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Compilers

Compilers. Machine Code. Program. Add v,v,0 cmp v,5 jmplt ELSE THEN: add x, 12,v ELSE: WHILE: cmp x,3. v = 5; if (v>5) x = 12 + v; while (x !=3) { x = x - 3; v = 10; }. Compiler. Compiler. Lexical analyzer. parser. input. output. machine code. program.

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Compilers

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  1. Compilers

  2. Machine Code Program Add v,v,0 cmp v,5 jmplt ELSE THEN: add x, 12,v ELSE: WHILE: cmp x,3 ... v = 5; if (v>5) x = 12 + v; while (x !=3) { x = x - 3; v = 10; } ...... Compiler

  3. Compiler Lexical analyzer parser input output machine code program

  4. A parser knows the grammar of the programming language

  5. Parser PROGRAM STMT_LIST STMT_LIST STMT; STMT_LIST | STMT; STMT EXPR | IF_STMT | WHILE_STMT | { STMT_LIST } EXPR EXPR + EXPR | EXPR - EXPR | ID IF_STMT if (EXPR) then STMT | if (EXPR) then STMT else STMT WHILE_STMT while (EXPR) do STMT

  6. The parser finds the derivation of a particular input derivation Parser input E => E + E => E + E * E => 10 + E*E => 10 + 2 * E => 10 + 2 * 5 E -> E + E | E * E | INT 10 + 2 * 5

  7. derivation tree derivation E E => E + E => E + E * E => 10 + E*E => 10 + 2 * E => 10 + 2 * 5 + E E 10 E E * 2 5

  8. derivation tree E machine code + E E mult a, 2, 5 add b, 10, a 10 E E * 2 5

  9. Parsing

  10. Parser input string derivation grammar

  11. Example: Parser derivation input ?

  12. Exhaustive Search Phase 1: Find derivation of All possible derivations of length 1

  13. Phase 2 Phase 1

  14. Phase 2 Phase 3

  15. Final result of exhaustive search (top-down parsing) Parser input derivation

  16. Time complexity of exhaustive search Suppose there are no productions of the form Number of phases for string :

  17. For grammar with rules Time for phase 1: possible derivations

  18. Time for phase 2: possible derivations

  19. Time for phase : possible derivations

  20. Total time needed for string : phase 1 phase 2|w| phase 2 Extremely bad!!!

  21. There exist faster algorithms for specialized grammars S-grammar: symbol string of variables appears once Pair

  22. S-grammar example: Each string has a unique derivation

  23. For S-grammars: In the exhaustive search parsing there is only one choice in each phase Time for a phase: Total time for parsing string :

  24. For general context-free grammars: There exists a parsing algorithm that parses a string in time

  25. Simplifications of Context-Free Grammars

  26. A Substitution Rule Equivalent grammar SubstituteB

  27. In general: Substitute B equivalent grammar

  28. Useless Production Some derivations never terminate... Useless Productions

  29. Useless Production Another grammar: Not reachable from S

  30. In general: If Then variable is useful Otherwise, variable is useless

  31. A production is useful if all its variables are useful

  32. Removing Useless Productions Example Grammar:

  33. First: find all variables that produce strings with only terminals Round 1: Round 2:

  34. Keep only the variables that produce terminal symbols

  35. Second: Find all variables reachable from Dependency Graph not reachable

  36. Keep only the variables reachable from S Final Grammar

  37. Nullable Variables Nullable Variable:

  38. Removing Nullable Variables Example Grammar: Nullable variable

  39. Final Grammar Substitute

  40. Unit-Productions Unit Production:

  41. Removing Unit Productions Observation: Is removed immediately

  42. Example Grammar:

  43. Substitute

  44. Remove

  45. Substitute

  46. Remove repeated productions Final grammar

  47. Removing All • Step 1: Remove Nullable Variables • Step 2: Remove Unit-Productions • Step 3: Remove Useless Variables

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