PreviousNext

Compiler Design LALR(1) Parsing

Introduction to Compiler Design

Compiler design is a crucial aspect of programming language development. It involves the creation of a software system that translates high-level programming language code into machine-readable code. The process of compiler design consists of various stages, including lexical analysis, syntax analysis, semantic analysis, code generation, and code optimization.

LALR(1) Parsing

LALR(1) parsing, also known as Look-Ahead Left-to-Right parsing with One symbol of Look-Ahead, is a widely used parsing technique in compiler design. It is a bottom-up parsing method that uses a deterministic finite automaton (DFA) to parse the input string. LALR(1) parsing combines the advantages of both LR(0) and SLR(1) parsing techniques.

How LALR(1) Parsing Works

The LALR(1) parsing algorithm uses a parsing table, which is constructed using a set of grammar rules and a set of states. The grammar rules define the syntax of the programming language, while the states represent the different stages of the parsing process.

Here is a step-by-step explanation of how LALR(1) parsing works:

  1. Grammar Analysis: The first step in LALR(1) parsing is to analyze the given grammar and identify the terminals, non-terminals, and production rules. The terminals are the individual symbols in the programming language, while the non-terminals represent groups of symbols.
  2. First and Follow Sets: After analyzing the grammar, the next step is to compute the First and Follow sets for each non-terminal. The First set of a non-terminal consists of the terminals that can appear as the first symbol of a string derived from that non-terminal. The Follow set of a non-terminal consists of the terminals that can appear immediately after the non-terminal in a valid string.
  3. Item Sets Construction: The next step is to construct the item sets, which represent the different stages of the parsing process. Each item set consists of a set of LR(0) items, which are augmented production rules with a dot (.) indicating the current position in the rule.
  4. DFA Construction: Once the item sets are constructed, the next step is to construct the DFA by determining the transitions between the item sets. Each transition is determined by the symbols that appear after the dot in the LR(0) items.
  5. Parsing Table Construction: After constructing the DFA, the next step is to construct the parsing table. The parsing table is a two-dimensional table that maps the current state and the next input symbol to an action or a state. The actions can be shift, reduce, or accept.
  6. Parsing Process: Finally, the parsing process begins by starting with an empty stack and the initial state. The input string is scanned from left to right, and based on the current state and the next input symbol, the parsing table is consulted to determine the action or the next state. If the action is a shift, the current state is pushed onto the stack, and the next input symbol is read. If the action is a reduce, the appropriate production rule is applied, and the corresponding non-terminal is pushed onto the stack. If the action is accept, the parsing process is successful, and the input string is syntactically correct.

Example of LALR(1) Parsing

Let’s consider an example to illustrate how LALR(1) parsing works. Suppose we have the following grammar:

1. S -> E2. E -> E + T3. E -> T4. T -> T * F5. T -> F6. F -> (E)7. F -> id

Using this grammar, we can construct the item sets, DFA, and parsing table. However, for brevity, let’s directly consider the parsing table:

+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+| State|+|*|(|)|id |$|E|T|F|+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+|0||| s2|| s3||1||||1| s4||||| acc |||||2|| s5|||||||||3|| r3|| r3|| r3|||||4|| r5|| r5|| r5|||||5||| s6|| s3|||7|||6|| r7|| r7|| r7|||||7|| r4|| r4|| r4||||+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+

In the parsing table, each cell represents an action or a state based on the current state and the next input symbol. The actions are represented by ‘s’ (shift), ‘r’ (reduce), and ‘acc’ (accept). The states represent the next state to transition to.

Let’s assume we have the input string “id + id * id”. The parsing process would be as follows:

  1. Step 1: Start with an empty stack and the initial state 0.
  2. Step 2: Read the next input symbol ‘id’ and consult the parsing table for state 0 and symbol ‘id’. The action is ‘s3’, so push the current state 0 onto the stack and transition to state 3.
  3. Step 3: Read the next input symbol ‘+’ and consult the parsing table for state 3 and symbol ‘+’. The action is ‘s4’, so push the symbol ‘+’ onto the stack and transition to state 4.
  4. Step 4: Read the next input symbol ‘id’ and consult the parsing table for state 4 and symbol ‘id’. The action is ‘s5’, so push the current state 4 onto the stack and transition to state 5.
  5. Step 5: Read the next input symbol ‘*’ and consult the parsing table for state 5 and symbol ‘*’. The action is ‘s6’, so push the symbol ‘*’ onto the stack and transition to state 6.
  6. Step 6: Read the next input symbol ‘id’ and consult the parsing table for state 6 and symbol ‘id’. The action is ‘s3’, so push the current state 6 onto the stack and transition to state 3.
  7. Step 7: Read the next input symbol ‘$’ and consult the parsing table for state 3 and symbol ‘$’. The action is ‘r3’, which means reduce using production rule 3: E -> T. Pop the symbols ‘id’ and ‘T’ from the stack, and push the non-terminal ‘E’ onto the stack.
  8. Step 8: Consult the parsing table for the current state (top of the stack) and the next input symbol (‘$’). The action is ‘r3’, which means reduce using production rule 3: E -> T. Pop the symbol ‘E’ from the stack and push the non-terminal ‘E’ onto the stack.
  9. Step 9: Consult the parsing table for the current state (top of the stack) and the next input symbol (‘$’). The action is ‘acc’, which means the parsing process is successful, and the input string is syntactically correct.

In this example, the LALR(1) parsing algorithm successfully parses the input string “id + id * id” and recognizes it as a valid expression according to the given grammar rules.

Conclusion

LALR(1) parsing is a powerful technique used in compiler design to parse programming language code. It combines the advantages of LR(0) and SLR(1) parsing techniques and provides an efficient and deterministic parsing process. By constructing item sets, DFA, and parsing tables, the LALR(1) parsing algorithm can effectively analyze the syntax of a programming language and identify any syntactic errors in the code.

PreviousNext
Scroll to Top