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Extensible syntax analyzers

Extensible syntax analyzers. Pavel Egorov pe@skbkontur.ru. Problem statements. L – some formal language; T : L  R – it’s translator; L ext  L – some extended language; T ext : L ext  R ext – it’s extended translator.    L T ext (  ) = T( ) We want compatibility!.

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Extensible syntax analyzers

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  1. Extensible syntax analyzers Pavel Egorov pe@skbkontur.ru

  2. Problem statements L – some formal language; T : L  R – it’s translator; Lext L – some extended language; Text : Lext Rext – it’s extended translator. L Text () = T() We want compatibility!

  3. Disclaimer • Consider syntax analyzers only. • Fixed algorithm of syntax analysis. • Extension due to modification of the grammar only.

  4. What is syntax analyzer? • SA converts a word to a syntax tree. • What is syntax tree? • Root is labeled by the axiom of the grammar • Inner nodes are labeled by non-terminals • Leaf nodes are labeled by terminals or non-terminals or e

  5. Classic parse tree A Grammar: AaBd B  b B  A Word: “aabdd” Derivation: A aBd  aAd   aaBdd  aabdd a B d A a B d b

  6. Classic parse treeIs it good enough? G1: Aabc Extended G2: AaBc Bb Word: “abc” A a b c They are different! A a B c b

  7. Classic parse treeIs it good enough? G1: Aa Extended G2: AaE Ee Word: “a” A a They are different! A a E e

  8. Cancelled tree • Driven by labeled grammar • Cut off some inner nodes from parse tree • Cut off e-leafs from parse tree Is much better for parser extension!

  9. Cancelled tree example parse tree A Labeled grammar: A a1B0d0B1 B b1E0 B  x1 E  e0 • Symbols labeled by 0 are not present in tree • e-leafs are always labeled by 0 B a B d x b E e A B a b cancelled tree x

  10. Intermediate results • Labeled grammar • Syntax analyzer driven by labeled grammar • Canceled tree as a result of syntax analysis So how can we extend grammars without breaking compatibility? Compatibility:L SAext () = SA ()

  11. Extending transformations of grammars f – extending grammar transformation G - grammar L(f(G))L(G)

  12. Extending transformations • ADD-transform adds some fixed new production to a grammar. • EXTRACT-transform: before: Aaxbygz after: AaxB0gz Bby

  13. Extending transformations AE* all transforms, composed from arbitrary number of ADD- and EXTRACT-transforms.

  14. Results

  15. Compatibility • Any transform from AE* doesn’t break compatibility of corresponding syntax analyzers. • A grammar extended by AE* transform has the same production labeling as initial grammar has on the common productions. (AE* doesn’t change labeling of unchanged productions)

  16. Independent transforms G y1, y2AE* y1 y2 G2 Domain(y1) ? G1 Domain(y2) ? G1 G2 G12??? When it is possible? How can we do it?

  17. Independent transforms What if G1 Domain(y2)? Sometimes we can solve this problem! Aabgd y1: AabCd; C  g y2: AaBd; Bbg y2/y1: A  aBd; BbC Conflict! Decision!

  18. y/f - afixed transform • y/f - “fixed” y, which can be applied after f • Sometimes we can’t fix y...  Aabg y: AXg; X ab f: AaY; Y bg • Recursive definition of the function y/f for y and f from AE*. • Sometimes y/f is not defined.

  19. Independent transforms G y1 y2 G1 G2 y2/ y1 y1/ y2 ? G12 G21 y2/ y1y1? y1/ y2y2

  20. Independent transforms G y1 y2 G1 G2 y2/ y1 y1/ y2 G12 y2/ y1y1 = y1/ y2y2

  21. Conclusion • Syntax analyzers • driven by labeled grammars • cancelled trees as a result • AE* - a way to extend grammars safelly • y/f – a way to compose independent grammar transforms • Order of application of the extending transforms doesn’t matter!

  22. Thank you!Questions?

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