LR parser
Introduction
An **LR parser** is a type of parser for processing deterministic context-free languages, commonly used in the field of compiler construction. The term "LR" stands for "Left-to-right, Rightmost derivation," which describes the order in which the parser reads the input and constructs the parse tree. LR parsers are a subset of bottom-up parsers, which build the parse tree from the leaves upwards to the root. They are known for their efficiency and ability to handle a wide range of grammars, making them a popular choice for programming language compilers.
Types of LR Parsers
LR parsers are categorized into several types, each with varying levels of complexity and power. The main types include:
Simple LR (SLR) Parser
The Simple LR parser is the most basic form of LR parser. It uses a simple method to construct the parsing table, which makes it less powerful than other LR parsers but easier to implement. SLR parsers use the Follow set of non-terminals to decide when to reduce, which can lead to conflicts in more complex grammars.
Canonical LR Parser
The Canonical LR parser, often referred to as the "full LR parser," is the most powerful type of LR parser. It constructs a comprehensive parsing table that can handle any deterministic context-free grammar. This parser uses the concept of LR(1) items, which include a lookahead symbol to resolve ambiguities during parsing. Although powerful, Canonical LR parsers are often impractical for large grammars due to the size of their parsing tables.
Lookahead LR (LALR) Parser
The Lookahead LR parser is a compromise between the simplicity of SLR and the power of Canonical LR parsers. LALR parsers merge similar states in the parsing table to reduce its size while maintaining the ability to handle more complex grammars than SLR parsers. This makes LALR parsers a popular choice for many practical applications, including the Yacc parser generator.
Construction of LR Parsers
The construction of an LR parser involves creating a parsing table, which consists of two main components: the action table and the goto table. These tables guide the parser in deciding whether to shift, reduce, accept, or report an error as it processes the input.
LR(0) Items
LR(0) items are the foundation of LR parsing. An LR(0) item is a production rule with a dot indicating the current position in the rule. For example, the item `A → α•β` indicates that the parser has recognized `α` and expects `β` next. The set of all LR(0) items forms the basis for constructing the state machine used in the parsing process.
Closure and Goto Functions
The closure and goto functions are essential in constructing the LR parsing table. The closure function expands a set of items by adding all possible continuations, while the goto function determines the next state based on the current state and input symbol. These functions are used to build the canonical collection of LR(0) items, which forms the states of the parser.
Parsing Table Construction
The parsing table is constructed by analyzing the canonical collection of items. The action table specifies the parser's actions (shift, reduce, accept, or error) based on the current state and input symbol. The goto table indicates the next state for each non-terminal symbol. Conflicts in the table, such as shift/reduce or reduce/reduce conflicts, indicate ambiguities in the grammar that need to be resolved.
Parsing Process
The LR parsing process involves reading the input from left to right and using the parsing table to construct the parse tree. The parser maintains a stack to keep track of states and symbols as it processes the input.
Shift Operation
The shift operation involves reading the next input symbol and pushing it onto the stack along with the new state. This operation is performed when the action table specifies a shift for the current state and input symbol.
Reduce Operation
The reduce operation involves applying a production rule to replace a sequence of symbols on the stack with the corresponding non-terminal. The parser pops the symbols from the stack, pushes the non-terminal, and transitions to the new state specified by the goto table.
Accept and Error States
The accept state indicates that the input has been successfully parsed, and the parse tree is complete. An error state occurs when there is no valid action for the current state and input symbol, indicating a syntax error in the input.
Advantages and Limitations
LR parsers offer several advantages, including their ability to handle a wide range of grammars and their deterministic nature, which ensures efficient parsing. However, they also have limitations, such as the complexity of constructing parsing tables for large grammars and the potential for conflicts that require manual resolution.
Advantages
- **Deterministic Parsing**: LR parsers are deterministic, meaning they do not require backtracking, which results in efficient parsing. - **Wide Grammar Coverage**: They can handle a broader range of grammars compared to other parsing techniques, such as LL parsers. - **Error Detection**: LR parsers can detect syntax errors at the earliest possible point in the input.
Limitations
- **Complexity**: Constructing the parsing table can be complex and time-consuming, especially for large grammars. - **Table Size**: The size of the parsing table can be large, particularly for Canonical LR parsers, making them impractical for some applications. - **Conflict Resolution**: Ambiguities in the grammar can lead to conflicts in the parsing table that require manual intervention to resolve.
Applications
LR parsers are widely used in the field of compiler construction for programming languages. They are employed in various stages of the compilation process, including syntax analysis and semantic analysis. Many parser generators, such as Bison and ANTLR, use LR parsing techniques to generate efficient parsers for different programming languages.