27 Aug - Compiler - Bottom up Parsers- LR(0) and SLR(1)
Duration: 1 hr 59 min
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AI Summary
An AI-generated summary of this video lecture.
This video is a detailed academic lecture on Compiler Design, focusing on the construction of LR(0) parsers. The instructor begins by defining grammar as a mathematical representation of language and listing its fundamental properties. He then introduces a specific arithmetic grammar (E -> E+T|T, T -> T*F|F, F -> (E)|id) and outlines the six-step process for constructing an LR(0) parsing table. The core of the lecture involves the manual construction of the Canonical LR(0) Item Sets (DFA), starting from the initial state I0 and expanding through closures and transitions for various terminals and non-terminals. Finally, the instructor uses the derived states to populate the Action and Goto parsing tables, demonstrating how to handle shifts, reductions, and goto actions.
Chapters
0:00 – 2:00 00:00-02:00
The video begins with a black screen displaying the name 'Sanchit Jain' in white text. This introductory segment serves as a title card before the main content begins, setting the stage for the lecture.
2:00 – 5:00 02:00-05:00
The screen transitions to a screen mirroring interface on an iPad. The desktop background features a statue of the Hindu deity Hanuman. The instructor navigates through the interface, preparing to open a note-taking application for the lecture.
5:00 – 10:00 05:00-10:00
The instructor begins writing on a digital blackboard. He writes the heading 'Grammar - Most powerful mathematical representation of language.' This sets the theoretical foundation for the lecture, emphasizing the role of grammar in compiler design.
10:00 – 15:00 10:00-15:00
The instructor lists six key points about grammar and language. These include: 1. If a language exists, a grammar exists for it. 2. Without grammar, language is not possible. 3. A language may have more than one valid grammar. 4. The language of a grammar can be empty. 5. Grammar can be useless. 6. A grammar is a set of productions.
15:00 – 20:00 15:00-20:00
A specific grammar example is written on the board: E -> E+T|T, T -> T*F|F, F -> (E)|id. This grammar represents a standard arithmetic expression language, which will be used as the primary example for constructing the LR(0) parser throughout the lecture.
20:00 – 25:00 20:00-25:00
The instructor outlines the six steps required to construct an LR(0) parsing table. These steps are: 1. Expand the grammar. 2. Number all the productions. 3. Augment the grammar. 4. Find First & Follow sets. 5. Find LR(0) Canonical Item Sets. 6. Construct the table.
25:00 – 30:00 25:00-30:00
The instructor numbers the productions from 1 to 6 and augments the grammar by adding a new start symbol E' -> E. This augmentation is a crucial step in LR parsing to ensure the parser can recognize the end of the input string.
30:00 – 35:00 30:00-35:00
A table is drawn with columns for 'First' and 'Follow' sets. The rows are labeled with the non-terminals E, T, and F. This table will be used to store the First and Follow sets calculated for the grammar.
35:00 – 40:00 35:00-40:00
The instructor fills in the First sets for the non-terminals. He writes '(, id' for E, T, and F. This indicates that all three non-terminals can eventually derive the terminals '(' and 'id'.
40:00 – 45:00 40:00-45:00
The Follow sets are filled in the table. For E, the Follow set is '$, +, )'. For T, it is '$, +, ), *'. For F, it is '$, +, ), *'. These sets are essential for determining reduction actions in the parsing table.
45:00 – 50:00 45:00-50:00
The construction of the LR(0) Canonical Item Sets begins with state I0. The initial item is E' -> .E. This represents the start of the parsing process where the parser expects to see the start symbol E.
50:00 – 55:00 50:00-55:00
The closure of I0 is computed. The instructor adds items E -> .E+T, E -> .T, T -> .T*F, T -> .F, F -> .(E), and F -> .id. This expansion ensures that all possible productions for the non-terminals following the dot are included.
55:00 – 60:00 55:00-60:00
Transitions from I0 are drawn. An arrow labeled 'E' points to state I1, and an arrow labeled 'T' points to state I2. These transitions represent the parser moving to new states upon recognizing the non-terminals E and T.
60:00 – 65:00 60:00-65:00
Further transitions from I0 are drawn. An arrow labeled 'F' points to state I3, an arrow labeled '(' points to state I4, and an arrow labeled 'id' points to state I5. These transitions handle the base cases of the grammar.
65:00 – 70:00 65:00-70:00
The instructor analyzes state I4. Transitions are drawn from I4. An arrow labeled 'E' points to state I8, and an arrow labeled '+' points to state I9. This shows how the parser handles expressions inside parentheses.
70:00 – 75:00 70:00-75:00
More transitions from I4 are drawn. An arrow labeled 'T' points to state I6, and an arrow labeled '*' points to state I7. These transitions handle the multiplication part of the grammar.
75:00 – 80:00 75:00-80:00
A transition from I4 labeled 'F' points to state I10. This transition is part of the closure process for state I4, ensuring all possible derivations are accounted for.
80:00 – 85:00 80:00-85:00
The instructor analyzes state I6. A transition labeled 'F' points to state I11. This transition represents the parser moving to a new state after recognizing a factor F in a multiplication expression.
85:00 – 90:00 85:00-90:00
The instructor analyzes state I7. A transition labeled 'F' points to state I12. This transition is similar to the one from I6, handling the factor F in a multiplication expression.
90:00 – 95:00 90:00-95:00
The instructor analyzes state I8. A transition labeled 'T' points to state I13. This transition represents the parser moving to a new state after recognizing a term T in an addition expression.
95:00 – 100:00 95:00-100:00
The instructor analyzes state I9. A transition labeled 'F' points to state I14. This transition is part of the closure process for state I9, ensuring all possible derivations are accounted for.
100:00 – 105:00 100:00-105:00
The instructor analyzes state I10. A transition labeled 'E' points to state I15. This transition represents the parser moving to a new state after recognizing an expression E inside parentheses.
105:00 – 110:00 105:00-110:00
The instructor analyzes state I11. A transition labeled 'T' points to state I16. This transition represents the parser moving to a new state after recognizing a term T in a multiplication expression.
110:00 – 115:00 110:00-115:00
The instructor analyzes state I12. A transition labeled 'T' points to state I17. This transition is similar to the one from I11, handling the term T in a multiplication expression.
115:00 – 119:12 115:00-119:12
The instructor constructs the Action and Goto parsing table. He fills in the table with shift (S), reduce (r), and goto (G) actions based on the states and transitions derived earlier. This final step completes the construction of the LR(0) parser.
The lecture provides a comprehensive, step-by-step guide to constructing an LR(0) parser. It begins with theoretical definitions of grammar and its properties, then moves to a practical example using an arithmetic grammar. The instructor meticulously demonstrates the calculation of First and Follow sets, the construction of the Canonical LR(0) Item Sets (DFA), and finally, the population of the Action and Goto parsing tables. This progression from theory to practice ensures a deep understanding of the parsing process.