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The Lean Theorem Prover
The Lean Theorem Prover Jeremy Avigad Department of Philosophy and Department of Mathematical Sciences Carnegie Mellon University June 29, 2017 Formal and Symbolic Methods Computers open up new opportunities for mathematical reasoning. Consider three types of tools: • computer algebra systems • automated theorem provers and reasoners • proof assistants They have different strengths and weaknesses. Computer Algebra Systems Computer algebra systems are widely used. Strengths: • They are easy to use. • They are useful. • They provide instant gratification. • They support interactive use, exploration. • They are programmable and extensible. Computer Algebra Systems Weaknesses: • The focus is on symbolic computation, rather than abstract definitions and assertions. • They are not designed for reasoning or search. • The semantics is murky. • They are sometimes inconsistent. Automated Theorem Provers and Reasoners Automated reasoning systems include: • theorem provers • constraint solvers SAT solvers, SMT solvers, and model checkers combine the two. Strengths: • They provide powerful search mechanisms. • They offer bush-button automation. Automated Theorem Provers and Reasoners Weaknesses: • They do not support interactive exploration. • Domain general automation often needs user guidance. • SAT solvers and SMT solvers work with less expressive languages. Ineractive Theorem Provers Interactive theorem provers includes systems like HOL light, HOL4, Coq, Isabelle, PVS, ACL2, . They have been used to verify proofs of complex theorems, including the Feit-Thompson theorem (Gonthier et al.) and the Kepler conjecture (Hales et al.). Strengths: • The results scale. • They come with a precise semantics. • Results are fully verified. Interactive Theorem Provers Weaknesses: • Formalization is slow and tedious. • It requires a high degree of commitment and experise. • It doesn’t promote exploration and discovery. -
Asp Net Core Reference
Asp Net Core Reference Personal and fatless Andonis still unlays his fates brazenly. Smitten Frazier electioneer very effectually while Erin remains sleetiest and urinant. Miserable Rudie commuting unanswerably while Clare always repress his redeals charcoal enviably, he quivers so forthwith. Enable Scaffolding without that Framework in ASP. API reference documentation for ASP. For example, plan content passed to another component. An error occurred while trying to fraud the questions. The resume footprint of apps has been reduced by half. What next the difference? This is an explanation. How could use the options pattern in ASP. Net core mvc core reference asp net. Architect modern web applications with ASP. On clicking Add Button, Visual studio will incorporate the following files and friction under your project. Net Compact spare was introduced for mobile platforms. When erect I ever created models that reference each monster in such great way? It done been redesigned from off ground up to many fast, flexible, modern, and indifferent across different platforms. NET Framework you run native on Windows. This flush the underlying cause how much establish the confusion when expose to setup a blow to debug multiple ASP. NET page Framework follows modular approaches. Core but jail not working. Any tips regarding that? Net web reference is a reference from sql data to net core reference asp. This miracle the nipple you should get if else do brought for Reminders. In charm to run ASP. You have to swear your battles wisely. IIS, not related to your application code. Re: How to reference System. Performance is double important for us. -
Sonic on Mellanox Spectrum™ Switches
SOFTWARE PRODUCT BRIEF SONiC on Mellanox Spectrum™ Switches Delivering the promises of data center disaggregation – SONiC – Software for Open Networking in the Cloud, is a Microsoft-driven open-source network operating system (NOS), HIGHLIGHTS delivering a collection of networking software components aimed at – scenarios where simplicity and scale are the highest priority. • 100% free open source software • Easy portability Mellanox Spectrum family of switches combined with SONiC deliver a performant Open Ethernet data center cloud solution with • Uniform Linux interfaces monitoring and diagnostic capabilities. • Fully supported by the Github community • Industry’s highest performance switch THE VALUE OF SONiC systems portfolio, including the high- Built on top of the popular Switch Abstraction Interface (SAI) specification for common APIs, SONiC density half-width Mellanox SN2010 is a fully open-sourced, hardware-agnostic network operating system (NOS), perfect for preventing • Support for home-grown applications vendor lock-in and serving as the ideal NOS for next-generation data centers. SONiC is built over such as telemetry streaming, load industry-leading open source projects and technologies such as Docker for containers, Redis for balancing, unique tunneling, etc. key-value database, or Quagga BGP and LLDP routing protocols. It’s modular containerized design makes it very flexible, enabling customers to tailor SONiC to their needs. For more information on • Support for small to large-scale deployments open-source SONiC development, visit https://github.com/Azure/SONiC. MELLANOX OPEN ETHERNET SOLUTIONS AND SONiC Mellanox pioneered the Open Ethernet approach to network disaggregation. Open Ethernet offers the freedom to use any software on top of any switches hardware, thereby optimizing utilization, efficiency and overall return on investment (ROI). -
