Designing LR(O) Parser Part-4
Duration: 7 min
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This lecture introduces the architecture of a Bottom-Up LR Parser, detailing its three main components: input buffer, parse stack, and parse table. It progresses to explain the construction of the LR parser table, covering augmented grammars, LR(0) items, canonical collections, and the closure and GOTO functions used to generate the parser states. The instructor uses diagrams and text slides to illustrate the flow of data and the logic behind parsing decisions, providing a comprehensive overview of the theoretical underpinnings of LR parsing.
Chapters
0:00 – 2:00 00:00-02:00
The video begins with a slide titled 'Model of an LR Parser', listing three components: i/p buffer, Parse stack, and Parse table. The instructor highlights the input buffer cells containing symbols $a_1, a_2, \dots, a_n, \$$ and the stack containing states $S_m, X_m, \dots, S_0$. He explains the central 'LR Parsing Program (driver)' box, which uses the parse table to decide operations. The table is split into 'action' and 'goto' parts, governing 'shift', 'reduce', 'accept', and 'error' operations based on the current state and input symbol. Arrows indicate the flow of information between the input, stack, and the driver program. The 'action' table lists 'shift', 'reduce', 'accept', 'error', while the 'goto' table is labeled 'DFA'.
2:00 – 5:00 02:00-05:00
The lecture transitions to text slides defining these components. The input buffer is described as cells holding one input symbol each. The stack holds grammar symbols pushed or popped via shift and reduce operations. The parse table is constructed using terminals, non-terminals, and LR(0) items, consisting of an 'Action' part for terminals and a 'Goto' part for non-terminals. A table structure is shown with columns for terminals ($t_1, t_2$) and non-terminals. The instructor then presents a grammar $A ightarrow aA / b$ and draws its state diagram with states $I_0$ through $I_4$, along with the corresponding parse table. He concludes this section by defining LR(K), where L stands for left-to-right scanning, R for reverse of right-most derivation, and K for the Look-Ahead symbol. The slide 'Operation in shift/reduced passer' lists 'shift', 'reduced', 'accept', 'error'. The table shows 'Action' for terminals and 'Goto' for non-terminals.
5:00 – 6:47 05:00-06:47
The final section details the 'Procedure for the construction of LR Parser table'. Step 1 is obtaining the augmented grammar by adding a new start symbol $S' ightarrow S$. Step 2 involves creating the canonical collection of LR items. Step 3 is drawing the DFA and preparing the table. The instructor defines an LR(0) item as a production with a dot anywhere on the RHS, such as $A ightarrow .abc$. He explains the 'Closure' function: if $A ightarrow \alpha.eta B$ is in the closure, add $B ightarrow .\delta$ for all productions $B ightarrow \delta$. He also explains the 'GOTO' function, where $GOTO(I, X)$ moves the dot past symbol X to form a new set of items, which is then closed. The slide 'Function used to generate LR(0) item's' shows the specific formulas for these operations, including $GOTO(A ightarrow \alpha.Xeta, X) = A ightarrow \alpha X . eta$. The instructor draws diagrams to illustrate the closure process, showing how new items are added to the set. He emphasizes that the GOTO function is used to transition between states in the DFA based on the input symbol.
The lecture systematically builds the theoretical foundation for LR parsing, moving from the high-level model of the parser to the specific algorithms required to construct the parsing table, emphasizing the roles of augmented grammars and item sets. It connects the abstract definitions of LR items to the concrete steps of building the parser table.