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Adapting Proofs as Programs The Curry Howard Protocol 1st Edition by Iman Poernomo, John Newsome Crossley, Martin Wirsing ISBN 9780387281834 0387281835

Name: Adapting Proofs as Programs The Curry Howard Protocol 1st Edition by Iman Poernomo, John Newsome Crossley, Martin Wirsing ISBN 9780387281834 0387281835
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Authors:Iman Hafiz Poernomo, John Newsome Crossley, Martin Wirsing , Series:Computer Science [117] , Tags:Engineering; Computer Sciences , Author sort:Iman Hafiz Poernomo, John Newsome Crossley, Martin Wirsing , Languages:Languages:eng , Published:Published:Jul 2006 , Publisher:Springer , Comments:Comments:This book finds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs in constructive logic. It has been over thirty years since the paradigm was first conceived. At that time, there was a belief that proofs-as-programs had the potential for practical application to semi-automated software development. Initial applications were mostly concerned with fine-grain, mathematical program synthesis. For various reasons, research interest in the area eventually tended toward more theoretic issues of constructive logic and type theory. However, in recent years, the situation has become more balanced, and there is increasingly active research in applying constructive techniques to industrial-scale, complex software engineering problems.

SKU: EB-9074 Category: eBook PDF Tags: Adapting Proofs, Iman Poernomo, John Newsome Crossley, Martin Wirsing, Programs

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ISBN 10: 0387281835
ISBN 13: 9780387281834
Author: Iman Poernomo, John Newsome Crossley, Martin Wirsing

This book ?nds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs in constructive logic. It has been over thirty years since the paradigm was ?rst conceived. At that time, there was a belief that proofs-as-programs had the – tential for practical application to semi-automated software development. I- tial applications were mostly concerned with ?ne-grain, mathematical program synthesis. For various reasons, research interest in the area eventually tended toward more theoretic issues of constructive logic and type theory. However, in recent years, the situation has become more balanced, and there is increasingly active research in applying constructive techniques to industrial-scale, complex software engineering problems. Thismonographdetailsseveralimportantadvancesinthisdirectionofpr- tical proofs-as-programs. One of the central themes of the book is a general, abstract framework for developing new systems of program synthesis by adapting proofs-as-programs to new contexts. Framework-oriented approaches that facilitate analogous – proaches to building systems for solving particular problems have been popular and successful. Thesemethodsarehelpful asthey providea formal toolbox that enablesa“roll-your-own”approachtodevelopingsolutions.Itishopedthatour framework will have a similar impact. The framework is demonstrated by example. We will give two novel – plications of proofs-as-programs to large-scale, coarse-grain software engine- ing problems: contractual imperative program synthesis and structured p- gram synthesis. These applications constitute an exemplary justi?cation of the framework. Also, in and of themselves, these approaches to synthesis should be interesting forresearchers working in the target problem domains.

Adapting Proofs as Programs The Curry Howard Protocol 1st Edition Table of contents:

Chapter 1: Introduction to the Curry-Howard Correspondence

History and Origins of the Curry-Howard Correspondence
The Connection Between Logic and Programming
Significance of Proofs as Programs

Chapter 2: Logic and Proof Systems

Propositional Logic and Predicate Logic
Sequent Calculus and Natural Deduction
Formalizing Proofs in Logical Systems

Chapter 3: Types and Programs

The Role of Types in Programming Languages
Types as Specifications of Programs
Introduction to the Curry-Howard Protocol

Chapter 4: Proofs as Programs

Interpreting Proofs as Computation
Types and Their Corresponding Programs
Constructive Proofs and Algorithm Extraction

Chapter 5: Adapting Proofs for Computational Purposes

Transforming Logical Proofs into Executable Programs
Optimization and Refinement of Programs from Proofs
Case Studies of Proof-to-Program Conversion

Chapter 6: Advanced Topics in Curry-Howard

Dependent Types and Program Refinement
Proofs of Termination and Correctness
Interaction Between Logic and Functional Programming

Chapter 7: Applications of Proofs as Programs

Applications in Functional Programming Languages (e.g., Haskell, ML)
Verifying Software Systems Using Logic
Proof Assistants and Automated Theorem Proving Tools

Chapter 8: Practical Implementation of the Curry-Howard Protocol

Implementing Type Systems and Proof Systems
Case Study: Developing a Proof Assistant
Tools and Software for Proof-Program Translation

Chapter 9: Challenges and Open Problems

Limitations of Current Approaches
Scalability and Automation in Proof-to-Program Translation
Future Directions for Research in Curry-Howard Correspondence

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