What are the most interesting equivalences arising from the Curry-Howard Isomorphism?
I came upon the Curry-Howard Isomorphism relatively late in my programming life, and perhaps this contributes to my being utterly fascinated by it. It implies that for every programming concept there exists a precise analogue in formal logic, and vice versa. Here's a "basic" list of such analogies, off the top of my head: program/definition | proof type/declaration | proposition inhabited type | t
Coq/SSReflect/MathCompの設定
[2023-02-24 Fri]: Ubuntu 22.04.1 LTS, Coq 8.16.1, MathComp 1.16 [2023-01-06 Fri]: Ubuntu 22.04.1, opam 2.1.4, ocaml 4.14.1, Coq 8.16.1, ProofGeneral 4.6, MathComp 1.15.0, MathComp-Analysys 0.6.0 [2022-09-09 Fri]: Ubuntu 22.04.1, Coq 8.15, MathComp 1.15 (opam), ProofGeneral 4.6 [2022-08-03 Wed]: Windows 11, Coq 8.15, MathComp 1.15 (WSL 2) [2022-03-01 Tue]: Windows 11 21H2, Coq 8.15, MathComp 1.14 (
Reddit - Dive into anything
Computer Science Theory and Application. We share and discuss any content that computer scientists find interesting. People from all walks of life welcome, including hackers, hobbyists, professionals, and academics.
A Tale of Two Provers
A Tale of Two Provers Verifying Monoidal String Matching in Liquid Haskell and Coq Niki Vazou University of Maryland Leonidas Lampropoulos University of Pennsylvania Jeff Polakow Awake Networks Abstract We demonstrate for the first time that Liquid Haskell, a refinement type checker for Haskell programs, can be used for arbitrary the- orem proving by verifying a parallel, monoidal string matching
Using Coq to Write Fast and Correct Haskell
Using Coq to Write Fast and Correct Haskell John Wiegley BAE Systems USA john.wiegley@baesystems.com Benjamin Delaware Purdue University USA bendy@purdue.edu Abstract Correctness and performance are often at odds in the field of sys- tems engineering, either because correct programs are too costly to write or impractical to execute, or because well-performing code involves so many tricks of the tr
Cosette: An Automated SQL Solver
Cosette is an automated prover for checking equivalences of SQL queries. It formalizes a substantial fragment of SQL in the Coq Proof Assistant and the Rosette symbolic virtual machine. It returns either a formal proof of equivalance or a counterexample for a pair of given queries. Checking SQL Equivalences in Cosette You can try the Cosette demo online, using Cosette Web API or download its sourc
Computation and Logic: Winter Semester 2016
お知らせ 宿題を遅れて提出する場合の最終期限は 2/3(金) 17:00 です．要再提出が残っている人もこの時刻までに解決してください． スライド8と配布資料その4をアップロードしました．(2017.1.23) 1/17(火)は、(講義ホームページにある)予定を変更して2回目の演習とします。過去の期末試験(ホームページからダウンロードしてください。)の問題も演習の範囲とします。(2017.1.9) 過去の期末試験(2012年度, 2013年度, 2014年度, 2015年度)をアップロードしました(テキストと同じパスワードでダウンロードしてください)．演習の追加題材とします．(2016.12.31) スライド7アップロード．宿題その7がでました．(2016.12.19) 宿題その6の問題 or_distributes_over_and_2 は or_distributes_over_and
An afternoon of DTT/theorem provers: Agda and Coq
Note from 23rd August, 2017 I found this draft blog post lying around, written in the spring of 2015 while I was working at Imperial College London as a Research Associate in the Mobility Reading Group with Nobuko Yoshida. This was the fruit of a discussion with Tiago Cogumbreiro where we were comparing Coq and Agda for theorem proving. I believe we had a few more “side-by-side” comparisons writte
Writing a Formally-Verified Porn Browser in Coq and Haskell
It’s uncommon to use formal verification when developing software. Most people are unfamiliar with the tools and techniques, or assume they’re only for specialized use. This article will show how to write a simple image browser with: Core data structures and operations formally verified using the Coq theorem prover. A Haskell web server that handles HTTP requests An HTML/CSS/Javascript frontend De
PowerPoint プレゼンテーション
Ruby Extension Library Verified using Coq Proof-assistant Tanaka Akira National Institute of Advanced Industrial Science and Technology (AIST) RubyKaigi 2017 2017-09-20 2 About This Talk • Formal verification for fast & safe program in C • Quality assurance other than test 3 Materials • Ruby • Coq • C • HTML escape • Intel SSE Do you know all of them? 4 Coq Proof-assistant • Proof assistant – Prog
CoqHammer - Learning-assisted automated reasoning for Coq
We present an architecture of a full hammer for dependent type theory together with its implementation for the Coq proof assistant. A key component of the hammer is a proposed translation from the Calculus of Inductive Constructions, with certain extensions introduced by Coq, to untyped first-order logic. The translation is "sufficiently" sound and complete to be of practical use for automated the
Coq Winter School 2018
COURSE 2018 From Monday January 22 to Friday January 26, 2018, Yves Bertot will be teaching a course entitled “SOFTWARE VERIFICATION AND COMPUTER PROOF” in the context of the international computer science master at the university of Nice, in Sophia Antipolis. This course is also supported by Université Côte d’Azur PROGRAM 1/ Basic programming with Coq’s functional programming language. Course not
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Can Haskell functions be proved/model-checked/verified with correctness properties?
What are the strengths and weaknesses of the Isabelle proof assistant compared to Coq?
Using forall within recursive Function definition
collacoq
GitHub - krtx/agda-handson: agda handson
初めて学ぶCoq
Typeclasses: A Tutorial on Typeclasses in Coq
https://www.mimuw.edu.pl/~lukaszcz/coqhammer.pdf