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September 13, 2014

Computer Science at Azusa Pacific University. CS400 Compiler Construction. Sheldon X. Liang Ph. D. September 13, 2014. Azusa, CA. 1. September 13, 2014. Azusa Pacific University, Azusa, CA 91702, Tel: (800) 8 25-5278

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September 13, 2014

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  1. Computer Science at Azusa Pacific University CS400 Compiler Construction Sheldon X. Liang Ph. D. September 13, 2014 Azusa, CA 1 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  2. CS@APU: CS400 Compiler Construction Parsing • Universal (any C-F grammar) • Cocke-Younger-Kasimi • Earley • Top-down (C-F grammar with restrictions) • Recursive descent (predictive parsing) • LL (Left-to-right, Leftmost derivation) methods • Bottom-up (C-F grammar with restrictions) • Operator precedence parsing • LR (Left-to-right, Rightmost derivation) methods • SLR, canonical LR, LALR 2 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  3. CS@APU: CS400 Compiler Construction Got it with following questions • Bottom Up Parsing • Left to right, rightmost • Reduce from leaves to root • Terminal is gradually eaten • SLR & LALR • Simple extension of LR(0) • Lookahead LR • Avoid unnecessary conflicts • Summary • LL, LR, SLR, LALR • Grammar types • Goto state transition 3 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  4. CS@APU: CS400 Compiler Construction SLR Grammars • SLR (Simple LR): a simple extension of LR(0) shift-reduce parsing • SLR eliminates some conflicts by populating the parsing table with reductions A on symbols in FOLLOW(A) Shift on + State I0:S  •EE  •id+EE  •id State I2:E  id•+EE  id• S  EE  id+EE  id goto(I0,id) goto(I3,+) FOLLOW(E)={$}thus reduce on $ 4 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  5. CS@APU: CS400 Compiler Construction SLR Parsing Table • Reductions do not fill entire rows • Otherwise the same as LR(0) 1. S  E2. E  id+E3. E  id Shift on + FOLLOW(E)={$}thus reduce on $ 5 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  6. CS@APU: CS400 Compiler Construction SLR Parsing • An LR(0) state is a set of LR(0) items • An LR(0) item is a production with a • (dot) in the right-hand side • Build the LR(0) DFA by • Closure operation to construct LR(0) items • Goto operation to determine transitions • Construct the SLR parsing table from the DFA • LR parser program uses the SLR parsing table to determine shift/reduce operations 6 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  7. CS@APU: CS400 Compiler Construction Constructing SLR Parsing Tables • Augment the grammar with S’S • Construct the set C={I0,I1,…,In} of LR(0) items • If [A•a]  Ii and goto(Ii,a)=Ij then set action[i,a]=shift j • If [A•]  Ii then set action[i,a]=reduce A for all a  FOLLOW(A) (apply only if AS’) • If [S’S•] is in Ii then set action[i,$]=accept • If goto(Ii,A)=Ij then set goto[i,A]=j • Repeat 3-6 until no more entries added • The initial state i is the Ii holding item [S’•S] 7 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  8. CS@APU: CS400 Compiler Construction LR(0) Items of a Grammar • An LR(0) item of a grammar G is a production of G with a • at some position of the right-hand side • Thus, a productionA X Y Zhas four items: [A • X Y Z][A X • Y Z][A X Y • Z][A X Y Z •] • Note that production A  has one item [A •] 8 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  9. CS@APU: CS400 Compiler Construction Constructing the set of LR(0) Items of a Grammar • The grammar is augmented with a new start symbol S’ and production S’S • Initially, set C = closure({[S’•S]})(this is the start state of the DFA) • For each set of items I  C and each grammar symbol X  (NT) such that goto(I,X)  C and goto(I,X)  , add the set of items goto(I,X) to C • Repeat 3 until no more sets can be added to C 9 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  10. CS@APU: CS400 Compiler Construction The Closure Operation for