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  • Non-Deterministic Finite Automation
    • Introduction to Compiler
    • The Structure of a Compiler
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    • Programming Language Basics
    • Minimisation of DFAs
    • Explicit Access Control
    • Parameter Passing Mechanisms
    • Introduction to Lexical Analysis
    • Regular expressions
    • Short hands
    • Nondeterministic finite automata
    • Converting a regular expression to an NFA
    • Deterministic finite automata
    • Converting an NFA to a DFA
    • The subset construction
    • Dead states
    • Lexers and lexer generators
    • Splitting the input stream
    • Lexical errors
    • Properties of regular languages
    • Limits to expressive power
    • The Role of the Lexical Analyzer
    • Input Buffering
    • Specification of Tokens
    • Operations on Languages
    • Regular Definitions and Extensions
    • Recognition of Tokens
    • The Lexical-Analyzer Generator Lex
    • Finite Automata
    • Construction of an NFA from a Regular Expression
    • Efficiency of String-Processing Algorithms
    • The Structure of the Generated Analyzer
    • Optimization of DFA-Based Pattern Matchers

  • Basic Parsing Techniques
    • Introduction to Syntax analysis
    • Context-free grammars
    • Writing context free grammars
    • Derivation
    • Syntax trees and ambiguity
    • Operator precedence
    • Writing ambiguous expression grammars
    • Other sources of ambiguity
    • Syntax analysis and Predictive parsing
    • Nullable and FIRST
    • Predictive parsing revisited
    • FOLLOW
    • LL(1) parsing
    • Methods for rewriting grammars for LL(1) parsing
    • SLR parsing
    • Constructions of SLR parse tables
    • Conflicts in SLR parse-tables
    • Using precedence rules in LR parse tables
    • Using LR-parser generators
    • Properties of context-free languages
    • Introduction to Syntax-Directed Translator
    • Evaluating an SDD at the Nodes of a Parse Tree
    • Evaluation Orders for SDD\'s
    • Ordering the Evaluation of Attributes
    • A larger example of calculating FIRST and FOLLOW
    • Syntax Definition
    • Associativity of Operators
    • Parse Trees
    • Ambiguity
    • Syntax-Directed Translation
    • Synthesized Attributes
    • Tree Traversals
    • Parsing
    • Predictive Parsing
    • Use e-Productions
    • Translator for Simple Expressions
    • Semantic Rules with Controlled Side Effects
    • Applications of Syntax-Directed Translation
    • The Structure of a Type of syntax
    • Switch-Statements
    • Syntax-Directed Translation Schemes
    • Postfix Translation Schemes
    • SDT\'s With Actions Inside Productions
    • Eliminating Left Recursion from SDT\'s
    • SDT\'s for L-Attributed Definitions
    • Implementing L-Attributed SDD\'s
    • On-The-Fly Code Generation
    • L-Attributed SDD\'s and LL Parsing
    • Bottom-Up Parsing of L-Attributed SDD\'s

