csci 3136 principles of programming languages
play

CSCI 3136 Principles of Programming Languages Syntactic Analysis - PowerPoint PPT Presentation

Aug 28, 2023 •497 likes •1.76k views

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 4 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 125 FOLLOW( X ) Definition 2 / 125 FOLLOW( X ) Definition For any A V we

  1. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } ← ∅∪ ( { q, ǫ }−{ ǫ } ) ∪∅∪ ( { ǫ }−{ ǫ } ) ∪∅ P C → f Q { q, ǫ } { b, e } B C { c, f } 25 / 125

  2. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } ← ∅∪ ( { q, ǫ }−{ ǫ } ) ∪∅∪ ( { ǫ }−{ ǫ } ) ∪∅ P C → f ← { q } Q { q, ǫ } { b, e } B C { c, f } 26 / 125

  3. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 27 / 125

  4. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 28 / 125

  5. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 29 / 125

  6. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 30 / 125

  7. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 31 / 125

  8. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } ← ∅ ∪ ∅ ∪ ∅ ∪ ∅ ∪ ∅ P C → f Q { q, ǫ } { b, e } B C { c, f } 32 / 125

  9. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } ← ∅ ∪ ∅ ∪ ∅ ∪ ∅ ∪ ∅ P C → f ← ∅ Q { q, ǫ } { b, e } B C { c, f } 33 / 125

  10. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 34 / 125

  11. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 35 / 125

  12. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 36 / 125

  13. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 37 / 125

  14. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( C ) − { ǫ } ) ∪ Fo ( A ) C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 38 / 125

  15. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( C ) −{ ǫ } ) ∪ Fo ( A ) ∪ ( F ( ǫ ) −{ ǫ } ) ∪ Fo ( B ) C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 39 / 125

  16. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( C ) −{ ǫ } ) ∪ Fo ( A ) ∪ ( F ( ǫ ) −{ ǫ } ) ∪ Fo ( B ) C → cC { p, ǫ } ← ∅ ∪ ∅ ∪ { ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 40 / 125

  17. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( C ) −{ ǫ } ) ∪ Fo ( A ) ∪ ( F ( ǫ ) −{ ǫ } ) ∪ Fo ( B ) C → cC { p, ǫ } ← ∅ ∪ ∅ ∪ { ǫ } ∪ { c, f } P C → f Q { q, ǫ } { b, e } B C { c, f } 41 / 125

  18. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( C ) − { ǫ } ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( B ) C → cC { p, ǫ } ← ∅ ∪ ∅ ∪ { ǫ } ∪ { c, f } P C → f Q { q, ǫ } { b, e } B C { c, f } 42 / 125

  19. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( C ) − { ǫ } ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( B ) C → cC { p, ǫ } ← ∅ ∪ ∅ ∪ { ǫ } ∪ { c, f } ∪ ∅ ∪ ∅ P C → f Q { q, ǫ } { b, e } B C { c, f } 43 / 125

  20. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ Q → ǫ { f } ∅ f C B → bB { p, q, b, e } • Fo ( B ) ← Fo ( B ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( T ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( C ) − { ǫ } ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( B ) C → cC { p, ǫ } ← ∅ ∪ ∅ ∪ { ǫ } ∪ { c, f } ∪ ∅ ∪ ∅ P C → f ← { ǫ, c, f } Q { q, ǫ } { b, e } B C { c, f } 44 / 125

  21. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 45 / 125

  22. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 46 / 125

  23. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 47 / 125

  24. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 48 / 125

  25. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 49 / 125

  26. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 50 / 125

  27. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 51 / 125

  28. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 52 / 125

  29. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } ← { q } ∪ ( { q, ǫ } − { ǫ } ) P C → f Q { q, ǫ } { b, e } B C { c, f } 53 / 125

  30. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } ← { q }∪ ( { q, ǫ }−{ ǫ } ) ∪{ b, e }∪ ( { ǫ }− P C → f { ǫ } ) Q { q, ǫ } { b, e } B C { c, f } 54 / 125

  31. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } ← { q }∪ ( { q, ǫ }−{ ǫ } ) ∪{ b, e }∪ ( { ǫ }− P C → f { ǫ } ) ∪ { q } Q { q, ǫ } { b, e } B C { c, f } 55 / 125

  32. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } ← { q }∪ ( { q, ǫ }−{ ǫ } ) ∪{ b, e }∪ ( { ǫ }− P C → f { ǫ } ) ∪ { q } Q { q, ǫ } { b, e } ← { q } ∪ { q } ∪ { b, e } ∪ { q } B C { c, f } 56 / 125

