Social processes, program verification and all that

@article{Asperti2009SocialPP,
  title={Social processes, program verification and all that},
  author={Andrea Asperti and Herman Geuvers and N. Raja},
  journal={Mathematical Structures in Computer Science},
  year={2009},
  volume={19},
  pages={877 - 896}
}
In a controversial paper (De Millo et al. 1979) at the end of the 1970's, R. A. De Millo, R. J. Lipton and A. J. Perlis argued against formal verifications of programs, mostly motivating their position by an analogy with proofs in mathematics, and, in particular, with the impracticality of a strictly formalist approach to this discipline. The recent, impressive achievements in the field of interactive theorem proving provide an interesting ground for a critical revisiting of their theses. We… Expand
Theory-Specific Automated Reasoning
TLDR
Set Theory is referred to as the unifying background, and to a specific proof-checker based on a slightly unorthodox formalization of it as an arena for experimentation as a key point of integration in the large-scale computerized proof system. Expand
A Vindication of Program Verification
Fetzer famously claims that program verification is not even a theoretical possibility, and offers a certain argument for this far-reaching claim. Unfortunately for Fetzer, and like-minded thinkers,Expand
Program Verification and Functioning of Operative Computing Revisited: How about Mathematics Engineering?
TLDR
It is concluded that “mathematics engineering” is a field to be both developed for practical improvement of doing mathematics and taken into consideration while philosophizing about mathematics as well. Expand
BP: Formal Proofs, the Fine Print and Side Effects
TLDR
This work revisits the meaning of security-related proofs about software, and considers in detail, for the first time to the authors' knowledge, possible relationships between proofs and side effects. Expand
How are programs found? speculating about language ergonomics with Curry-Howard
TLDR
A sampling of mathematicians' attitudes towards formal proof suggests that the crucial role of intuition and experimentation in programming tasks may be under appreciated, hinting at a possible explanation of the challenges rigorously disciplined languages face in practical applications. Expand
A Formal Proof of Borodin-Trakhtenbrot's Gap Theorem
TLDR
The proof is done at an abstract, machine independent level, and is particularly aimed to identify the minimal set of assumptions required to prove the result (smaller than expected, actually). Expand
Position paper: the science of deep specification
TLDR
This article introduces the key formal underpinnings of industrial-scale formal specifications of software and hardware components, and identifies an important class of specification that has already been used in a few experiments that connect strong component-correctness theorems across the work of different teams. Expand
Strong Types for Direct Logic
This article follows on the introductory article “Direct Logic for Intelligent Applications” [Hewitt 2017a]. Strong Types enable new mathematical theorems to be proved including the FormalExpand
Some considerations on the usability of interactive provers
TLDR
The overall usability of interactive provers does not seem to be sensibly improved since the advent of the "second generation" of systems, in the mid of the eighties. Expand
The QED manifesto — Version 2.0
  • Ittay Weiss
  • Computer Science
  • Asia-Pacific World Congress on Computer Science and Engineering
  • 2014
In 1994 the QED Manifesto described an ideal whereby mathematics is communicated via a computerized system in a fully formalized fashion complete with automatic proof checking and other derived toolsExpand
...
1
2
3
...

References

SHOWING 1-10 OF 230 REFERENCES
Social processes and proofs of theorems and programs
TLDR
It is argued that formal verifications of programs will not play the same key role in the development of computer science and software engineering as proofs do in mathematics because of the absence of continuity, inevitability of change, and the complexity of specification of significantly many real programs. Expand
Lambda-Mu-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
TLDR
This paper presents a way of extending the paradigm "proofs as programs" to classical proofs, which can be seen as a simple extension of intuitionistic natural deduction, whose algorithmic interpretation is very well known. Expand
Proof assistants: History, ideas and future
TLDR
This paper is also a position paper that pushes the further use of proof assistants, believing that these systems will become the future of mathematics, where definitions, statements, computations and proofs are all available in a computerized form. Expand
Towards the Formal Verification of a C0 Compiler: Code Generation and Implementation Correctnes
TLDR
An operational small steps semantics for C0 which is formalized in Isabelle/HOL and the implementation of the compiler in C0 and a formal proof that the implementation produces the same code as the specification. Expand
A Syntactic Approach to Foundational Proof-Carrying Code
TLDR
A syntactic approach to FPCC is presented that gives a translation from a typed assembly language into FPCC and demonstrates the advantages of the new system through an implementation in the Coq proof assistant. Expand
Construction and deduction in type theories
TLDR
This dissertation concludes with a discussion of some techniques that make proof search practically applicable, such as unification and pruning of the proof search space by exploiting impermutabilities of the sequent calculus. Expand
On the Uses of Rigorous Proof. (Book Reviews: Proofs and Refutations. The Logic of Mathematical Discovery)
TLDR
This chapter discusses criticism of the proof by counterexamples which are local but not global and how criticism may turn mathematical truth into logical truth. Expand
A Critique of OpenMath and Thoughts on Encoding Mathematics , January , 2001
The OpenMath project, as portrayed in the Special Issue of the SIGSAM Bulletin (volume 34 no. 2), seems to have a number of problems to face. One of them is the (apparently implicit) assumption thatExpand
Cooperative Repositories for Formal Proofs A Wiki-Based Solution
TLDR
A new framework for the online development of formalized mathematics is presented, which allows wiki-style collaboration while providing users with a rendered and browsable version of their work and a modified version of the MediaWiki code-base. Expand
Isar - A Generic Interpretative Approach to Readable Formal Proof Documents
TLDR
Isar's main aspect is its formal language for natural deduction proofs, which sets out to bridge the semantic gap between internal notions of proof given by state-of-the-art interactive theorem proving systems and an appropriate level of abstraction for user-level work. Expand
...
1
2
3
4
5
...