  • Syntax-directed Translation
    • Register Allocation and Assignment
    • Semantic Analysis
    • Introduction to Intermediate Code Generation
    • Variants of Syntax Trees
    • Variants of Syntax Trees
    • The Value-Number Method for Constructing DAG\'s
    • Three-Address Code
    • Quadruples
    • Triples
    • Static Single-Assignment Form
    • Types and Declarations
    • Type Equivalence
    • Sequences of Declarations
    • Translation of Expressions
    • Incremental Translation
    • Addressing Array Elements
    • Translation of Array References
    • Type Checking
    • Type Conversions
    • Overloading of Functions and Operators
    • Type Inference and Polymorphic Functions
    • Algorithm for Unification
    • Control Flow
    • Flow-of-Control Statements
    • Control-Flow Translation of Boolean Expressions
    • Boolean Values and Jumping Code
    • Back patching
    • Backpatching for Boolean Expressions
    • Flow-of-Control Statements
    • Break-, Continue-, and Goto-Statements
    • Introduction to Run-Time Environments
    • Stack Allocation of Space
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    • Variable-Length Data on the Stack
    • Access to Nonlocal Data on the Stack
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    • Locality in Programs
    • Reducing Fragmentation
    • Managing and Coalescing Free Space
    • Manual Deallocation Requests
    • Reachability
    • Introduction to Garbage Collection
    • Reference Counting Garbage Collectors
    • Introduction to Trace-Based Collection
    • Basic Abstraction
    • Optimizing Mark-and-Sweep
    • Mark-and-Compact Garbage Collectors
    • Copying collectors
    • Short-Pause Garbage Collection
    • Incremental Reachability Analysis
    • Partial-Collection Basics
    • The Train Algorithm
    • Parallel and Concurrent Garbage Collection
    • Partial Object Relocation
    • Introduction Code Generation
    • Issues in the Design of a Code Generator
    • Instruction Selection
    • Register Allocation
    • The Target Language
    • Addresses in the Target Code
    • Stack Allocation
    • Run-Time Addresses for Names
    • Basic Blocks and Flow Graphs
    • Basic Blocks
    • Next-Use Information
    • Representation of Flow Graphs
    • Optimization of Basic Blocks
    • Dead Code Elimination
    • Representation of Array References
    • Pointer Assignments and Procedure Calls
    • A Simple Code Generator
    • The Code-Generation Algorithm
    • Design of the Function getReg
    • Peephole Optimization
    • Algebraic Simplification and Reduction in Strength
    • Register Assignment for Outer Loops
    • Instruction Selection by Tree Rewriting
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    • Pattern Matching by Parsing
    • General Tree Matching
    • Optimal Code Generation for Expressions
    • Evaluating Expressions with an Insufficient Supply of Registers
    • Dynamic Programming Code-Generation

  • Data Flow Analysis
    • The Lazy-Code-Motion Algorithm
    • Introduction to Machine-Independent Optimizations
    • The Dynamic Programming Algorithm
    • The Principal Sources of Optimization
    • Semantics-Preserving Transformations
    • Copy Propagation
    • Induction Variables and Reduction in Strength
    • Introduction to Data-Flow Analysis
    • The Data-Flow Analysis Schema
    • Reaching Definitions
    • Live-Variable Analysis
    • Available Expressions
    • Foundations of Data-Flow Analysis
    • Transfer Functions
    • The Iterative Algorithm for General Frameworks
    • Meaning of a Data-Flow Solution
    • Constant Propagation
    • Transfer Functions for the Constant-Propagation Framework
    • Partial-Redundancy Elimination
    • The Lazy-Code-Motion Problem
    • Loops in Flow Graphs
    • Depth-First Ordering
    • Back Edges and Reducibility
    • Natural Loops
    • Speed of Convergence of Iterative Data-Flow Algorithms
    • Region-Based Analysis
    • Necessary Assumptions About Transfer Functions
    • An Algorithm for Region-Based Analysis
    • Handling Non-reducible Flow Graphs
    • Symbolic Analysis
    • Data-Flow Problem Formulation
    • Region-Based Symbolic Analysis

