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CS 412/413 Spring 2007 Introduction to Compilers 1
CS412/CS
Introduction to Compilers
Tim Teitelbaum
Lecture 7: LL parsing and AST construction
February 5, 2007
CS 412/413 Spring 2007 Introduction to Compilers 2
LL(1) Parsing
• Last time:
– how to build a parsing table for an LL(1)
grammar (use FIRST/FOLLOW sets)
– how to construct a recursive-descent parser
from the parsing table
• Grammars may not be LL(1)
– Use left factoring when grammar has multiple
productions starting with the same symbol.
– Other problematic cases?
CS 412/413 Spring 2007 Introduction to Compilers 3
if-then-else
• How to write a grammar for if stmts?
S → if (E) S
S → if (E) S else S
S → other
Is this grammar ok?
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No—Ambiguous!
• How to parse?
if (E 1 ) if (E 2 ) S 1 else S 2
Which “if” is the “else” attached to?
S → if (E) S → if (E) if (E) S else S
S → if (E) S else S → if (E) if (E) S else S
S → if (E) S S → if (E) S else S S → other
if E 1 if E 2 S 1 S (^2) if E 1 if S (^2) E 2 S (^1)
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Grammar for Closest-if Rule
• Want to rule out if (E) if (E) S else S
• Impose that unmatched “if” statements
occur only on the “else” clauses
statement → matched | unmatched matched → if (E) _______ else __________ | other unmatched → if (E) ________ | if (E) _______ else __________
CS 412/413 Spring 2007 Introduction to Compilers 6
Grammar for Closest-if Rule
• Want to rule out if (E) if (E) S else S
• Impose that unmatched “if” statements
occur only on the “else” clauses
statement → matched | unmatched matched → if (E) matched else matched | other unmatched → if (E) ________ | if (E) _______ else __________
CS 412/413 Spring 2007 Introduction to Compilers 7
Grammar for Closest-if Rule
• Want to rule out if (E) if (E) S else S
• Impose that unmatched “if” statements
occur only on the “else” clauses
statement → matched | unmatched matched → if (E) matched else matched | other unmatched → if (E) ________ | if (E) matched else unmatched
CS 412/413 Spring 2007 Introduction to Compilers 8
Grammar for Closest-if Rule
• Want to rule out if (E) if (E) S else S
• Impose that unmatched “if” statements
occur only on the “else” clauses
statement → matched | unmatched matched → if (E) matched else matched | other unmatched → if (E) statement | if (E) matched else unmatched
CS 412/413 Spring 2007 Introduction to Compilers 9
LL(1) if-then-else?
statement → if (E) matched optional-tail | other
matched → if (E) matched else matched | other
optional-tail → else tail | ε tail → if (E) tail | other
CS 412/413 Spring 2007 Introduction to Compilers 10
LL(1) if-then-else?
statement → if (E) matched optional-tail | other matched → if (E) matched else matched | other optional-tail → else tail | ε tail → if (E) tail | other
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Left-Recursive Grammars
• Left-recursive grammars are not LL(1)!
S → S α
S → β
• FIRST(β) ⊆ FIRST(Sα)
• Both productions will appear in the predictive
table, at row S in all the columns corresponding
to symbols in FIRST(β)
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Eliminate Left Recursion
• Method for left-recursion elimination:
Replace
A → A α 1 | … | A αm
A → β 1 | … | βn
with
A → β 1 A’ | … | βn A’
A’ → α 1 A’ | … | αm A’ | ε
- (See the complete algorithm in the Dragon Book)
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AST Creation: parse_S
Expr parse_S() { switch (token) { case num: case ‘(’: Expr left = parse_E(); Expr right = parse_S’(); if (right == null) return left; else return new Add(left, right); default : throw new ParseError(); } }
S → ES'
S' → ε | +S E → num | (S)
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EBNF: Extended BNF Notation
• Extended Backus-Naur Form = a form of
specifying grammars which allows some regular
expression syntax on RHS
*, +, ( ),? operators (also [X] means X?)
S → ES’
S’ → ε |+S
• EBNF version: agnostic on + associativity
S → E(+E)*
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Top-down Parsing EBNF
• Recursive-descent code can directly implement
the EBNF grammar:
S → E(+E)*
void parse_S () { // parses sequence of E+E+E ... parse_E (); while (true) { switch (token) { case ‘+’: token = input.read(); parse_E(); break ; case ‘)’: case EOF: return ; default : throw new ParseError(); } }
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Reassociating the AST
Expr parse_S() { Expr result = parse_E(); while ( true ) { switch (token) { case ‘+’: token = input.read(); result = new Add(result, parse_E()); break ; case ‘)’: case EOF: return result; default : throw new ParseError(); } }
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Top-Down Parsing Summary
Language grammar
LL(1) grammar
predictive parsing table
recursive-descent parser
parser with AST generation
Left-recursion elimination Left-factoring
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Exercises
• Which of the following are LL(1)?
A → aACd | b C → c | ε
A → aACd | b C → A | ε
A → aAC | b C → c | ε
