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10. Writing a parser for a CF language

10.1. The grammar

10.1.1. Write a grammar which accurately describes regular expressions. Consider the following definition: A regular expression is built in the normal way, using the symbols (,),*,| and any other alpha-numeric caracter. Free spaces may occur freely within the expression.

10.1.2. Starting from the solution to the previous exercise, write an unambiguous grammar for regexes:

  • Make sure to take precedence into account

10.2. A basic functional structure for a parser

Consider the following language encoding expressions:

  • $ S \leftarrow M \mid M + S$
  • $ M \leftarrow A \mid A * M$
  • $ A \leftarrow 0 \mid 1 \mid (S)$

10.2.1. Implement an AST for expressions. 10.2.2. Implement a parser for expressions. Consider the following guidelines:

  • A parser is a function which takes a string and has two tasks:
    • returns the rest of the string to be parsed, or an error if parsing failed. Examples:
      • parse_whitespace(“ lfa”) = “lfa”
      • parse_whitespace(“lfa”) = None