  33. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( P ) ← Fo ( P ) ∪ ( F ( Q ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( P ) C → cC { p, ǫ } ← { q }∪ ( { q, ǫ }−{ ǫ } ) ∪{ b, e }∪ ( { ǫ }− P C → f { ǫ } ) ∪ { q } Q { q, ǫ } { b, e } ← { q } ∪ { q } ∪ { b, e } ∪ { q } B ← { q, b, e } C { c, f } 57 / 125

  34. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 58 / 125

  35. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 59 / 125

  36. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 60 / 125

  37. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 61 / 125

  38. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 62 / 125

  39. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) P C → f Q { q, ǫ } { b, e } B C { c, f } 63 / 125

  40. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } ← ∅∪ ( { ǫ }−{ ǫ } ) ∪{ b, e }∪ ( { ǫ }−{ ǫ } ) P C → f Q { q, ǫ } { b, e } B C { c, f } 64 / 125

  41. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) ∪ { b, e } ∪ ( { ǫ } − P C → f { ǫ } ) ∪ ∅ Q { q, ǫ } { b, e } B C { c, f } 65 / 125

  42. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) ∪ { b, e } ∪ ( { ǫ } − P C → f { ǫ } ) ∪ ∅ Q { q, ǫ } { b, e } ← ∅ ∪ ∅ ∪ { b, e } ∪ ∅ ∪ ∅ B C { c, f } 66 / 125

  43. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( Q ) ← Fo ( Q ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( Q ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) ∪ { b, e } ∪ ( { ǫ } − P C → f { ǫ } ) ∪ ∅ Q { q, ǫ } { b, e } ← ∅ ∪ ∅ ∪ { b, e } ∪ ∅ ∪ ∅ B ← { b, e } C { c, f } 67 / 125

  44. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 68 / 125

  45. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 69 / 125

  46. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 70 / 125

  47. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 71 / 125

  48. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 72 / 125

  49. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( C ) C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 73 / 125

  50. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( C ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) P C → f Q { q, ǫ } { b, e } B C { c, f } 74 / 125

  51. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( C ) C → cC { p, ǫ } ← ∅∪ ( { ǫ }−{ ǫ } ) ∪{ b, e }∪ ( { ǫ }−{ ǫ } ) P C → f Q { q, ǫ } { b, e } B C { c, f } 75 / 125

  52. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( C ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) ∪ { b, e } ∪ ( { ǫ } − P C → f { ǫ } ) ∪ ∅ Q { q, ǫ } { b, e } B C { c, f } 76 / 125

  53. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( C ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) ∪ { b, e } ∪ ( { ǫ } − P C → f { ǫ } ) ∪ ∅ Q { q, ǫ } { b, e } ← ∅ ∪ ∅ ∪ { b, e } ∪ ∅ ∪ ∅ B C { c, f } 77 / 125

  54. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ f C B → bB { p, q, b, e } • Fo ( C ) ← Fo ( C ) ∪ ( F ( ǫ ) − { ǫ } ) ∪ Fo ( A ) ∪ T B → e A { p, q, ǫ, b, e } ( F ( ǫ ) − { ǫ } ) ∪ Fo ( C ) C → cC { p, ǫ } ← ∅ ∪ ( { ǫ } − { ǫ } ) ∪ { b, e } ∪ ( { ǫ } − P C → f { ǫ } ) ∪ ∅ Q { q, ǫ } { b, e } ← ∅ ∪ ∅ ∪ { b, e } ∪ ∅ ∪ ∅ B ← { b, e } C { c, f } 78 / 125

  55. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ { b, e } f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 79 / 125

  56. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ { b, e } f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 80 / 125

  57. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ { b, e } f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 81 / 125

  58. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ { b, e } f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 82 / 125

  59. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ { b, e } f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 83 / 125

  60. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ { b, e } f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 84 / 125

  61. Computing FOLLOW: Example X FIRST( X ) FOLLOW( V ) V T → AB It. 1 It. 2 It. 3 It. 4 A → PQ p { p } T { ǫ } { ǫ } { ǫ } { ǫ } A → BC { q } ∅ { b, e } { b, e } { b, e } q A P → pP b { b } P ∅ { q } { q, b, e } { q, b, e } P → ǫ { e } ∅ ∅ { b, e } { b, e } e Q Q → qQ c { c } B ∅ { ǫ, c, f } { ǫ, c, f } { ǫ, c, f } Q → ǫ { f } ∅ ∅ { b, e } { b, e } f C B → bB { p, q, b, e } T B → e A { p, q, ǫ, b, e } C → cC { p, ǫ } P C → f Q { q, ǫ } { b, e } B C { c, f } 85 / 125

