Context-Free Path Queries

Alexander Tchitchigin

Positive Technologies

Path Queries

Constrained Path Queries

S -> a b

Context-Free Path Queries

S -> a S b | a b

Use Cases

  • Graph DB Queries
  • Geographical Routes
  • Alias Analysis
  • Taint Analysis
  • Label Flow Analysis

Programming Language Embedding

Parser Combinators

Examples

let simplePath () =
  <@
    let rec connected() = tok "road" <|> connected() + connected()
    in connected()
  @>


let alias () =
  <@
    let rec aliasTo() = tok "field1_rev" + aliasTo() + tok "field1" <|>
                        tok "field2_rev" + aliasTo() + tok "field2" <|> 
                        ...
                        aliasTo() + aliasTo() <|>
                        Eps
    in aliasTo()
  @>

Problems

  • Left Recursion
  • Ambiguity
  • Infinite Paths

Remedy

  • Generalized LL Parsing
  • Shared Packed Parse Forest

Generalized LL Parsing

  • Top-down parser
  • Supports left-recursion and ambiguity
  • Returns multiple derivations
  • Discovers derivations in parallel
  • Founded by E. Scott and A. Johnstone

LL Parsing

S -> a S a | B
B -> b

let B = function
  | 'b'::tl -> Some tl
  | _       -> None

let rec S = function
  | 'a'::tl ->
    match S tl with
      | Some ('a'::tl2) -> Some tl2
      | _ -> None
  | input   ->
    match B input with
      | Some tl -> Some tl
      | None    -> None

Limitations

  • No left recursion
    • E -> E "+" "1" | "1"
    • Call-stack can't record cycles
  • No non-determinism
    • Call-stack tracks single derivation

Use Continuations, Luke! :D

Explicit state, continuation and position in input

(S -> • a S a, S -> a S • a, aba)

Shared Packed Parse Forest

  • Symbol nodes
    • have labels of the form (x,j,i) where x is a terminal, nonterminal, or ε
  • Packed nodes
    • have labels of the form (t,k), where t is of the form X -> α⋅β
  • Intermediate nodes
    • have the same labels as symbol nodes
    • are used to binarize the SPPF

An Image Worth a Hundred Words

S -> ABCD; A -> a; B -> b; C -> c; D -> d

References

Thanks for your attention!

Questions?

CFPQ

By Alexander Letov

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CFPQ

Context-Free Path Queries for Graphs.

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