Program Proof PDF Download
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Author | : Samuel Mimram |
Publisher | : |
Total Pages | : 539 |
Release | : 2020-07-03 |
Genre | : |
ISBN | : |
Download Program = Proof Book in PDF, ePub and Kindle
This course provides a first introduction to the Curry-Howard correspondence between programs and proofs, from a theoretical programmer's perspective: we want to understand the theory behind logic and programming languages, but also to write concrete programs (in OCaml) and proofs (in Agda). After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.
Author | : Adam Chlipala |
Publisher | : MIT Press |
Total Pages | : 437 |
Release | : 2013-12-06 |
Genre | : Computers |
ISBN | : 0262317885 |
Download Certified Programming with Dependent Types Book in PDF, ePub and Kindle
A handbook to the Coq software for writing and checking mathematical proofs, with a practical engineering focus. The technology of mechanized program verification can play a supporting role in many kinds of research projects in computer science, and related tools for formal proof-checking are seeing increasing adoption in mathematics and engineering. This book provides an introduction to the Coq software for writing and checking mathematical proofs. It takes a practical engineering focus throughout, emphasizing techniques that will help users to build, understand, and maintain large Coq developments and minimize the cost of code change over time. Two topics, rarely discussed elsewhere, are covered in detail: effective dependently typed programming (making productive use of a feature at the heart of the Coq system) and construction of domain-specific proof tactics. Almost every subject covered is also relevant to interactive computer theorem proving in general, not just program verification, demonstrated through examples of verified programs applied in many different sorts of formalizations. The book develops a unique automated proof style and applies it throughout; even experienced Coq users may benefit from reading about basic Coq concepts from this novel perspective. The book also offers a library of tactics, or programs that find proofs, designed for use with examples in the book. Readers will acquire the necessary skills to reimplement these tactics in other settings by the end of the book. All of the code appearing in the book is freely available online.
Author | : Klaus Mainzer |
Publisher | : World Scientific |
Total Pages | : 425 |
Release | : 2021-07-27 |
Genre | : Mathematics |
ISBN | : 9811236496 |
Download Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification Book in PDF, ePub and Kindle
This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Author | : Yves Bertot |
Publisher | : Springer Science & Business Media |
Total Pages | : 492 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 366207964X |
Download Interactive Theorem Proving and Program Development Book in PDF, ePub and Kindle
A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.
Author | : Donald MacKenzie |
Publisher | : MIT Press |
Total Pages | : 448 |
Release | : 2004-01-30 |
Genre | : Social Science |
ISBN | : 9780262632959 |
Download Mechanizing Proof Book in PDF, ePub and Kindle
Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.
Author | : Armand Puccetti |
Publisher | : Springer Science & Business Media |
Total Pages | : 349 |
Release | : 2013-11-11 |
Genre | : Computers |
ISBN | : 3642845428 |
Download The Programming and Proof System ATES Book in PDF, ePub and Kindle
Today, people use a large number of "systems" ranging in complexity from washing machines to international airline reservation systems. Computers are used in nearly all such systems: accuracy and security are becoming increasingly essential. The design of such computer systems should make use of development methods as systematic as those used in other engineering disciplines. A systematic development method must provide a way of writing specifications which are both precise and concise; it must also supply a way of relating design to specification. A concise specification can be achieved by restricting attention to what a system has to do: all considerations of implementation details are postponed. With computer systems, this is done by: 1) building an abstract model of the system -operations being specified by pre-and post-conditions; 2) defining languages by mapping program texts onto some collection of objects modelizing the concepts of the system to be dealt with, whose meaning is understood; 3) defining complex data objects in terms of abstractions known from mathematics. This last topic, the use of abstract data types, pervades all work on specifications and is necessary in order to apply ideas to systems of significant complexity. The use of mathematics based notations is the best way to achieve precision. 1.1 ABSTRACT DATA TYPES, PROOF TECHNIQUES From a practical point of view, a solution to these three problems consists to introduce abstract data types in the programming languages, and to consider formal proof methods.
Author | : Iman Poernomo |
Publisher | : Springer Science & Business Media |
Total Pages | : 726 |
Release | : 2005-06-21 |
Genre | : Computers |
ISBN | : 9780387237596 |
Download Adapting Proofs-as-Programs Book in PDF, ePub and Kindle
This monograph details several important advances in the direction of a practical proofs-as-programs paradigm, which constitutes a set of approaches to developing programs from proofs in constructive logic with applications to industrial-scale, complex software engineering problems. One of the books central themes is a general, abstract framework for developing new systems of programs synthesis by adapting proofs-as-programs to new contexts.
Author | : Richard Bornat |
Publisher | : OUP Oxford |
Total Pages | : 264 |
Release | : 2005-07-21 |
Genre | : Mathematics |
ISBN | : 0191586765 |
Download Proof and Disproof in Formal Logic Book in PDF, ePub and Kindle
Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system—a collection of rules and axioms which define a universe of logical proofs—is what gives us programming languages and modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses—natural deduction—is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: · Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. · Part II "Formal syntactic proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. · Part III "Formal semantic disproof" shows you how to construct mathematical counterexamples to show that proof is impossible. Jape can check the counterexamples you build. · Part IV "Program specification and proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.
Author | : Dave Barker-Plummer |
Publisher | : Stanford Univ Center for the Study |
Total Pages | : 606 |
Release | : 2011 |
Genre | : Computers |
ISBN | : 9781575866321 |
Download Language, Proof, and Logic Book in PDF, ePub and Kindle
Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy.
Author | : Annabelle McIver |
Publisher | : Springer Science & Business Media |
Total Pages | : 412 |
Release | : 2005 |
Genre | : Computers |
ISBN | : 9780387401157 |
Download Abstraction, Refinement and Proof for Probabilistic Systems Book in PDF, ePub and Kindle
Provides an integrated coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a focused survey on probabilistic program semantics. This book illustrates, by examples, the typical steps necessary to build a mathematical model of any programming paradigm.