Elimination of left recursion
Left recursion is a common issue in compiler design, which can cause infinite loops and other errors during parsing. The process of eliminating left recursion involves modifying the grammar to remove any productions that have left-recursive symbols. Here are the steps involved in eliminating left recursion in compiler design:
Identify left-recursive productions:
A left-recursive production is one in which the non-terminal symbol appears as the first symbol in the production. For example, consider the following grammar:
A -> Aa | b
Here, the production A -> Aa is left-recursive.
Create a new non-terminal symbol:
To eliminate left recursion, we need to create a new non-terminal symbol for each left-recursive production. For
example, we can create a new non-terminal symbol A' for the production
A -> Aa.
Rewrite the left-recursive production:
Next, we need to rewrite the left-recursive production using the new non-terminal symbol. For example, we can rewrite the production A -> Aa as follows:
A -> bA'
A' -> aA' | ε
Here, we have replaced the left-recursive production A -> Aa with the production A -> bA', and we have created a new production A' -> aA' | ε, which generates the same set of strings as the original production A -> Aa.
Update other productions:
Finally, we need to update other productions that use the left-recursive symbol to use the new non-terminal symbol instead. For example, if we have the production B -> Ac, we need to update it as follows:
B -> Ac | bA'
Here, we have added the new non-terminal symbol A' to the production.
By following these steps, we can eliminate left recursion in the grammar and ensure that the compiler can parse the input without encountering any errors.