List of Section 13F Securities
List of Section 13F Securities 1st Quarter FY 2004 Copyright (c) 2004 American Bankers Association. CUSIP Numbers and descriptions are used with permission by Standard & Poors CUSIP Service Bureau, a division of The McGraw-Hill Companies, Inc. All rights reserved. No redistribution without permission from Standard & Poors CUSIP Service Bureau. Standard & Poors CUSIP Service Bureau does not guarantee the accuracy or completeness of the CUSIP Numbers and standard descriptions included herein and neither the American Bankers Association nor Standard & Poor's CUSIP Service Bureau shall be responsible for any errors, omissions or damages arising out of the use of such information. U.S. Securities and Exchange Commission OFFICIAL LIST OF SECTION 13(f) SECURITIES USER INFORMATION SHEET General This list of “Section 13(f) securities” as defined by Rule 13f-1(c) [17 CFR 240.13f-1(c)] is made available to the public pursuant to Section13 (f) (3) of the Securities Exchange Act of 1934 [15 USC 78m(f) (3)]. It is made available for use in the preparation of reports filed with the Securities and Exhange Commission pursuant to Rule 13f-1 [17 CFR 240.13f-1] under Section 13(f) of the Securities Exchange Act of 1934. An updated list is published on a quarterly basis. This list is current as of March 15, 2004, and may be relied on by institutional investment managers filing Form 13F reports for the calendar quarter ending March 31, 2004. Institutional investment managers should report holdings--number of shares and fair market value--as of the last day of the calendar quarter as required by Section 13(f)(1) and Rule 13f-1 thereunder. -
Build Reliable Cloud Networks with Sonic and ONE
Build Reliable Cloud Networks with SONiC and ONE Wei Bai 白巍 Microsoft Research Asia OCP China Technology Day, Shenzhen, China 1 54 100K+ 130+ $15B+ REGIONS WORLDWIDE MILES OF FIBER AND SUBSEA CABLE EDGE SITES Investments Two Open Source Cornerstones for High Reliability Networking OS: SONiC Network Verification: ONE 3 Networking OS: SONiC 4 A Solution to Unblock Hardware Innovation Monitoring, Management, Deployment Tools, Cutting Edge SDN SONiC SONiC SONiC SONiC Switch Abstraction Interface (SAI) Merchant Silicon Switch Abstraction Interface (SAI) NetworkNetwork ApplicationsApplicationsNetwork Applications Simple, consistent, and stable Hello network application stack Switch Abstraction Interface Help consume the underlying complex, heterogeneous частный 你好 नमते Bonjour hardware easily and faster https://github.com/opencomputeproject/SAI 6 SONiC High-Level Architecture Switch State Service (SWSS) • APP DB: persist App objects • SAI DB: persist SAI objects • Orchestration Agent: translation between apps and SAI objects, resolution of dependency and conflict • SyncD: sync SAI objects between software and hardware Key Goal: Evolve components independently 8 SONiC Containerization 9 SONiC Containerization • Components developed in different environments • Source code may not be available • Enables choices on a per- component basis 10 SONiC – Powering Microsoft At Cloud Scale Tier 3 - Regional Spine T3-1 T3-2 T3-3 T3-4 … … … Tier 2 - Spine T2-1-1 T2-1-2 T2-1-8 T2-4-1 T2-4-2 T2-4-4 Features and Roadmap Current: BGP, ECMP, ECN, WRED, LAG, SNMP, -
Designing SUPPORTABILITY Into Software by Prashant A
Designing SUPPORTABILITY into Software by Prashant A. Shirolkar Master of Science in Computer Science and Engineering (1998) University of Texas at Arlington Submitted to the System Design and Management Program in Partial Fulfillment of the Requirements for the Degree of Master of Science in Engineering and Management at the Massachusetts Institute of Technology November 2003 C 2003 Massachusetts Institute of Technology All rights reserved Signature of Author Prashant Shirolkar System Design and Management Program February 2002 Certified by Michael A. Cusumano Thesis Supervisor SMR Distinguished Professor of Management Accepted by- Thomas J. Allen Co-Director, LFM/SDM Howard W. Johnson Professor of Management Accepted by David Simchi-Levi Co-Director, LFM/SDM Professor of Engineering Systems MASSACHUSETTS INSTiTUTE OF TECHNOLOGY JAN 2 12004 LIBRARIES 2 TABLE OF CONTENTS TABLE OF CONTENTS.......................................................................................................... 