  62. PREDICT Definition 86 / 125

  63. PREDICT Definition • For any A → α ∈ R we define PREDICT( A → α ) as follows: − for all a ∈ Σ ∪ { ǫ } , a ∈ PREDICT( A → α ) iff either a ∈ FIRST ( α ) \{ ǫ } or α ⇒ ∗ ǫ and a ∈ FOLLOW( A ) 87 / 125

  64. Computing PREDICT • PREDICT( A → α ):= ∅ , for every production A → α • For every production A → α : − PREDICT( A → α ):=FIRST( α ) \{ ǫ } − If ǫ ∈ FIRST( α ), then PREDICT( A → α ):=PREDICT( A → α ) ∪ FOLLOW(A) 88 / 125

  65. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ T { p, q, b, e } Q → ǫ A { p, q, ǫ, b, e } B → bB P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 89 / 125

  66. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ A { p, q, ǫ, b, e } B → bB P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 90 / 125

  67. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( A ) − { ǫ } ) A { p, q, ǫ, b, e } B → bB P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 91 / 125

  68. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( A ) − { ǫ } ) ∪ F ( B ) − { ǫ } A { p, q, ǫ, b, e } B → bB P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 92 / 125

  69. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( A ) − { ǫ } ) ∪ F ( B ) − { ǫ } A { p, q, ǫ, b, e } B → bB ← ( { p, q, ǫ, b, e } − { ǫ } ) P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 93 / 125

  70. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( A ) − { ǫ } ) ∪ F ( B ) − { ǫ } A { p, q, ǫ, b, e } B → bB ← ( { p, q, b, e } ) ∪{ b, e } − { ǫ } P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 94 / 125

  71. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( A ) − { ǫ } ) ∪ F ( B ) − { ǫ } A { p, q, ǫ, b, e } B → bB ← ( { p, q, b, e } ) ∪{ b, e } − { ǫ } P { p, ǫ } ← { p, q, b, e } − { ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 95 / 125

  72. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( A ) − { ǫ } ) ∪ F ( B ) − { ǫ } A { p, q, ǫ, b, e } B → bB ← ( { p, q, b, e } ) ∪{ b, e } − { ǫ } P { p, ǫ } ← ( { p, q, b, e } − { ǫ } ) ∪ Fo ( T ) B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 96 / 125

  73. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( T ) ← F ( AB ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( A ) − { ǫ } ) ∪ F ( B ) − { ǫ } A { p, q, ǫ, b, e } B → bB ← ( { p, q, b, e } ) ∪{ b, e } − { ǫ } P { p, ǫ } ← ( { p, q, b, e } − { ǫ } ) ∪ Fo ( T ) B → e ← { p, q, b, e } { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 97 / 125

  74. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB { p, q, b, e } p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ T { p, q, b, e } Q → ǫ A { p, q, ǫ, b, e } B → bB P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 98 / 125

  75. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB { p, q, b, e } p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( A ) ← F ( PQ ) − { ǫ } T { p, q, b, e } Q → ǫ A { p, q, ǫ, b, e } B → bB P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 99 / 125

  76. Computing PREDICT: Example X FIRST( X ) V FOLLOW( V ) Rule R PREDICT( R ) { p } { ǫ } T → AB { p, q, b, e } p T q { q } A { b, e } A → PQ { b } { q, b, e } b P A → BC e { e } Q { b, e } P → pP { c } { ǫ, c, f } c B P → ǫ { f } { b, e } f C Q → qQ P ( A ) ← F ( PQ ) − { ǫ } T { p, q, b, e } Q → ǫ ← ( F ( P ) − { ǫ } ) A { p, q, ǫ, b, e } B → bB P { p, ǫ } B → e { q, ǫ } Q C → cC B { b, e } C → f { c, f } C 100 / 125

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Perl Tutorial-Part II CSCI 3136 Principles of Programming and Languages Slides mainly taken from

Perl Tutorial-Part II CSCI 3136 Principles of Programming and Languages Slides mainly taken from

Perl Tutorial-Part II CSCI 3136 Principles of Programming and Languages Slides mainly taken from Perl Programming, Quentin Smith 1 http://stuff.mit.edu/iap/perl/ Outline Run a Perl Program Data Types Context Operators Flow

