- Compiler Design - Home
- Compiler Design - Overview
- Compiler Design - Architecture
- Phases
- Compiler Design - Phases
- Compiler Design - Global Optimization
- Compiler Design - Local Optimization
- Lexical Analysis
- Compiler Design - Lexical Analysis
- Compiler Design - Regular Expressions
- Compiler Design - Finite Automata
- Compiler Design - Language Elements
- Compiler Design - Lexical Tokens
- Compiler Design - FSM
- Compiler Design - Lexical Table
- Compiler Design - Sequential Search
- Compiler Design - Binary Search Tree
- Compiler Design - Hash Table
- Syntax Analysis
- Compiler Design - Syntax Analysis
- Compiler Design - Parsing Types
- Compiler Design - Grammars
- Compiler Design - Classes Grammars
- Compiler Design - Pushdown Automata
- Compiler Design - Ambiguous Grammar
- Parsing
- Compiler Design - Top-Down Parser
- Compiler Design - Bottom-Up Parser
- Compiler Design - Simple Grammar
- Compiler Design - Quasi-Simple Grammar
- Compiler Design - LL(1) Grammar
- Error Recovery
- Compiler Design - Error Recovery
- Semantic Analysis
- Compiler Design - Semantic Analysis
- Compiler Design - Symbol Table
- Run Time
- Compiler Design - Run-time Environment
- Code Generation
- Compiler Design - Code Generation
- Converting Atoms to Instructions
- Compiler Design - Transfer of Control
- Compiler Design - Register Allocation
- Forward Transfer of Control
- Reverse Transfer of Control
- Code Optimization
- Compiler Design - Code Optimization
- Compiler Design - Intermediate Code
- Basic Blocks and DAGs
- Control Flow Graph
- Compiler Design - Peephole Optimization
- Implementing Translation Grammars
- Compiler Design - Attributed Grammars
Language Elements in Compiler Design
Lexical analysis is an important phase in compiler design that takes care of the syntax of codes. It is in this phase we come across "language elements" which are also known as "tokens". Understanding language elements is needed to understand this phase properly.
Language elements form the basis of how we define, organize, and work with programming languages. Programming languages demand precision and language elements help us achieve this precision by providing clear rules and structures for defining valid strings and expressions.
In this chapter, we will cover the basic concepts of sets, strings, and formal languages. We will also go through relatable examples for a better understanding.
Sets: The Building Blocks of Languages
A set is a collection of unique objects. Think of it as a basket holding different items where each item appears only once. For instance, the set {apple, orange, banana} contains three fruits. If we rearrange them, the order may get different, but the items does not change. This is a set. So, {banana, orange, apple} is the same as the first example.
Empty Set − Sometimes, a set contains nothing at all. This is called an empty set or null set and is represented by { } or φ. It is like having an empty basket. There is nothing inside, but it is still a basket.
Strings: Lists with Order and Repetition
After the sets we can talk about strings. As we know a string is like a list, but here the order matters, and items can repeat. Imagine characters on a string—changing the order of the characters or adding duplicates gives a completely different design.
For instance −
- "abc" and "cba" are different strings.
- "abb" and "ab" are also different.
Just like sets can be empty, a string can have no characters. This is called the null string. This is represented by .
Formal Languages: Sets of Strings
We understood the sets and string with examples. Sometimes we get a set of strings or collection of strings. Let us see what formal languages is. A formal language is simply a set of strings that follow specific rules. It is like defining a club where only certain types of strings are allowed.
Examples of Formal Languages
Take a look at the following examples −
- {0, 10, 1011} − A finite language with three specific strings.
- {, 0, 00, 000} − An infinite language with strings of zeros, starting from the null string.
- Java syntax − A formal language where each string is a valid Java program.
- Italian syntax − A natural language with grammatically correct Italian sentences.
Notice how formal languages can range from simple sets of numbers to complex programming languages.
Difference between Null Strings and Empty Sets
A null string () is a valid string with no characters. It is like a blank piece of paper. For example, consider the language {, 0, 00}. It includes the null string and strings of zeros, but it is not an empty set because it contains elements.
An empty set (φ), on the other hand, contains no strings at all. It is like having no paper to write on.
Real-Life Analogy: Formal Languages and Club Memberships
Think of a formal language as a club. Now the alphabet (e.g., {0,1}) represents the pool of people eligible to join. The rules of the language define who gets in.
- A string like "101" might be a member if it follows the rules.
- A string like "abc" would not qualify if the language only accepts binary strings.
Finite and Infinite Languages
Formal languages can be either finite or infinite −
- A finite language has a fixed number of strings. For example, {0, 10, 1011} is finite because it only has three elements.
- An infinite language has no limit. {, 0, 00, 000, …} is infinite because we can keep adding more zeros.
Example: Languages from the Alphabet {0,1}
If we want to make languages from alphabets, we must follow a set of rules. Let us understand this with examples. Take example of binary alphabet {0,1}:
- {0, 10, 1011} − A finite set of specific strings.
- {, 0, 00, 000} − An infinite set of strings of zeros, starting with the null string.
- Strings with an even number of ones, such as "0", "1010", "111000".
Conclusion
In this chapter, we explained the concept of language elements and how they form the basis of formal languages. We started with sets and explained their role as collections of unique objects. We then covered strings, noting their importance in defining order and repetition. Finally, we touched upon formal languages and highlighted their application in computer science.
Language elements in compiler design appear seemingly simple, but they are at the heart of how we define and understand programming languages.