CSE302: Compiler Design

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1 CSE302: Compiler Design Instructor: Dr. Liang Cheng Department of Computer Science and Engineering P.C. Rossin College of Engineering & Applied Science Lehigh University March 20, 2007

2 Outline Recap LR(0) parsing and SLR(1) parsing General/Canonical LR(1) parsing Lookahead LR(1) / LALR(1) parsing Summary and homework

3 LR Parsing: A Schematic View Bottom-up parsing Rightmost derivations and right-sentential forms Parsing stack Input buffer Actions \$ InputString\$ lookahead zero or one token, decide S/R \$StartSymbol \$ accept

4 Finite Automata for Both LR(0) and SLR(1) Parsing Finite automata of parsing states LR(0) items are used to identify the parsing states A α A.α is an item (initial item) We may about to recognize A by A α A α. is also an item (complete item) α may be a handle for reduction A βγ A β.γ, A.βγ, and A βγ. are LR(0) items NFA construction Subset construction for NFA to DFA

5 LR(0) Parser NFA Construction X A α.xβ A αx.β Shift action if X is a terminal ε A α.xβ X.γ Reduction action if X is a non-terminal

6 The LR(0) and SLR(1) Parsing Algorithms LR(0) parsing If state s contains A α.xβ where X is a terminal, then shift and the state changes to s containing A αx.β If state s contains A γ., then reduce by A γ(stack ops) and the state changes to s containing B λa.η SLR(1) parsing If state s contains A α.xβ where X is a terminal, and the lookahead token is X, then shift and the state changes to s containing A αx.β If state s contains A γ., and the lookahead token is in FOLLOW(A), then reduce by A γ(stack ops) and the state changes to s containing B λa.η Examples S (S)S ε Input: () A (A) a Input: ((a))

7 Limits of LR(0) and SLR(1) Parsing LR(0) parsing cannot handle a grammar that in its DFA there is a state s s contains a shift item A α.xβ and a complete item B δ. s contains two complete items A γ. and B δ. SLR(1) parsing cannot handle a grammar that in its DFA there is a state s s contains a shift item A α.xβ with X a terminal and a complete item B δ. with X in Follow(B) s contains two complete items A γ. and B δ. with a nonempty Follow(A) Follow(B)

8 Observations SLR(1) parsing is more powerful than LR(0) parsing due to its consideration of lookaheads in the parsing process

9 Another Example Another example stmt call-stmt assign-stmt call-stmt identifier assign-stmt var=expr var identifier expr var number Is this an SLR(1) grammar? An equivalent grammar S id V=E V id E V n

10 Observations SLR(1) parsing is more powerful than LR(0) parsing due to its consideration of lookaheads in the parsing process However, the lookaheads are not used in the finite automata construction The limit of SLR(1) parsing can be improved if its NFA/DFA construction does not ignore lookaheads

11 Outline Recap LR(0) parsing and SLR(1) parsing General/Canonical LR(1) parsing Lookahead LR(1) / LALR(1) parsing Summary and homework

12 Finite Automata of Parsing States Finite automata for LR(1) parsers LR(1) items are used to identify the parsing states An LR(1) item is a pair consisting of an LR(0) item and a lookahead token [A α.β, a] NFA construction: transitions between LR(1) items Non-ε transitions Given an LR(1) item [A α.xβ, a], where X is any symbol, there is a transition on X to the item [A αx.β, a] ε-transitions Given an LR(1) item [A α.bγ, a], where B is a nonterminal, there are ε-transitions to items [B.β, b] for every production B βand for every token b in First(γa)

13 LR(1) NFA/DFA and Parsing Table Construction Examples Grammar S S S id V=E V id E V n NFA construction: transitions between LR(1) items Non-ε transitions Given an LR(1) item [A α.xβ, a], where X is any symbol, there is a transition on X to the item [A αx.β, a] ε-transitions Given an LR(1) item [A α.bγ, a], where B is a nonterminal, there are ε-transitions to items [B.β, b] for every production B βand for every token b in First(γa) Input: id=n

14 LR(1) Parsing Algorithm LR(1) parsing If state s contains [A α.xβ,a] where X is a terminal, and the lookahead token is X, then shift and the state changes to s containing [A αx.β,a] If state s contains [A γ.,a], and the lookahead token is a, then reduce by A γ(stack ops) and the state changes to s containing [B λa.η,b] LR(0) parsing If state s contains A α.xβ where X is a terminal, then shift and the state changes to s containing A αx.β If state s contains A γ., then reduce by A γ(stack ops) and the state changes to s containing B λa.η SLR(1) parsing If state s contains A α.xβ where X is a terminal, and the lookahead token is X, then shift and the state changes to s containing A αx.β If state s contains A γ., and the lookahead token is in FOLLOW(A), then reduce by A γ(stack ops) and the state changes to s containing B λa.η

15 Another LR(1) DFA and Parsing Table Construction Examples Grammar A A A (A) A a NFA construction: transitions between LR(1) items Non-ε transitions Given an LR(1) item [A α.xβ, a], where X is any symbol, there is a transition on X to the item [A αx.β, a] ε-transitions Given an LR(1) item [A α.bγ, a], where B is a nonterminal, there are ε-transitions to items [B.β, b] for every production B βand for every token b in First(γa) Compare the LR(1) DFA with the LR(0) DFA

16 Outline Recap LR(0) parsing and SLR(1) parsing General/Canonical LR(1) parsing Lookahead LR(1) / LALR(1) parsing Summary and homework

17 Two Principles of LALR(1) Parsing The core of a state in LR(1) DFA is a state in the LR(0) DFA. Given two states s1 and s2 in the LR(1) DFA that have the same core. Suppose there is a transition on X from s1 to a state t1. Then there is also a transition on X from s2 to a state t2, and t1 and t2 have the same core. Therefore based on LR(1) DFA, we can transform it to a DFA that is identical to the LR(0) DFA, except that each state consists of items with sets of lookaheads.

18 Constructing LALR(1) DFA Identifying all states that have the same core and forming the union of the lookaheads for each LR(0) item Linking the new states based on the links in the LR(1) DFA An example A A A (A) A a

19 Outline Recap Bottom-up parsing (Section 4.5) Summary and homework

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