2 LIST OF FIGURES ........................................................................................................................ 6 LIST OF TABLES.......................................................................................................................... 8 ACKNOW LEDGEM ENTS...................................................................................................... 9 ACKNOW LEDGEM ENTS...................................................................................................... 9 1. INTRODUCTION ............................................................................................................... -
Elaboration in Dependent Type Theory
Elaboration in Dependent Type Theory Leonardo de Moura, Jeremy Avigad, Soonho Kong, and Cody Roux∗ December 18, 2015 Abstract To be usable in practice, interactive theorem provers need to pro- vide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathemat- ical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean’s elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computa- tional reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully de- signed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved. 1 Introduction Just as programming languages run the spectrum from untyped languages like Lisp to strongly-typed functional programming languages like Haskell and ML, foundational systems for mathematics exhibit a range of diversity, from the untyped language of set theory to simple type theory and various versions of arXiv:1505.04324v2 [cs.LO] 17 Dec 2015 dependent type theory. Having a strongly typed language allows the user to convey the intent of an expression more compactly and efficiently, since a good deal of information can be inferred from type constraints. Moreover, a type discipline catches routine errors quickly and flags them in informative ways. -
Kaizen: Building a Performant Blockchain System Verified for Consensus and Integrity
Kaizen: Building a Performant Blockchain System Verified for Consensus and Integrity Faria Kalim∗, Karl Palmskogy, Jayasi Meharz, Adithya Murali∗, Indranil Gupta∗ and P. Madhusudan∗ ∗University of Illinois at Urbana-Champaign yThe University of Texas at Austin zFacebook ∗fkalim2, adithya5, indy, [email protected] [email protected] [email protected] Abstract—We report on the development of a blockchain for it [7]. This protocol can then be automatically translated to system that is significantly verified and performant, detailing equivalent code in a functional language and deployed using the design, proof, and system development based on a process of a shim layer to a network to obtain working reference imple- continuous refinement. We instantiate this framework to build, to the best of our knowledge, the first blockchain (Kaizen) that is mentations of the basic protocol. However, there are several performant and verified to a large degree, and a cryptocurrency drawbacks to this—it is extremely hard to work further on protocol (KznCoin) over it. We experimentally compare its the reference implementation to refine it to correct imperative performance against the stock Bitcoin implementation. and performant code, and to add more features to it to meet practical requirements for building applications. I. INTRODUCTION The second technique, pioneered by the IronFleet sys- Blockchains are used to build a variety of distributed sys- tems [8], is to use a system such as Dafny to prove a system tems, e.g., applications such as cryptocurrency (Bitcoin [1] and correct with respect to its specification via automated theorem altcoins [2]), banking, finance, automobiles, health, supply- proving (using SMT solvers) guided by manual annotations. -
The Race of Sound: Listening, Timbre, and Vocality in African American Music
UCLA Recent Work Title The Race of Sound: Listening, Timbre, and Vocality in African American Music Permalink https://escholarship.org/uc/item/9sn4k8dr ISBN 9780822372646 Author Eidsheim, Nina Sun Publication Date 2018-01-11 License https://creativecommons.org/licenses/by-nc-nd/4.0/ 4.0 Peer reviewed eScholarship.org Powered by the California Digital Library University of California The Race of Sound Refiguring American Music A series edited by Ronald Radano, Josh Kun, and Nina Sun Eidsheim Charles McGovern, contributing editor The Race of Sound Listening, Timbre, and Vocality in African American Music Nina Sun Eidsheim Duke University Press Durham and London 2019 © 2019 Nina Sun Eidsheim All rights reserved Printed in the United States of America on acid-free paper ∞ Designed by Courtney Leigh Baker and typeset in Garamond Premier Pro by Copperline Book Services Library