*(3+4)” pPrim ary “2*(3+4)”

  32. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” ⇒ Parsed 2 “*(3+4)” pPrim ary “2*(3+4)” pCh ar '*' “*(3+4)”

  33. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” ⇒ Parsed 2 “*(3+4)” pPrim ary “2*(3+4)” ⇒ Parsed () “(3+4)” pCh ar '*' “*(3+4)”

  34. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” ⇒ Parsed 2 “*(3+4)” pPrim ary “2*(3+4)” ⇒ Parsed () “(3+4)” pCh ar '*' “*(3+4)” pMu ltitive “(3+4)”

  35. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” ⇒ Parsed 2 “*(3+4)” pPrim ary “2*(3+4)” ⇒ Parsed () “(3+4)” pCh ar '*' “*(3+4)” pMu ltitive “(3+4)” . . .

  36. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” M → P '*' M pMu ltitive “2*(3+4)” ⇒ Parsed 2 “*(3+4)” pPrim ary “2*(3+4)” ⇒ Parsed () “(3+4)” pCh ar '*' “*(3+4)” ⇒ Parsed 7 “” pMu ltitive “(3+4)”

  37. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” ⇒ Parsed 14 “” pMu ltitive “2*(3+4)”

  38. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” ⇒ Parsed 14 “” pMu ltitive “2*(3+4)” pCh ar '+' “”

  39. Parsin g Exam ple A → M '+' A pAdditive “2*(3+4)” ⇒ Parsed 14 “” pMu ltitive “2*(3+4)” pCh ar '+' “”

  40. Parsin g Exam ple A → M pAdditive “2*(3+4)”

  41. Parsin g Exam ple A → M pAdditive “2*(3+4)” pMu ltitive “2*(3+4)”

  42. Parsin g Exam ple A → M pAdditive “2*(3+4)” pMu ltitive “2*(3+4)” . . .

  43. � Th e Backtrackin g Problem Can yield expon en tial worst-case parse tim es

  44. � � � � � Th e Backtrackin g Problem Can yield expon en tial worst-case parse tim es T ypic a l solution: avoid backtrackin g by Prediction u sin g on e-token lookah ead Hackin g th e gram m ar Design in g th e lan gu age for easy parsin g

  45. � � � � � � � Th e Backtrackin g Problem Can yield expon en tial worst-case parse tim es T ypic a l solution: avoid backtrackin g by Prediction u sin g on e-token lookah ead Hackin g th e gram m ar Design in g th e lan gu age for easy parsin g Alte rna te solution: allow backtrackin g; m em oize all interm ediate res ults .

  46. � � � ✁ ✂ ✂ Mem oization of Resu lts Assu m ption s: Parsin g fu n ction s depen d only on in pu t strin g. Parsin g fu n ction s yield at m os t one res ult . Im plication : Requ ires resu lts table of size ( m ( n +1)) m = n u m ber of n on term in als/ parsin g fu n ction s n = len gth of in pu t strin g

  47. Bu ildin g a Packrat Parser

  48. Bu ildin g a Packrat Parser data Result v = Parsed v String | NoParse pAdditive :: String -> Result Int pMultitive:: String -> Result Int pPrimary :: String -> Result Int pDecimal :: String -> Result Int

  49. Bu ildin g a Packrat Parser data Result v = Parsed v String | NoParse pAdditive :: String -> Result Int pMultitive:: String -> Result Int pPrimary :: String -> Result Int pDecimal :: String -> Result Int

  50. Bu ildin g a Packrat Parser data Result v = Parsed v Derivs | NoParse pAdditive :: Derivs -> Result Int pMultitive:: Derivs -> Result Int pPrimary :: Derivs -> Result Int pDecimal :: Derivs -> Result Int

  51. Bu ildin g a Packrat Parser data Result v = Parsed v Derivs | NoParse data Derivs = Derivs { dvAdditive :: Result Int, dvMultitive :: Result Int, dvPrimary :: Result Int, dvDecimal :: Result Int, dvChar :: Result Char}

  52. Bu ildin g th e Derivs Stru ctu re parse :: String -> Derivs parse s = d where

  53. Bu ildin g th e Derivs Stru ctu re parse :: String -> Derivs parse s = d where d = Derivs add mult prim dec chr

  54. Bu ildin g th e Derivs Stru ctu re parse :: String -> Derivs parse s = d where d = Derivs add mult prim dec chr chr = case s of (c:s') -> Parsed c (parse s') [] -> NoParse

  55. Bu ildin g th e Derivs Stru ctu re parse :: String -> Derivs parse s = d where d = Derivs add mult prim dec chr chr = case s of (c:s') -> Parsed c (parse s') [] -> NoParse

  56. Bu ildin g th e Derivs Stru ctu re parse :: String -> Derivs parse s = d where d = Derivs add mult prim dec chr chr = case s of (c:s') -> Parsed c (parse s') [] -> NoParse

  57. Bu ildin g th e Derivs Stru ctu re parse :: String -> Derivs parse s = d where d = Derivs add mult prim dec chr chr = case s of (c:s') -> Parsed c (parse s') [] -> NoParse

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