802 views • 56 slides
CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 1

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 1

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 1 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 13 Constructing a Scanner: Example (1) Language : Strings of 0s and 1s containing

270 views • 13 slides
CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 2

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 2

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 2 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 13 Language defined by a CFG L ( G ) = { w | S w } If G is a grammar, the

683 views • 13 slides
CSCI 3136 Principles of Programming Languages Names, Scopes, and Bindings - 1 Summer 2013

CSCI 3136 Principles of Programming Languages Names, Scopes, and Bindings - 1 Summer 2013

CSCI 3136 Principles of Programming Languages Names, Scopes, and Bindings - 1 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 18 Name A name is a mnemonic character string representing something else: For example:

194 views • 18 slides
CSCI 3136 Principles of Programming Languages Names, Scopes, and Bindings - 1 Summer 2013

CSCI 3136 Principles of Programming Languages Names, Scopes, and Bindings - 1 Summer 2013

CSCI 3136 Principles of Programming Languages Names, Scopes, and Bindings - 1 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 87 Name A name is a mnemonic character string representing something else: 2 / 87 Name A name is

1.23k views • 87 slides
CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 4 Summer

CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 4 Summer

CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 4 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 11 Regular Expression to NFA (Example) d ( . d | d . )d . d d

385 views • 11 slides
CSCI 3136 Principles of Programming Languages Subroutines and Control Abstraction Summer 2013

CSCI 3136 Principles of Programming Languages Subroutines and Control Abstraction Summer 2013

CSCI 3136 Principles of Programming Languages Subroutines and Control Abstraction Summer 2013 Faculty of Computer Science Dalhousie University 1 / 17 Basic Definitions Subroutines are what we normally call Functions, if they return a

513 views • 17 slides
CSCI 3136 Principles of Programming Languages Subroutines and Control Abstraction Summer 2013

CSCI 3136 Principles of Programming Languages Subroutines and Control Abstraction Summer 2013

CSCI 3136 Principles of Programming Languages Subroutines and Control Abstraction Summer 2013 Faculty of Computer Science Dalhousie University 1 / 42 Basic Definitions Subroutines are what we normally call Functions, if they return a

610 views • 42 slides
CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 6

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 6

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 6 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 74 Push-Down Automata: Formal Definition A push-down automaton (PDA) is a 6-tuple:

858 views • 74 slides
CSCI 3136 Principles of Programming Languages Control Flow - 2 Summer 2013 Faculty of Computer

CSCI 3136 Principles of Programming Languages Control Flow - 2 Summer 2013 Faculty of Computer

CSCI 3136 Principles of Programming Languages Control Flow - 2 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 20 Short-Circuit Evaluation of Boolean Expressions (and a b) : If a is false, b has no effect on the value of

377 views • 20 slides
CSCI 3136 Principles of Programming Languages Control Flow - 2 Summer 2013 Faculty of Computer

CSCI 3136 Principles of Programming Languages Control Flow - 2 Summer 2013 Faculty of Computer

CSCI 3136 Principles of Programming Languages Control Flow - 2 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 40 Short-Circuit Evaluation of Boolean Expressions (and a b) : If a is false, b has no effect on the value of

661 views • 40 slides
CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 2

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 2

CSCI 3136 Principles of Programming Languages Syntactic Analysis and Context-Free Grammars - 2 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 102 Language defined by a CFG L ( G ) = { w | S w } 2 / 102 Language

1.25k views • 102 slides
CSCI 3136 Principles of Programming Languages Logic Languages (Prolog) Summer 2013 Faculty of

CSCI 3136 Principles of Programming Languages Logic Languages (Prolog) Summer 2013 Faculty of

CSCI 3136 Principles of Programming Languages Logic Languages (Prolog) Summer 2013 Faculty of Computer Science Dalhousie University 1 / 37 Logic Programming Concepts H B 1 , B 2 , . . . , B n 2 / 37 Logic Programming Concepts H

504 views • 37 slides
CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 2 Summer

CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 2 Summer

CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 2 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 12 Class Location Change for two days in July Lecture class on Monday July 15 and Wed.

