Slide 1
Slide 1 text
Parsing with
Derivatives
David Nolen
Papers We Love NYC, August 2016
Slide 2
Slide 2 text
Parsing with
Derivatives
David Nolen
Papers We Love NYC, August 2016
Slide 3
Slide 3 text
Parsing with
Derivatives
David Nolen
Papers I Should Read NYC, August 2016
Slide 4
Slide 4 text
No content
Slide 5
Slide 5 text
No content
Slide 6
Slide 6 text
No content
Slide 7
Slide 7 text
No content
Slide 8
Slide 8 text
No content
Slide 9
Slide 9 text
No content
Slide 10
Slide 10 text
No content
Slide 11
Slide 11 text
No content
Slide 12
Slide 12 text
No content
Slide 13
Slide 13 text
No content
Slide 14
Slide 14 text
No content
Slide 15
Slide 15 text
No content
Slide 16
Slide 16 text
Overview
• Preliminaries
• Brzozowski’s derivative
• Derivatives of context-free languages
• Parsers & parser combinators
• Derivatives of parser combinators
Slide 17
Slide 17 text
• Performance and complexity
• Compaction
Slide 18
Slide 18 text
Preliminaries
Slide 19
Slide 19 text
A language L is a set of strings
Slide 20
Slide 20 text
{foo, bar}
{cat, dog}
{papers, we, love}
Slide 21
Slide 21 text
A string w is a sequence of characters
from an alphabet A
Slide 22
Slide 22 text
2 typical atomic languages
• The empty language, ∅, contains no strings
•
∅ = {}
• The null language 㸜 contains only the length zero
“null” string
• 㸜 = {w} where length(w) = 0
Slide 23
Slide 23 text
Given an alphabet A there is a
singleton language for every
character c in the alphabet
c ≡{c}
Slide 24
Slide 24 text
No content
Slide 25
Slide 25 text
union → alt
concatenation → cat
Kleene star → rep
Slide 26
Slide 26 text
No content
Slide 27
Slide 27 text
No content
Slide 28
Slide 28 text
Brzozowski’s derivative
Slide 29
Slide 29 text
The derivative of a language L with
respect to character c is a new language
that has been “filtered” and “chopped”
Dc(L)
Slide 30
Slide 30 text
No content
Slide 31
Slide 31 text
To determine membership, derive a
language with respect to each character,
and check if the final language contains
the null string: if yes, the original string
was in; if not, it wasn’t.
Slide 32
Slide 32 text
A recursive definition
of the derivative
Slide 33
Slide 33 text
No content
Slide 34
Slide 34 text
No content
Slide 35
Slide 35 text
No content
Slide 36
Slide 36 text
No content
Slide 37
Slide 37 text
No content
Slide 38
Slide 38 text
Derivatives of context-
free languages
Slide 39
Slide 39 text
Laziness
Slide 40
Slide 40 text
Memoization
Slide 41
Slide 41 text
No content
Slide 42
Slide 42 text
No content
Slide 43
Slide 43 text
Parser & Parser
Combinators
Slide 44
Slide 44 text
No content
Slide 45
Slide 45 text
No content
Slide 46
Slide 46 text
Derivatives of parser
combinators
Slide 47
Slide 47 text
No content
Slide 48
Slide 48 text
No content
Slide 49
Slide 49 text
No content
Slide 50
Slide 50 text
No content
Slide 51
Slide 51 text
Performance &
complexity
Slide 52
Slide 52 text
O(n2nG + (2nG)2) = O(22nG2)
Slide 53
Slide 53 text
Compaction
Slide 54
Slide 54 text
No content
Slide 55
Slide 55 text
No content
Slide 56
Slide 56 text
Demo
Slide 57
Slide 57 text
Thanks!
Slide 58
Slide 58 text
Questions?