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Unformatted text preview: Parsers Monday, September 13, 2010 Agenda Terminology LL(1) Parsers Overview of LR Parsing Monday, September 13, 2010 Terminology Grammar G = (V t , V n , S, P) V t is the set of terminals V n is the set of nonterminals S is the start symbol P is the set of productions Each production takes the form: V n  (V n  V t )+ Grammar is contextfree (why?) A simple grammar: G = ({a, b}, {S, A, B}, {S A B $, A A a, A a, B B b, B b}, S) Monday, September 13, 2010 Context free: single nonterminal on left side. Can apply a production without worrying about the context Context sensitive: nonterminal and terminals on left side. Choosing which production to apply requires looking at the context Terminology V is the vocabulary of a grammar, consisting of terminal (V t ) and nonterminal (V n ) symbols For our sample grammar V n = {S, A, B} Nonterminals are symbols on the LHS of a production Nonterminals are constructs in the language that are recognized during parsing V t = {a, b} Terminals are the tokens recognized by the scanner They correspond to symbols in the text of the program Monday, September 13, 2010 Terminology Productions (rewrite rules) tell us how to derive strings in the language Apply productions to rewrite strings into other strings We will use the standard BNF form P = { S A B $ A A a A a B B b B b } Monday, September 13, 2010 Generating strings Given a start rule, productions tell us how to rewrite a nonterminal into a different set of symbols By convention, Frst production applied has the start symbol on the left, and there is only one such production S A B $ A A a A a B B b B b To derive the string a a b b b we can do the following rewrites: S A B $ A a B $ a a B $ a a B b $ a a B b b $ a a b b b $ Monday, September 13, 2010 Terminology Strings are composed of symbols A A a a B b b A a is a string We will use Greek letters to represent strings composed of both terminals and nonterminals L(G) is the language produced by the grammar G All strings consisting of only terminals that can be produced by G In our example, L(G) = a+b+$ All regular expressions can be expressed as grammars for contextfree languages, but not viceversa Consider: a i b i $ (what is the grammar for this?) Monday, September 13, 2010 Parse trees Tree which shows how a string was produced by a language Interior nodes of tree: non terminals Children: the terminals and nonterminals generated by applying a production rule Leaf nodes: terminals S A B A a B b B b b a Monday, September 13, 2010 Leftmost derivation Rewriting of a given string starts with the leftmost symbol Exercise: do a leftmost derivation of the input program F(V + V) using the following grammar: What does the parse tree look like?...
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