Designing LL(1) Parser Part-1
Duration: 8 min
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The video is a detailed lecture on compiler design, specifically focusing on the construction of an LL(1) parsing table. The instructor, Sanchit Jain Sir, starts with a standard arithmetic expression grammar that exhibits left recursion: E -> E+T / T, T -> T*F / F, F -> (E) / id. He demonstrates the systematic process of eliminating left recursion to make the grammar suitable for top-down parsing. He rewrites the productions for E and T using new non-terminals (E' and T') and epsilon productions. Following the grammar transformation, he proceeds to calculate the First and Follow sets for each non-terminal. Finally, he constructs a parsing table, mapping the grammar productions to the appropriate cells based on the computed sets, effectively demonstrating how to build an LL(1) parser for the given grammar. This process is essential for understanding how compilers parse source code.
Chapters
0:00 – 2:00 00:00-02:00
The instructor begins by displaying a context-free grammar on the top left of the screen: E -> E+T / T, T -> T*F / F, and F -> (E) / id. He underlines this grammar to emphasize it as the starting point. He explains that this grammar contains left recursion, which prevents it from being used for top-down parsing. To fix this, he starts rewriting the productions. He writes E -> T E' and E' -> + T E' / epsilon. He then applies the same transformation to the T productions, writing T -> F T' and T' -> * F T' / epsilon. Finally, he writes the F productions as F -> (E) / id. This section focuses on the algebraic manipulation of the grammar rules to eliminate left recursion, a prerequisite for LL(1) parsing. The instructor is identified as Sanchit Jain Sir from Knowledge Gate Educator. He uses red ink to write the new grammar, distinguishing it from the original orange text. The transformation involves introducing new non-terminals E' and T' to handle the recursive parts of the original grammar.
2:00 – 5:00 02:00-05:00
With the grammar transformed, the instructor moves to calculating the First and Follow sets. He writes F(E) = { (, id } to denote the First set of E. He continues with F(E') = { +, epsilon }, F(T) = { (, id }, F(T') = { *, epsilon }, and F(F) = { (, id }. He then calculates the Follow sets, writing Follow(E) = { $, ) }, Follow(E') = { $, ) }, Follow(T) = { +, $, ) }, Follow(T') = { +, $, ) }, and Follow(F) = { *, +, $, ) }. These sets are written in a column on the right side of the board. The instructor explains that these sets determine which production to apply based on the current input symbol. He uses the notation F for First and Follow for Follow sets. He writes the Follow sets in blue ink, contrasting with the red First sets. The calculation of these sets is crucial for determining the entries in the parsing table.
5:00 – 8:28 05:00-08:28
The instructor draws a large table with rows labeled E, E', T, T', F and columns labeled +, *, (, ), id, $. He begins filling the table cells. For E -> T E', he places the production in the columns corresponding to First(T), which are ( and id. For E' -> + T E', he places it in the + column. For E' -> epsilon, he places it in the columns corresponding to Follow(E'), which are $ and ). He repeats this for T and T', placing T -> F T' in ( and id, T' -> * F T' in *, and T' -> epsilon in +, $, ). Finally, he places F -> (E) in ( and F -> id in id. This demonstrates the construction of the LL(1) parsing table. The table is a grid where each cell represents a decision point for the parser. He uses red ink for the table lines and black ink for the productions. The final table allows the parser to determine the correct production to apply for any given input symbol.
The lecture provides a complete walkthrough of transforming a recursive grammar into an LL(1) form. It connects the theoretical steps of removing left recursion with the practical application of building a parsing table. By calculating First and Follow sets and then populating the table, the instructor shows the full pipeline from grammar definition to parser construction, a fundamental concept in compiler design. This process ensures that the parser can handle the grammar without ambiguity.