Parsers v Grammars can be used to describe

Parsers v Grammars can be used to describe a set of strings (Language) that have certain properties. Moreover, the productions in a grammar can be used to “generate” strings in the specified language. v Given a particular string a parser can be used to determine whether or not the string is in the language generated by a specified grammar. A parser can produce a parse tree which provides a derivation for the string. v Concepts Ø Parse tree Ø Ambiguous grammars Ø Recursive descent parsers

Parse Tree v. A derivation is conveniently stored in a tree, where internal nodes correspond to syntactic categories and the children of a node correspond to the element of the rhs in the rule that was applied

Grammars v Grammar 1 Ø <number> <digit> <number> Ø <digit> 0|1|2|3|4|5|6|7|8|9 v Grammar 2 Ø <expr> + <expr> Ø <expr> <number> v Grammar 3 Ø <Balanced> (<Balanced>) <Balanced> Ø <Balanced>

Example Parse Tree <number> / <digit> <number> | / 1 <digit> <number> | | 2 <digit> | 3

More Grammars v. Grammar 3 Ø<Balanced> (<Balanced>) Ø<Balanced> Ø<Balanced> v. Grammar 4 Ø<Balanced> (<Balanced>) <Balanced> Ø<Balanced>

Ambiguous Grammars v. A grammar is ambiguous if a particular string in the language can be represented by 2 different parse trees. v. Inherently ambiguous langues are languages that can only be generated by ambiguous grammars v. Other grammars can be disambiguated

Ambiguous Grammars <expr> / | <expr>+<expr> (See www. cs. drexel. edu/~kschmidt/CS 520/Lectures/6/grammar. Eg 1. swf)

Recursive Descent Parser v. For some grammars it is simple to write a parser that recognizes strings in the language generated by the grammar. v. Sometimes it is possible to determine which production to apply based on the next character in the input string. This may not always be possible, but when it is, it is simple to construct a parser.

Problem 1 v. Using the grammar Ø<Balanced> Ø<Balanced> (<Balanced>) Ø<Balanced> v. Show two different parse trees for the input Ø()()()

Problem 2 v. Show the sequence of calls made by the program in Fig. 11. 27 on the inputs Ø(()()) ØDraw the resulting parse tree ØWhat happens with the input Ø())(

Problem 3 v. Consider the following grammar Ø<Number> <Digit><Number>| Ø<Digit> 0|1|2|3|4|5|6|7|8|9 v. Design a recursive-descent parser for this grammar; that is, write a pair of functions, one for <Number> and the other for <Digit>