First-Order Programming Theories

1. Front Matter

   Pages I-IX

   PDF

2. Introduction

   1. Introduction

      • Tamás Gergely, László Úry

      Pages 1-12

3. Mathematical Background

   1. Front Matter

      Pages 13-13

      PDF

   2. Logic and Model Theory

      • Tamás Gergely, László Úry

      Pages 15-35

   3. Inductive Definability

      • Tamás Gergely, László Úry

      Pages 37-45

4. Computability

   1. Front Matter

      Pages 47-47

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   2. Introduction to Part I

      • Tamás Gergely, László Úry

      Pages 49-52

   3. Main Properties of Program Schemas

      • Tamás Gergely, László Úry

      Pages 53-76

   4. Extension of Program Schemas

      • Tamás Gergely, László Úry

      Pages 77-89

   5. Program Schemas with Stacks

      • Tamás Gergely, László Úry

      Pages 91-102

   6. Computability

      • Tamás Gergely, László Úry

      Pages 103-117

   7. On Inductive Definability of 1- and 2- Computable Relations

      • Tamás Gergely, László Úry

      Pages 119-131

5. Extended Dynamic Logics

   1. Front Matter

      Pages 133-133

      PDF

   2. Introduction to Part II

      • Tamás Gergely, László Úry

      Pages 135-138

   3. Description of Program Properties

      • Tamás Gergely, László Úry

      Pages 139-142

   4. Den-based Descriptive Languages

      • Tamás Gergely, László Úry

      Pages 143-153

   5. The Problem of Completeness

      • Tamás Gergely, László Úry

      Pages 155-170

   6. Dynamic Logic Generated by Extension

      • Tamás Gergely, László Úry

      Pages 171-178

   7. Continuous Denotational Semantics

      • Tamás Gergely, László Úry

      Pages 179-210

   8. Definable Denotational Semantics

      • Tamás Gergely, László Úry

      Pages 211-225

This work presents a purely classical first-order logical approach to the field of study in theoretical computer science sometimes referred to as the theory of programs, or programming theory. This field essentially attempts to provide a precise mathematical basis for the common activities involved in reasoning about computer programs and programming languages, and it also attempts to find practical applications in the areas of program specification, verification and programming language design. Many different approaches with different mathematical frameworks have been proposed as a basis for programming theory. They differ in the mathe­ matical machinery they use to define and investigate programs and program properties and they also differ in the concepts they deal with to understand the programming paradigm. Different approaches use different tools and viewpoints to characterize the data environment of programs. Most of the approaches are related to mathe­ matical logic and they provide their own logic. These logics, however, are very eclectic since they use special entities to reflect a special world of programs, and also, they are usually incomparable with each other. This Babel's mess irritated us and we decided to peel off the eclectic com­ ponents and try to answer all the questions by using classical first-order logic.

• Logik erster Ordnung
• Programmiertheorie
• Programmierung (EDV)
• Programming Theory
• Programmverifikation
• Temporale Logik
• first-order reasoning
• formal method
• logic
• program verification
• programming
• programming language
• semantics
• temporal logic
• verification

• Applied Logic Laboratory, Budapest, Hungary

  Tamás Gergely, László Úry

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