328 views • 12 slides
CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 1 Summer

CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 1 Summer

CSCI 3136 Principles of Programming Languages Lexical Analysis and Automata Theory - 1 Summer 2013 Faculty of Computer Science Dalhousie University 1 / 78 Phases of Compilation Character Stream Scanner (lexical analysis) Token Stream

887 views • 78 slides
CSCI 3136 Principles of Programming Languages Summer 2013 Faculty of Computer Science Dalhousie

CSCI 3136 Principles of Programming Languages Summer 2013 Faculty of Computer Science Dalhousie

CSCI 3136 Principles of Programming Languages Summer 2013 Faculty of Computer Science Dalhousie University 1 / 100 CSCI 3136 Principles of Programming Languages Summer 2013 Aminul Islam Faculty of Computer Science Dalhousie University 2

1.34k views • 100 slides
Ventura River Ventura River Multi- -Species HCP Species HCP Multi Presentation to: Ventura

Ventura River Ventura River Multi- -Species HCP Species HCP Multi Presentation to: Ventura

Ventura River Ventura River Multi- -Species HCP Species HCP Multi Presentation to: Ventura River Watershed Council Presentation to: Ventura River Watershed Council Laura Riege Riege, , Entrix Entrix, Inc. , Inc. Laura March 13, 2007

713 views • 21 slides
American Cyanamid Superfund Site Joe Battipaglia, Region 2 RPM Climate Change Adaptation Webinar

American Cyanamid Superfund Site Joe Battipaglia, Region 2 RPM Climate Change Adaptation Webinar

American Cyanamid Superfund Site Joe Battipaglia, Region 2 RPM Climate Change Adaptation Webinar 4/1/2015 cluin.org Site Location & Background Located in Bridgewater Twp. in Central Northern NJ Pfizer acquired the property from

507 views • 24 slides
Rebuilding After Disaster Strikes: Strategies That Work September 25, 2018 Rebuilding after

Rebuilding After Disaster Strikes: Strategies That Work September 25, 2018 Rebuilding after

Rebuilding After Disaster Strikes: Strategies That Work September 25, 2018 Rebuilding after Disaster Strikes Jeff Pomeranz, City Manager, Cedar Rapids, IA 2008 Flood Strikes Cedar Rapids $5.4 billion in community-wide damage

657 views • 28 slides
The DFG JIT, Inside & Out JavaScriptCores Optimizing Compiler JSConf.EU 2012 Andy Wingo

The DFG JIT, Inside & Out JavaScriptCores Optimizing Compiler JSConf.EU 2012 Andy Wingo

The DFG JIT, Inside & Out JavaScriptCores Optimizing Compiler JSConf.EU 2012 Andy Wingo wingo@igalia.com Compiler hacker at Igalia Contract work on language implementations V8, JavaScriptCore Schemer Hubris Now that

702 views • 30 slides
Overview of the Celebrity Profiling Task at PAN 2020 Lil Wayne WEEZY F LeFloid Kendall Neymar

Overview of the Celebrity Profiling Task at PAN 2020 Lil Wayne WEEZY F LeFloid Kendall Neymar

Overview of the Celebrity Profiling Task at PAN 2020 Lil Wayne WEEZY F LeFloid Kendall Neymar Jr @ LilTunechi @ LeFloid @ KendallJenner @ nejmarjr Matti Wiegmann , Benno Stein, Martin Potthast Bauhaus-Universitt Weimar webis.de Celebrity

518 views • 29 slides
Joseph Gonzalez Joint work with: Yucheng Haijie Danny Carlos Low Gu Bickson Guestrin

Joseph Gonzalez Joint work with: Yucheng Haijie Danny Carlos Low Gu Bickson Guestrin

Distributed Graph-Parallel Computation on Natural Graphs Joseph Gonzalez Joint work with: Yucheng Haijie Danny Carlos Low Gu Bickson Guestrin Graphs are ubiquitous.. 2 Social Media Science Advertising Web Graphs encode

780 views • 58 slides
Tao: Facebook's Distributed Data Store For The Social Graph Bronson et. al., ATC 2013 Joy

Tao: Facebook's Distributed Data Store For The Social Graph Bronson et. al., ATC 2013 Joy

Tao: Facebook's Distributed Data Store For The Social Graph Bronson et. al., ATC 2013 Joy Arulraj CMU 15-799 : Paper Presentation Talk Overview Graph-aware cache backed by a database Efficiency vs. consistency Motivation Memcached

778 views • 24 slides
Election in Trees and Rings T-79.4001 Seminar on Theoretical Computer Science Ilari Nieminen

Election in Trees and Rings T-79.4001 Seminar on Theoretical Computer Science Ilari Nieminen

Leader Election Election in Trees Election in Rings Election in Trees and Rings T-79.4001 Seminar on Theoretical Computer Science Ilari Nieminen 21.02.2007 Ilari Nieminen Election in Trees and Rings Leader Election Election in Trees

655 views • 30 slides

More recommend