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Chap. 5, Top-Down Parsing J. H. Wang Mar. 29, 2011

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Outline Overview LL(k) Grammars Recursive-Descent LL(1) Parsers Table-Driven LL(1) Parsers Obtaining LL(1) Grammars A Non-LL(1) Language Properties of LL(1) Parsers Parse Table Representation Syntactic Error Recovery and Repair

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Overview Two forms of top-down parsers –Recursive-descent parsers –Table-driven LL parsers: LL(k) – to be explained later Compiler compilers (or parser generators) –CFG as a language’s definition, parsers can be automatically constructed –Language revision, update, or extension can be easily applied to a new parser –Grammar can be proved unambiguous if parser construction is successful

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Top-Down Parsing Top-down –To grow a parse tree from root to leaves Predictive –Must predict which production rule to be applied LL(k) –Scan input left to right, leftmost derivation, k symbol lookahead Recursive descent –Can be implemented by a set of mutually recursive procedures

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LL(k) Grammars Recall from Chap.2 –A parsing procedure for each nonterminal A –The procedure is responsible for accomplishing one step of derivation for the corresponding production –Choosing production by inspecting the next k tokens. Predict Set for production A is the set of tokens that trigger the production –Predict Set is determined by the right-hand side (RHS)

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We need a strategy for choosing productions –Predict k (p): the set of length-k token strings that predict the application of rule p Input string: a * S=>* lm Ay 1 …y n –P={p ProductionsFor(A)|a Predict(p)} P: empty set -> syntax error P: more than one productions -> nondeterminism P: exactly one production

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How to Compute Predict(p) To predict production p: A X 1 …X m, m>=0 –The set of terminal symbols that are first produced in some derivation from X 1 …X m –Those terminal symbols that can follow A –(Fig. 5.1)

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For LL(1) grammar, the productions for each nonterminal A must have disjoint predict sets Not all CFGs are LL(1) –More lookahead may be needed: LL(k), k>1 –A more powerful parsing method may be required (Chap. 6) –The grammar may be ambiguous

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S MATCH PEEK ADVANCE ERROR

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Recursive-Descent LL(1) Parsers Input: token stream ts –PEEK(): to examine the next input token without advancing the input –ADVANCE(): to advances the input by one token To construct a recursive-descent parser –We write a separate procedure for each nonterminal A –For each production pi, we check each symbol in the RHS X 1 …X m Terminal symbol: MATCH( ts, X i ) Nonterminal symbol: call X i (ts)

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PEEK

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MATCH

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Table-Driven LL(1) Parsers Creating recursive-descent parsers can be automated, but –Size of parser code –Inefficiency: overhead of method calls and returns To create table-driven parsers, we use stack to simulate the actions by MATCH() and calls to nonterminals’ procedures –Terminal symbol: MATCH –Nonterminal symbol: table lookup –(Fig. 5.8)

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PUSH MATCH POP ERROR APPLY POP PUSH PEEK PARSER

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How to Build LL(1) Parse Table The table is indexed by the top-of-stack (TOS) symbol and the next input token –Row: nonterminal symbol –Column: next input token –(Fig. 5.9)

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ILL ABLE

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Obtaining LL(1) Grammars It’s easy to violate the requirement of a unique prediction for each combination of nonterminal and lookahead symbols –Common prefixes –Left recursion

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Common Prefixes Two productions for the same nonterminal begin with the same string of grammar symbols –Ex. (Fig. 5.12) Not LL(k) Factoring transformation –Fig. 5.13 –Ex. (Fig. 5.14)

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ACTOR

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LIMINATE EFT ECURSION

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Left Recursion A production is left recursive if its LHS symbol is also the first symbol of its RHS –E.g. StmtList StmtList ; Stmt –A A | –(Fig. 5.15 & Fig. 5.16)

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A Non-LL(1) Language Almost all common programming language constructs: LL(1) –One exception: if-then-else ( dangling else program) –Can be resolved by mandating that each else is matched to its closest unmatched then –(Fig. 5.17)

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Ambiguous (Chap. 6) –E.g. if expr then if expr then other else other If expr then { if expr then other else other } If expr then { if expr then other } else other -> at least two distinct parses Dangling bracket language (DBL) –DBL={[ i ] j |i≥j≥0} if expr then Stmt -> [ (opening bracket) else Stmt -> ] (optional closing bracket)

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Fig. 5.18(a) –S [ S CL | λ CL ] | λ E.g. [[] Fig. 5.18(b) –S [ S | T T [ T ] | λ

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It’s not LL(k) –[ Predict( S [S ) [ Predict( S T ) [[ Predict 2 ( S [S ) [[ Predict 2 ( S T ) … [ k Predict k ( S [S ) [ k Predict k ( S T )

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Properties of LL(1) Parsers A correct, leftmost parse is constructed All grammars in LL(1) are unambiguous All table-driven LL(1) parsers operate in linear time and space with respect to the length of the parsed input

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Thanks for Your Attention!

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