Top Down Parsers - LL(1) Parsers

Introduction to LL(1) Parsers

Overview of Today's Session

• The session focuses on understanding LL(1) parsers, building upon previous knowledge of top-down parsers.

• Key concepts to be covered include the organization of LL(1) parsers and the functions of "first" and "follow."

Recap of Recursive Descent Parsers

• A brief review is provided on recursive descent parsers, explaining their function and structure.

• The term "recursive descent" is clarified; it refers to how non-terminals are represented as functions in code.

Memory Layout in C Programs

Understanding Memory Segments

• The memory layout for a C program includes various segments: text/code segment, initialized data, uninitialized data (BSS), stack, and heap.

• The stack's role is emphasized; it grows downwards while the heap grows upwards. This distinction aids in understanding recursive descent parsing.

Execution Flow in Recursive Descent Parsing

Activation Records and Function Calls

• When executing the main function, an activation record is created that tracks control flow through function calls.

• Each function call updates its respective activation record with line numbers as anchor points for returning control after execution.

Role of the Stack

• The stack facilitates tracking multiple function calls during parsing. Each successful execution signifies progress in constructing the parse tree.

• As functions complete execution, their activation records are popped from the stack, maintaining order and control flow.

Understanding Recursive Descent Parsing

Why It's Called Recursive Descent Parsing

• The name derives from using a recursion stack to descend from start symbols to generate parse trees for input streams.

Introduction to LL(1) Parsers

Components Needed for LL(1) Parser Construction

• An input buffer is required for storing inputs, which typically ends with a dollar symbol indicating termination.

Understanding the LL(1) Parser

Overview of LL(1) Parsing

• The LL(1) parser utilizes elements from its construction to build a parse tree, incorporating an input buffer and an LL(1) parsing table. The stack's bottom is represented by the dollar symbol.

Characteristics of the LL(1) Parser

• The first 'L' in LL(1) indicates that the parser scans input from left to right. This means that strings are processed sequentially as they appear in the input buffer.

• The second 'L' signifies that it employs a top-down parsing approach, specifically using leftmost derivation during parsing.

• The '1' denotes that the parser looks ahead at one symbol from the input buffer for making parsing decisions based on the LL(1) parsing table.

Constructing the LL(1) Parsing Table

Understanding First Function

• The "first" function identifies terminals derived from a non-terminal in a context-free grammar (CFG). It captures what can be produced first when deriving strings from a given non-terminal.

• For example, if S can derive "aABc", then 'a' is considered the first terminal for S since it's the leading character in this production rule.

Examples of First Function

• If we derive all possible strings from non-terminal A and find it leads only to terminal B, then B becomes A's first terminal.

• Continuing with B, if it derives C, which further derives D, then D is recognized as B's first terminal.

Further Exploration of First Function

• In another example where S can produce "abc", if A can also derive ε (epsilon), indicating no terminal has been produced yet, both 'a' and 'b' will be included in S’s first set.

Understanding Follow Function

Definition of Follow Set

• The follow set consists of terminals that may directly follow a non-terminal during derivation. It helps determine what symbols can appear after a given non-terminal.

Examples of Follow Set Calculation

• For start symbol S, since it begins derivation followed by nothing else initially but eventually ends with a dollar sign ($), this dollar sign is included in its follow set.

• When examining non-terminal A followed by other symbols like B or C during derivation processes, we identify their respective terminals to include them in A's follow set.

Additional Insights on Follow Sets

Understanding First and Follow Functions in LL(1) Parsing

Overview of First and Follow Concepts

• The follow of a non-terminal includes the terminal symbols that can appear immediately after it in derivations. For example, the follow of 'C' is the dollar symbol ($), indicating the end of input.

• In addition to '$', for non-terminal 'a', there are two terminal symbols: 'B' and 'C'. The follow function helps identify these terminals based on their position in derivations.

• It is important to note that epsilon (ε), which represents an empty string, is never included in the follow sets. This distinction is crucial for accurate parsing.

Session Summary

• The session provided an overview of how first and follow functions are organized within LL(1) parsing, setting the stage for deeper exploration in future sessions.