Introduction to Compilers

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Introduction:

Welcome to our series on compiler development using Python! In this series of articles, we will explore the fundamentals of grammars and their role in defining the syntax of programming languages. We’ll also discuss different notation systems used to express grammars, such as BNF, EBNF, and PEG, and their relation to lexical analysis. Understanding these concepts will pave the way for our implementation of a lexer in the subsequent article.

Grammars and Their Significance:

Grammars are essential tools for defining the syntax rules of programming languages. They provide a formal structure that guides the interpretation and analysis of source code. A grammar consists of a set of production rules that describe how valid statements and expressions can be constructed within the language. By adhering to these rules, we ensure that programs are correctly formed and can be analyzed and executed by the compiler or interpreter.

Backus-Naur Form (BNF) and Extended Backus-Naur Form (EBNF):

Backus-Naur Form (BNF) and Extended Backus-Naur Form (EBNF): One commonly used notation for expressing grammars is Backus-Naur Form (BNF). BNF uses production rules consisting of non-terminal symbols, represented in angle brackets (< >), and terminal symbols, written in regular text. The production rules define the valid structure of a programming language.

For example, let’s consider a simplified BNF snippet for an assignment statement in the C programming language:

<statement> ::= <identifier> = <expression>
<identifier> ::= [a-zA-Z_]\w*
<expression> ::= <term> | <term> + <expression>
<term> ::= <factor> | <factor> * <term>
<factor> ::= <identifier> | <number>

Here, the <statement> non-terminal symbol represents an assignment statement, which consists of an <identifier> followed by an equals sign and an <expression>. Similarly, <expression>, <term>, and <factor> are defined recursively to build more complex expressions.

Extended Backus-Naur Form (EBNF) is an extension of BNF that incorporates additional constructs, such as repetition and optional elements, to provide more flexibility in defining grammars. EBNF is often used in conjunction with BNF to express more complex language features concisely.

Parsing Expression Grammar (PEG):

Another notation commonly used for specifying grammars is Parsing Expression Grammar (PEG). PEG is similar to BNF but allows for more expressive power by incorporating prioritized choice and unlimited lookahead. PEG grammars are typically easier to read and maintain compared to traditional CFGs (Context-Free Grammars).

Abstract Syntax Trees (ASTs):

During the parsing process, the output of a parser is often represented as an Abstract Syntax Tree (AST). An AST is a hierarchical structure that captures the syntactic structure of the program. It provides a more organized representation of the code, making subsequent phases, such as semantic analysis and code generation, easier to perform.

Examples of Grammars and ASTs in Programming Languages:

Let’s explore some examples of grammars and corresponding ASTs for popular programming languages:

Let’s first look at a portion of the grammar for the C programming language:

<expression> ::= <assignment-expression> | <binary-expression>
<assignment-expression> ::= <identifier> = <expression>
<binary-expression> ::= <expression> <operator> <expression>
<identifier> ::= [a-zA-Z_]\w*
<operator> ::= + | - | * | /

This portion of the grammar covers mathematic expressions like: x = 1 + 3.

AST for the expression a = 2 + 3:

AssignmentExpression
  ├─ Identifier: a
  └─ BinaryExpression
      ├─ Literal: 2
      └─ Literal: 3

Python EBNF Grammar:

<expression> ::= <assignment-expression> | <binary-expression>
<assignment-expression> ::= <identifier> '=' <expression>
<binary-expression> ::= <expression> <operator> <expression>
<identifier> ::= [a-zA-Z_]\w*
<operator> ::= '+' | '-' | '*' | '/'

AST for the expression a = 2 + 3:

AssignmentExpression
  ├─ Identifier: a
  └─ BinaryExpression
      ├─ Literal: 2
      └─ Literal: 3

Lua PEG Grammar:

statement <- identifier '=' expression
expression <- term '+' expression / term
term <- factor '*' term / factor
factor <- identifier / number
identifier <- [a-zA-Z_]\w*
number <- [0-9]+

AST for the expression a = 2 + 3:

AssignmentStatement
  ├─ Identifier: a
  └─ AdditionExpression
      ├─ Literal: 2
      └─ Literal: 3

Conclusion:

Understanding grammars and their various notations, such as BNF, EBNF, PEG, and ASTs, is essential for building compilers and interpreters. In this article, we explored the significance of grammars in programming languages, the BNF and EBNF notations, and the PEG approach. We also provided examples of grammars and corresponding ASTs for real programming languages like C, Python, Lua, Pascal, Zig, Lisp, and Haskell. Armed with this knowledge, we are now ready to proceed to the next article, where we will dive into building a lexer for our SimpleLang programming language using Python.