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Jack Brooks
Jack Brooks

Learn Compiler Design with Aho Ullman Book and Solutions



Aho Ullman Compiler Design Solution 11




Compiler design is one of the most fascinating and challenging topics in computer science. It involves creating programs that can translate source code written in one language into executable code in another language. In this article, we will explore the basics of compiler design, the famous book by Aho and Ullman on this subject, and a specific solution to one of the problems in the book.




Aho Ullman Compiler Design Solution 11



Introduction




Before we dive into the details of compiler design, let us first understand what it is and why it is important.


What is compiler design?




A compiler is a program that takes source code written in one language (called the source language) and converts it into executable code in another language (called the target language). For example, a C compiler takes C source code and produces machine code that can run on a specific hardware platform.


Compiler design is the process of designing and implementing a compiler. It involves various tasks such as lexical analysis, syntax analysis, semantic analysis, intermediate code generation, code optimization, and code generation. Each task has its own challenges and techniques that require knowledge of formal languages, automata theory, data structures, algorithms, and optimization methods.


What are the main challenges of compiler design?




Some of the main challenges of compiler design are:


  • Handling different types of source languages and target languages, such as imperative, functional, object-oriented, scripting, assembly, etc.



  • Dealing with complex and ambiguous syntax and semantics of source languages, such as operator precedence, scoping rules, type checking, etc.



  • Generating efficient and correct code for different target platforms, such as processors, memory architectures, operating systems, etc.



  • Ensuring portability, compatibility, security, and reliability of the compiled code.



  • Managing trade-offs between speed, memory usage, and quality of the compilation process and the compiled code.



What are the benefits of compiler design?




Some of the benefits of compiler design are:


  • Enabling programmers to write code in high-level languages that are easier to read, write, debug, and maintain than low-level languages.



  • Improving the performance and functionality of programs by applying various optimizations and transformations to the source code.



  • Supporting cross-platform development by allowing programs to run on different hardware and software platforms without requiring manual changes.



  • Enhancing the security and reliability of programs by detecting and preventing errors and vulnerabilities in the source code.



  • Facilitating innovation and research by enabling new languages, paradigms, features, and tools to be developed and tested.



Aho Ullman Compiler Design Book




One of the most authoritative and comprehensive books on compiler design is the one by Alfred V. Aho and Jeffrey D. Ullman, titled "Compilers: Principles, Techniques, and Tools". It is also known as the "dragon book" because of its cover image of a dragon holding a book.


Who are Aho and Ullman?




Aho and Ullman are two eminent computer scientists who have made significant contributions to the fields of compiler design, formal languages, automata theory, algorithms, and database systems. They are both professors emeritus at Columbia University and Stanford University, respectively. They have also co-authored several other books, such as "The Design and Analysis of Computer Algorithms", "The Theory of Parsing, Translation, and Compiling", and "Foundations of Computer Science".


What is the scope and content of the book?




The book covers the fundamental principles, techniques, and tools of compiler design, as well as some advanced topics and applications. It is divided into four parts:


  • Part I: Introduction - This part introduces the basic concepts and terminology of compilers, such as languages, grammars, automata, regular expressions, finite automata, context-free grammars, parsing, etc.



  • Part II: Techniques - This part describes the main techniques used in compiler design, such as lexical analysis, syntax analysis, semantic analysis, intermediate code generation, code optimization, and code generation. It also discusses various algorithms and data structures used for these tasks.



  • Part III: Tools - This part presents some tools that can help in compiler design, such as lexical analyzers, parsers, syntax-directed translators, symbol tables, error handlers, etc. It also shows how to use these tools to build a simple compiler.



  • Part IV: Advanced Topics - This part explores some advanced topics and applications of compiler design, such as runtime environments, garbage collection, object-oriented languages, functional languages, parallelism and concurrency, code generation for modern architectures, etc.



How is the book organized and structured?




The book is organized and structured in a logical and pedagogical way. Each chapter begins with an introduction that motivates the topic and states the learning objectives. Then, it presents the main concepts and techniques with clear explanations and examples. Next, it provides exercises and problems that test the understanding and application of the concepts and techniques. Finally, it ends with a summary that reviews the main points and highlights the key terms. The book also includes appendices that provide additional information on topics such as mathematical notation, ASCII character set, etc.


Aho Ullman Compiler Design Solution 11




In this section, we will look at a specific solution to one of the problems in the book. The problem is from Chapter 4: Syntax Analysis (Section 4.7: Syntax-Directed Translation), Problem 4.11:


Consider the following grammar for arithmetic expressions involving + and *:


E -> E + T T T -> T * F F F -> (E) id


Assume that + has lower precedence than *, both operators associate left-to-right, and id stands for an identifier.


a) Construct an annotated parse tree for id1 + id2 * id3.


b) Construct a syntax-directed translation scheme that translates an arithmetic expression into postfix notation (also known as reverse Polish notation), in which an operator appears after its operands. For example, the expression id1 + id2 * id3 should be translated into id1 id2 id3 * +.


c) Show how your scheme works on the expression in part (a) by annotating each node of your parse tree with its translation.