LR(0) Items • Start with closure(I) = I • If [A•B]  closure(I) then for each production B in the grammar, add the item [B•] to I if not already in I • Repeat 2 until no new items can be added 10 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  11. CS@APU: CS400 Compiler Construction The Closure Operation (Example) closure({[E’ •E]}) = { [E’  • E] } { [E’  • E][E  • E+T][E  • T][T  • T*F] [T  • F] [F  • (E)] [F  • id] } { [E’  • E][E  • E+T][E  • T]} { [E’  • E][E  • E+T][E  • T][T  • T*F] [T  • F] } Add [E•] Add [T•] Grammar:E  E+T | TT  T*F | FF  (E)F  id Add [F•] 11 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  12. CS@APU: CS400 Compiler Construction The Goto Operation for LR(0) Items • For each item [A•X]  I, add the set of items closure({[AX•]}) to goto(I,X) if not already there • Repeat step 1 until no more items can be added to goto(I,X) • Intuitively, goto(I,X) is the set of items that are valid for the viable prefix X when I is the set of items that are valid for  12 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  13. CS@APU: CS400 Compiler Construction The Goto Operation (Example 1) Suppose I = Then goto(I,E)= closure({[E’  E •, E  E •+T]})= { [E’  • E][E  • E+T][E  • T][T  • T*F] [T  • F] [F  • (E)] [F  • id] } { [E’  E •] [E  E •+T] } Grammar:E  E+T | TT  T*F | FF  (E)F  id 13 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  14. CS@APU: CS400 Compiler Construction The Goto Operation (Example 2) Suppose I = { [E’  E •], [E  E • +T]} Then goto(I,+) = closure({[E  E + • T]}) = { [E  E + • T] [T  • T * F] [T  • F] [F  • ( E )] [F  • id] } Grammar:E  E+T | TT  T*F | FF  (E)F  id 14 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  15. CS@APU: CS400 Compiler Construction Example SLR Grammar and LR(0) Items I0 = closure({[C’  •C]})I1 = goto(I0,C) = closure({[C’  C•]})… Augmentedgrammar:1. C’  C2. C  A B3. A  a4. B  a 15 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  16. CS@APU: CS400 Compiler Construction Example SLR Parsing Table 16 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  17. CS@APU: CS400 Compiler Construction SLR and Ambiguity • Every SLR grammar is unambiguous, but not every unambiguous grammar is SLR • Consider for example the unambiguous grammarS L=R | RL  *R | idR  L 17 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  18. CS@APU: CS400 Compiler Construction LR(1) Grammars • SLR too simple • LR(1) parsing uses lookahead to avoid unnecessary conflicts in parsing table • LR(1) item = LR(0) item + lookahead LR(0) item:[A•] LR(1) item:[A•, a] 18 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  19. CS@APU: CS400 Compiler Construction SLR Versus LR(1) • Split the SLR states byadding LR(1) lookahead • Unambiguous grammar1. S L=R2.| R3. L  *R4. | id5. R  L Should not reduce on =, because noright-sentential form begins with R= 19 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  20. CS@APU: CS400 Compiler Construction LR(1) Items • An LR(1) item [A•, a]contains a lookahead terminal a, meaning  already on top of the stack, expect to see a • For items of the form[A•, a]the lookahead a is used to reduce A only if the next input is a • For items of the form[A•, a]with  the lookahead has no effect 20 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  21. CS@APU: CS400 Compiler Construction The Closure Operation for LR(1) Items • Start with closure(I) = I • If [A•B, a]  closure(I) then for each production B in the grammar and each terminal b  FIRST(a), add the item [B•, b] to I if not already in I • Repeat 2 until no new items can be added 21 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  22. CS@APU: CS400 Compiler Construction The Goto Operation for LR(1) Items • For each item [A•X, a]  I, add the set of items closure({[AX•, a]}) to goto(I,X) if not already there • Repeat step 1 until no more items can be added to goto(I,X) 22 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  23. CS@APU: CS400 Compiler Construction Constructing the set of LR(1) Items of a Grammar • Augment the grammar with a new start symbol S’ and production S’S • Initially, set C = closure({[S’•S, $]})(this is the start state of the DFA) • For each set of items I  C and each grammar symbol X  (NT) such that goto(I,X)  C and goto(I,X)  , add the set of items goto(I,X) to C • Repeat 3 until no more sets can be added to C 23 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  24. CS@APU: CS400 Compiler Construction Example Grammar and LR(1) Items • Unambiguous LR(1) grammar:S L=R | RL  *R| idR  L • Augment with S’  S • LR(1) items (next slide) 24 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  25. CS@APU: CS400 Compiler Construction 25 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  26. CS@APU: CS400 Compiler Construction Constructing Canonical LR(1) Parsing Tables • Augment the grammar with S’S • Construct the set C={I0,I1,…,In} of LR(1) items • If [A•a, b]  Ii and goto(Ii,a)=Ij then set action[i,a]=shift j • If [A•, a]  Ii then set action[i,a]=reduce A (apply only if AS’) • If [S’S•, $] is in Ii then set action[i,$]=accept • If goto(Ii,A)=Ij then set goto[i,A]=j • Repeat 3-6 until no more entries added • The initial state i is the Ii holding item [S’•S,$] 26 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  27. CS@APU: CS400 Compiler Construction Example LR(1) Parsing Table Grammar:1. S’ S2. S L=R3. S R4. L  *R5. L  id6. R  L 27 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  28. CS@APU: CS400 Compiler Construction LALR(1) Grammars • LR(1) parsing tables have many states • LALR(1) parsing (Look-Ahead LR) combines LR(1) states to reduce table size • Less powerful than LR(1) • Will not introduce shift-reduce conflicts, because shifts do not use lookaheads • May introduce reduce-reduce conflicts, but seldom do so for grammars of programming languages 28 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  29. CS@APU: CS400 Compiler Construction Constructing LALR(1) Parsing Tables • Construct sets of LR(1) items • Combine LR(1) sets with sets of items that share the same first part 29 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  30. CS@APU: CS400 Compiler Construction Example LALR(1) Grammar • Unambiguous LR(1) grammar:S L=R | RL  *R | idR  L • Augment with S’  S • LALR(1) items (next slide) 30 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  31. CS@APU: CS400 Compiler Construction 31 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  32. CS@APU: CS400 Compiler Construction Example LALR(1) Parsing Table Grammar:1. S’ S2. S L=R3. S R4. L  *R5. L  id6. R  L 32 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  33. CS@APU: CS400 Compiler Construction LL, SLR, LR, LALR Summary • LL parse tables computed using FIRST/FOLLOW • Nonterminals  terminals  productions • Computed using FIRST/FOLLOW • LR parsing tables computed using closure/goto • LR states  terminals  shift/reduce actions • LR states  nonterminals  goto state transitions • A grammar is • LL(1) if its LL(1) parse table has no conflicts • SLR if its SLR parse table has no conflicts • LALR(1) if its LALR(1) parse table has no conflicts • LR(1) if its LR(1) parse table has no conflicts 33 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  34. CS@APU: CS400 Compiler Construction LL, SLR, LR, LALR Grammars 34 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  35. CS@APU: CS400 Compiler Construction Got it with following questions • Bottom Up Parsing • Left to right, rightmost • Reduce from leaves to root • Terminal is gradually eaten • SLR & LALR • Simple extension of LR(0) • Lookahead LR • Avoid unnecessary conflicts • Summary • LL, LR, SLR, LALR • Grammar types • Goto state transition 35 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

  36. CS@APU: CS400 Compiler Construction Thank you very much! Questions? 36 September 13, 2014 Azusa Pacific University, Azusa, CA 91702,Tel: (800) 825-5278 Department of Computer Science,http://www.apu.edu/clas/computerscience/

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