  • Code Generation
    • Introduction to Software Pipelining of Loops
    • Matrix Multiply: An In-Depth Example
    • Software Pipelining of Loops
    • Introduction Instruction-Level Parallelism
    • Multiple Instruction Issue
    • A Basic Machine Model
    • Code-Scheduling Constraints
    • Finding Dependences Among Memory Accesses
    • Phase Ordering Between Register Allocation and Code Scheduling
    • Speculative Execution Support
    • Basic-Block Scheduling
    • List Scheduling of Basic Blocks
    • Global Code Scheduling
    • Upward Code Motion
    • Updating Data Dependences
    • Advanced Code Motion Techniques
    • Software Pipelining
    • Register Allocation and Code Generation
    • A Software-Pipelining Algorithm
    • Scheduling Cyclic Dependence Graphs
    • Improvements to the Pipelining Algorithms
    • Conditional Statements and Hardware Support for Software Pipelining
    • Basic Concepts of Parallelism and Locality
    • Parallelism in Applications
    • Loop-Level Parallelism
    • Introduction to Affine Transform Theory
    • Optimizations
    • Iteration Spaces
    • Affine Array Indexes
    • Controlling the Order of Execution
    • Changing Axes
    • Intermediate Code for Procedures
    • Data Reuse
    • Self Reuse
    • Self-Spatial Reuse
    • Array Data-Dependence Analysis
    • Integer Linear Programming
    • Heuristics for Solving Integer Linear Programs
    • Solving General Integer Linear Programs
    • Finding Synchronization-Free Parallelism
    • Affine Space Partitions
    • Space-Partition Constraints
    • Solving Space-Partition Constraints
    • A Simple Code-Generation Algorithm
    • Eliminating Empty Iterations
    • Synchronization Between Parallel Loops
    • The Parallelization Algorithm and Hierarchical Time
    • Pipelining
    • Solving Time-Partition Constraints by Farkas' Lemma
    • Code Transformations
    • Parallelism With Minimum Synchronization
    • Locality Optimizations
    • Partition Interleaving
    • Putting it All Together
    • Uses of Affine Transforms
    • Interprocedural Analysis
    • Context Sensitivity
    • Cloning-Based Context-Sensitive Analysis
    • Importance of Interprocedural Analysis
    • SQL Injection
    • A Logical Representation of Data Flow
    • Execution of Datalog Programs
    • Problematic Datalog Rules
    • A Simple Pointer-Analysis Algorithm
    • Flow Insensitivity
    • Context-Insensitive Interprocedural Analysis
    • Context-Sensitive Pointer Analysis
    • Adding Context to Datalog Rules
    • Datalog Implementation by BDD's
    • Relational Operations as BDD Operations

Branch : Computer Science and Engineering
Subject : Compiler design
Unit : Syntax-directed Translation

Type Equivalence


Introduction: Many type-checking rules have the form, "if two type expressions are equal t h e n return a certain type else error." Potential ambiguities arise when names are given to type expressions and the names are then used in subsequent type expressions. The key issue is whether a name in a type expression stands for itself or whether it is an abbreviation for another type expression.

Since type names denote type expressions, they can set up implicit cycles; see the box on "Type Names and Recursive Types." If edges to type names are redirected to the type expressions denoted by the names, then the resulting graph can have cycles due to recursive types.

When type expressions are represented by graphs, two types are structurally equivalent if and only if one of the following conditions is true:

  • They are the same basic type.
  • They are formed by applying the same constructor to structurally equivalent types.
  • One is a type name that denotes the other.

If type names are treated as standing for themselves, then the first two conditions in the above definition lead to name equivalence of type expressions.

Name-equivalent expressions are assigned the same value number; Structural equivalence can be tested using the unification algorithm.

Declarations: We shall study types and declarations using a simplified grammar that declares just one name at a time; declarations with lists of names can be handled as discussed in Example 5.10. The grammar is

D               T id ; D | e

T       ->     B C | record ' { ' D '}'

B       ->     int | float

C                e| [num] C

The fragment of the above grammar that deals with basic and array types was used to illustrate inherited attributes in Section 5.3.2. The difference in this section is that we consider storage layout as well as types. Nonterminal D generates a sequence of declarations. Nonterminal T generates basic, array, or record types. Nonterminal B generates one of the basic types int and float. Nonterminal C, for "component," generates strings of zero or more integers, each integer surrounded by brackets. An array type consists of a basic type specified by B, followed by array components specified by nonterminal C. A record type (the second production for T) is a sequence of declarations for the fields of the record, all surrounded by curly braces.

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