What is the problem statement?




The problem statement asks us to do three things:


  • a) Construct an annotated parse tree for id1 + id2 * id3.



  • b) Construct a syntax-directed translation scheme that translates an arithmetic expression into postfix notation.



  • c) Show how our scheme works on the expression in part (a) by annotating each node of our parse tree with its translation.



What are the steps to solve the problem?




We will follow these steps to solve the problem:


Step 1: Lexical analysis




In this step, we scan the input expression and identify the tokens (lexical units) that make up the expression. We also assign attributes to each token that store its value or type. For example:


Token Attribute --- --- id id1 Token Attribute --- --- + + id id2 * * id id3 Step 2: Syntax analysis




In this step, we parse the input expression and construct a parse tree that represents its syntactic structure according to the given grammar. We also assign inherited and synthesized attributes to each node of the parse tree that store information needed for semantic analysis and translation. For example:


E / \ / \ / \ E T / \ / \ / \ / \ T + T F / \ / \ \ / \ / \ id F * F F \ / \ \ id3 id F F id id2 id1 (E) id / \ / \ E T / \ / \ T + T F / \ / \ \ F * F F id \ / \ \ id F F id id1 id2 id (E) id id1 id2


The annotated parse tree for part (a) is shown below, where each node is labeled with its nonterminal or terminal symbol and its attribute value (if any):


E.val = "id1 id2 id3 * +" / \ / \ / \ E.val = "id1" T.val = "id2 id3 *" / \ / \ / \ / \ T.val = "id1" + T.val = "id2" F.val = "id3" / \ / \ / / \ / \ / F.val = "id1" * F.val = "id2" F.val = "id3" \ / \ \ id.lexval = "id1" F.val = "(E)" id.lexval = "id3" / / (E).val = "id1 id2 +" / / \ / \ E.val = "id1 id2 +" T.val = "id1" / \ / \ / \ / \ T.val = "id1" + T.val = "id2" F.val = "id1" / \ / \ / / \ / \ / F.val = "id1" * F.val = "id2" F.val = "id1" \ / \ \ id.lexval = "id1" F.val = "(E)" id.lexval = "id1" / / (E).val = "id1" / / \ E.val = "id1" T.val = "" / T.val = "" / F.val = "" / (E).val = ""


Step 3: Semantic analysis




In this step, we check the semantic validity of the input expression and report any errors or warnings. We also perform type checking, type conversion, and symbol table management. For example:


  • We check that each identifier is declared and defined before use.



  • We check that each operator is applied to operands of compatible types.



  • We check that each expression has a valid type and value.



  • We convert any operands of different types to a common type if necessary.



  • We store and retrieve information about identifiers and their attributes in a symbol table.



In this case, we assume that all identifiers are of type int and have some predefined values. We also assume that there are no semantic errors or warnings in the input expression.


Step 4: Intermediate code generation




In this step, we generate intermediate code that represents the input expression in a more abstract and platform-independent way. We also perform some optimizations and transformations on the intermediate code to improve its quality and efficiency. For example:


  • We use three-address code as the intermediate code, which consists of a sequence of instructions of the form x = y op z, where x, y, and z are operands and op is an operator.



  • We use temporary variables to store intermediate values and results.



  • We eliminate unnecessary parentheses and redundant operations.



  • We apply constant folding and algebraic simplification to reduce the number of instructions and operands.



The intermediate code for the input expression is shown below, where each instruction is numbered and commented:


1. t1 = id2 * id3 // multiply id2 and id3 and store the result in t1 2. t2 = id1 + t1 // add id1 and t1 and store the result in t2


Step 5: Code optimization




In this step, we apply further optimizations and transformations on the intermediate code to improve its quality and efficiency. We also perform some analysis and annotation on the intermediate code to facilitate code generation. For example:


  • We use data-flow analysis to compute the live ranges and use-def chains of variables.



  • We use loop analysis to identify loops and their characteristics.



  • We use register allocation to assign registers to variables based on their live ranges and usage frequencies.



  • We use instruction scheduling to reorder instructions to reduce stalls and dependencies.



  • We use peephole optimization to eliminate local redundancies and improve instruction patterns.



The optimized intermediate code for the input expression is shown below, where each instruction is numbered and commented:


1. r1 = id2 * id3 // multiply id2 and id3 and store the result in register r1 2. r2 = id1 + r1 // add id1 and r1 and store the result in register r2


Step 6: Code generation




In this step, we generate target code that represents the input expression in a platform-specific way. We also perform some adjustments and refinements on the target code to improve its quality and efficiency. For example:


  • We use assembly language as the target code, which consists of a sequence of instructions that can be executed by a specific processor.



