CS 230 Programming Languages

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1 CS 230 Programming Languages 10 / 16 / 2013 Instructor: Michael Eckmann

2 Today s Topics Questions/comments? Top Down / Recursive Descent Parsers

3 Top Down Parsers We have a left sentential form xa Expand A (the leftmost non-terminal) using a production that has A as its LHS. How might we do this? We would call the lexical analyzer to get the next lexeme. Then determine which production to expand based on the lexeme/token returned. For grammars that are one lookahead, exactly one RHS of A will have as its first symbol the lexeme/token returned. If there is no RHS of A with its first symbol being the lexeme/token returned --- what do we think occurred?

4 Top Down Parsers Top down parsers can be implemented as recursive descent parsers --- that is, a program based directly on the BNF description of the language. Or they can be represented by a parsing table that contains all the information in the BNF rules in table form. These top down parsers are LL algorithms --- L for left-to-right scan of the input and L for leftmost derivation.

5 Top Down Parsers Left recursion is problematic for top-down parsers. e.g. <A> -> <A> b Each non-terminal is written as a function in the parser. So, a recursive descent parser function for this production would continually call itself first and never get out of the recursion. Similarly for any top-down parser. Left recursion is problematic for top-down parsers even if it is indirect. e.g. <A> -> <B> b <B> -> <A> a Bottom up parsers do not have this problem with left recursion.

6 Top Down Parsers When a nonterminal has more than one RHS, the first terminal symbol that can be generated in a derivation for each of them must be unique to that RHS. If it is not unique, then top-down parsing (with one lookahead) is impossible for that grammar. Because there is only one lookahead symbol, which lex would return to the parser, that one symbol has to uniquely determine which RHS to choose. Does that make sense?

7 Top Down Parsers Example: Here are two productions in a possible grammar: <variable> -> identifier identifier [ <expression> ] Assuming we have a left sentential form where the next nonterminal to be expanded is <variable> and we call out to lex() to get the next token and it returns identifier. Which production will we pick?

8 Top Down Parsers The pairwise disjointness test is used on grammars to determine if they have this problem. What it does is, it determines the first symbol for every RHS of a production and for those with the same LHS, the first symbols must be different for each. <A> -> a <B> b<a>b c <C> d The 4 RHSs of A here each have as their first symbol {a}, {b}, {c}, {d} respectively. These sets are all disjoint so these productions would pass the test. The ones on the previous slide would not.

9 Top Down Parsers Note: if the first symbol on the RHS is a nonterminal, we would need to expand it to determine the first symbol. e.g. <A> -> <B> a b<a>b c <C> d <B> -> <C> f <C> -> s <F> Here, to determine the first symbol of the first RHS of A, we need to follow <B> then <C> to find out that it is s. So, the 4 RHSs of A here each have as their first symbol {s}, {b}, {c}, {d} respectively. These sets are all disjoint so the productions for <A> would pass the test. How about for the <B> and <C> productions?

10 Recursive descent example So called because many of its subroutines (one for each non-terminal) are recursive and descent because it is a topdown parser. EBNF is well suited for these parsers because EBNF reduces the number of non-terminals (as compared to plain BNF) which in turn, reduces the number of subroutines. A grammar for simple expressions: <expr> <term> {(+ -) <term>} <term> <factor> {(* /) <factor>} <factor> id ( <expr> ) Anyone remember what the curly braces mean in EBNF?

11 Recursive descent example Assume we have a lexical analyzer named lex, which puts the next token code in nexttoken The coding process when there is only one RHS: For each terminal symbol in the RHS, compare it with the next input token; if they match, continue, else there is an error For each nonterminal symbol in the RHS, call its associated parsing subroutine

12 Recursive descent example /* Function expr (written in the C language) Parses strings in the language generated by the rule: <expr> <term> {(+ -) <term>} */ void expr() { /* Parse the first term */ term(); /* term() is it's own function representing the non-terminal <term>*/ /* As long as the next token is + or -, call lex to get the next token, and parse the next term */ } while (nexttoken == PLUS_OP nexttoken == MINUS_OP) { lex(); term(); }

13 Recursive descent example Note: by convention each subroutine leaves the most recent token in nexttoken A nonterminal that has more than one RHS requires an initial process to determine which RHS it is to parse The correct RHS is chosen on the basis of the next token of input (the lookahead) The next token is compared with the first token that can be generated by each RHS until a match is found If no match is found, it is a syntax error Let's now look at an example of how the parser would handle multiple RHS's.

14 Recursive descent example /* Function term Parses strings in the language generated by the rule: <term> <factor> {(* /) <factor>} */ void expr() { /* Parse the first factor */ factor(); /* factor() is it's own function representing the non-terminal <factor>*/ /* As long as the next token is * or /, call lex to get the next token, and parse the next term */ } while (nexttoken == MULT_OP nexttoken == DIV_OP) { lex(); factor(); }

15 Recursive descent example /* Function factor Parses strings in the language generated by the rule: <factor> -> id (<expr>) */ void factor() { if (nexttoken == IDENT) /* For the RHS id, call lex to get the next token*/ } lex(); /* If the RHS is ( <expr> ) call lex to pass over the left parenthesis, call expr, and check for the right parenthesis */ else if (nexttoken == LEFT_PAREN) { lex(); expr(); if (nexttoken == RIGHT_PAREN) lex(); else error(); } else error(); /* Neither RHS matches */

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