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 | : 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 | : Paolo Mancosu |
Publisher | : Oxford University Press |
Total Pages | : 336 |
Release | : 2021-08-12 |
Genre | : Philosophy |
ISBN | : 0192649299 |
Download An Introduction to Proof Theory Book in PDF, ePub and Kindle
An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
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 | : Stefania Centrone |
Publisher | : Springer Nature |
Total Pages | : 375 |
Release | : 2019-10-25 |
Genre | : Philosophy |
ISBN | : 3030204472 |
Download Mathesis Universalis, Computability and Proof Book in PDF, ePub and Kindle
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Author | : N. Shankar |
Publisher | : Cambridge University Press |
Total Pages | : 224 |
Release | : 1997-01-30 |
Genre | : Computers |
ISBN | : 9780521585330 |
Download Metamathematics, Machines and Gödel's Proof Book in PDF, ePub and Kindle
Describes the use of computer programs to check several proofs in the foundations of mathematics.