  • We use machine registers, memory locations, and labels to represent operands and addresses.



  • We use instruction selection to choose the best instruction for each operation based on the processor's instruction set.



  • We use instruction encoding to convert each instruction into a binary format that can be stored and executed by the processor.



The target code for the input expression is shown below, where each instruction is numbered and commented:


1. LOAD R3, id2 // load the value of id2 into register R3 2. LOAD R4, id3 // load the value of id3 into register R4 3. MUL R5, R3, R4 // multiply R3 and R4 and store the result in register R5 4. LOAD R6, id1 // load the value of id1 into register R6 5. ADD R7, R6, R5 // add R6 and R5 and store the result in register R7


What are the results and outputs of the solution?




The results and outputs of the solution are:


  • a) The annotated parse tree for id1 + id2 * id3 is shown above in step 2.



  • b) The syntax-directed translation scheme that translates an arithmetic expression into postfix notation is shown below, where each production rule is augmented with semantic actions that append the translation of each symbol to a string S:



E -> E + T S = S + E.val + T.val + "+" E -> T S = S + T.val T -> T * F S = S + T.val + F.val + "*" T -> F S = S + F.val F -> (E) S = S + E.val F -> id S = S + id.lexval


  • c) The translation of the expression in part (a) is shown above in step 2, where each node of the parse tree is annotated with its translation value. The final translation is stored in E.val at the root node, which is "id1 id2 id3 * +" in postfix notation.



Conclusion




Summary of the main points




programs that can translate source code written in one language into executable code in another language. We have also explored the basics of compiler design, the famous book by Aho and Ullman on this subject, and a specific solution to one of the problems in the book. We have followed the main steps of compiler design, such as lexical analysis, syntax analysis, semantic analysis, intermediate code generation, code optimization, and code generation. We have also applied various techniques and tools to perform these tasks, such as grammars, parse trees, attributes, three-address code, assembly language, etc.


Recommendations for further reading or practice




If you are interested in learning more about compiler design, here are some recommendations for further reading or practice:


  • Read the book by Aho and Ullman, "Compilers: Principles, Techniques, and Tools", which covers the topic in depth and detail. You can also find online lectures and slides based on the book.



  • Read other books on compiler design, such as "Engineering a Compiler" by Keith Cooper and Linda Torczon, "Modern Compiler Implementation in Java" by Andrew Appel and Jens Palsberg, "Compiler Design in C" by Allen Holub, etc.



  • Practice solving problems and exercises on compiler design from various sources, such as textbooks, websites, online courses, etc. You can also find solutions and hints for some of the problems online.



  • Build your own compiler or interpreter for a simple or toy language of your choice. You can use existing tools and libraries to help you with some of the tasks, such as lexers, parsers, code generators, etc.



  • Explore some advanced topics and applications of compiler design, such as compiler construction tools, domain-specific languages, just-in-time compilation, static analysis, program verification, etc.



FAQs




Here are some frequently asked questions about compiler design:


What is the difference between a compiler and an interpreter?




A compiler is a program that translates source code written in one language into executable code in another language. An interpreter is a program that executes source code written in one language directly without producing executable code. A compiler usually produces faster and more efficient code than an interpreter, but an interpreter usually provides more flexibility and interactivity than a compiler.


What are some examples of compilers and interpreters?




Some examples of compilers are GCC (GNU Compiler Collection), which compiles C, C++, and other languages into machine code; Java (Java Compiler), which compiles Java source code into bytecode that can run on the Java Virtual Machine (JVM); Python (Python Compiler), which compiles Python source code into bytecode that can run on the Python Virtual Machine (PVM); etc.


Some examples of interpreters are Ruby (Ruby Interpreter), which executes Ruby source code directly; JavaScript (JavaScript Engine), which executes JavaScript source code directly in web browsers; Bash (Bash Shell), which executes shell commands and scripts directly; etc.


What are some advantages and disadvantages of compilers and interpreters?




Some advantages of compilers are:


  • They produce faster and more efficient code than interpreters.



  • They perform more error checking and optimization than interpreters.



  • They protect the source code from being modified or copied by others.



Some disadvantages of compilers are:


  • They take more time and resources to compile than interpreters.



  • They require recompilation when the source code or the target platform changes.



  • They may not support dynamic features or cross-platform compatibility as well as interpreters.



Some advantages of interpreters are:


  • They provide more flexibility and interactivity than compilers.



  • They do not require compilation time or resources.



  • They support dynamic features and cross-platform compatibility better than compilers.



Some disadvantages of interpreters are:


  • They execute slower and less efficiently than compilers.



They perform less error checking and optimization than


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