15-212: Principles of Programming

In this lecture we continue our discussion of context-free grammars, and demonstrate their role in parsing.

Shift-reduce parsing uses a stack to delay application of rewrite rules, enabling operator precedence to be enforced. Recursive descent parsing is another style that uses recursion in a way that mirrors the grammar productions. Although parser generator tools exist for restricted classes of grammars, a direct implementation can allow greater flexibility and better error handling. We present an example of a shift-reduce parser for a grammar of arithmetic expressions.

Key Concepts

• Recursive descent parsing
• Shift-reduce parsing

Sample Code

On-line Notes by Robert Harper

• Overview of Standard ML (contains a sample parser for regular expressions)

Suggested Reading in Programming in Standard ML:

• Section 1.1: A Regular Expression Package

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Michael Erdmann