of Congress Cataloging-in-Publication Data Title: The race of sound : listening, timbre, and vocality in African American music / Nina Sun Eidsheim. Description: Durham : Duke University Press, 2018. | Series: Refiguring American music | Includes bibliographical references and index. Identifiers:lccn 2018022952 (print) | lccn 2018035119 (ebook) | isbn 9780822372646 (ebook) | isbn 9780822368564 (hardcover : alk. paper) | isbn 9780822368687 (pbk. : alk. paper) Subjects: lcsh: African Americans—Music—Social aspects. | Music and race—United States. | Voice culture—Social aspects— United States. | Tone color (Music)—Social aspects—United States. | Music—Social aspects—United States. | Singing—Social aspects— United States. | Anderson, Marian, 1897–1993. | Holiday, Billie, 1915–1959. | Scott, Jimmy, 1925–2014. | Vocaloid (Computer file) Classification:lcc ml3917.u6 (ebook) | lcc ml3917.u6 e35 2018 (print) | ddc 781.2/308996073—dc23 lc record available at https://lccn.loc.gov/2018022952 Cover art: Nick Cave, Soundsuit, 2017. -
Using Pubsub for Scheduling in Azure SDN Qi Zhang (Microsoft - Azure Networking)
Using PubSub For Scheduling in Azure SDN Qi Zhang (Microsoft - Azure Networking) Azure Networking Azure Region ‘A’ Regional Cable Network Consumers Regional CDN Network Carrier Microsoft Edge Enterprise, SMB, WAN mobile Azure Region ‘B’ ExpressRoute Regional Internet Network Exchanges Enterprise Regional DC/Corpnet Network DC Hardware Services Intra-Region WAN Backbone Edge and ExpressRoute CDN Last Mile • SmartNIC/FPGA • Virtual Networks • DC Networks • Software WAN • Internet Peering • Acceleration for • E2E monitoring • SONiC • Load Balancing • Regional Networks • Subsea Cables • ExpressRoute applications and (Network Watcher, • VPN Services • Optical Modules • Terrestrial Fiber content Network Performance • Firewall • National Clouds Monitoring) • DDoS Protection • DNS & Traffic Management Microsoft Global Network Svalbard Greenland United States Sweden Norway Russia Canada United Kingdom Poland Ukraine Kazakistan France Russia United States Turkey Iran China One of the largest private Algeria Pacific Ocean Atlanta Saudi Ocean Libya networks in the world Mexico Egypt Arabia India Myanmar Niger (Burma) Mali Chad Sudan Pacific Ocean Nigeria • 8,000+ ISP sessions Ethiopi Venezuela a Colombia Dr Congo • 130+ edge sites Indonesia Peru Angola Brazil Zambia Indian Ocean • Bolivia 44 ExpressRoute locations Nambia Australia • 33,000 miles of lit fiber South Africa Owned Capacity Data Argentina • SDN Managed (SWAN, OLS) center Leased Capacity Moving to Owned Edge Site DCs and Network sites not exhaustive Software Defined Management Central Commodity -
Sonic: Software for Open Networking in the Cloud
SONiC: Software for Open Networking in the Cloud Lihua Yuan Microsoft Azure Network Team for the SONiC Community SONiC Community @ OCP Mar 2018 Application & Management Application Management & SONiC [Software For Open Networking in the Cloud] Switch Platform Platform Switch SAI [Switch Abstraction Interface] Silicon/ASIC Microsoft Cloud Network - 15 Billion Dollar Bet SONiC Is Powering Microsoft Cloud At Scale Tier 3 - Regional Spine T3-1 T3-2 T3-3 T3-4 … … … Tier 2 - Spine T2-1-1 T2-1-2 T2-1-8 T2-4-1 T2-4-2 T2-4-4 … … … T1-1 T1-2 SONICT1-7 TSONIC1-8 T1-1 T1-2 T1-7 T1-8 Tier 1 – Row Leaf SONICT1-1 SONICT1-2 SONICT1-7 T1SONIC-8 SONIC SONIC SONIC SONIC SONIC SONIC … … … Tier 0 - Rack SONICT0-1 SONICT0-2 SONICT0-20 SONICT0-1 SONICT0-2 T0SONIC-20 SONICT0-1 SONICT0-2 SONICT0-20 Servers Servers Servers Goals of SONiC Faster Reduce Technology Operational Evolution Burden Disaggregation with SONiC Open & Choices of Vendors & Modular Platforms Software SONiC: Software for Open Networking in the Cloud • Switch Abstraction Interface (SAI) • Cross-ASIC portability • Modular Design with Switch State Service (SwSS) • Decoupling software components • Consistent application development model • Containerization of SONiC • Serviceability • Cross-platform portability • SONiC Operational Scenarios • Hitless upgrade • Network emulation with CrystalNet Switch Abstraction Interface (SAI) NetworkNetwork ApplicationsApplications Simple, consistent, and Network Applications stable network application stack Hello Switch Abstraction Interface Helps consume the underlying -
Leg 140 Preliminary Report
OCEAN DRILLING PROGRAM LEG 140 PRELIMINARY REPORT HOLE 504B Dr. Henry Dick Dr. Jörg Erzinger Co-Chief Scientist, Leg 140 Co-Chief Scientist, Leg 140 Woods Hole Oceanographic Institution Institut fur Geowissenschaften Woods Hole, MA 02543 und Lithosphárenforschung Universitàt Giessen Senckenbergstraße 3 6300 Giessen Federal Republic of Germany Dr. Laura Stokking Staff Scientist, Leg 140 Ocean Drilling Program Texas A&M University Research Park 1000 Discovery Drive College Station, Texas 77845-9547 Philip D. Rabinoütffz" Director ODP/TAMU λuànülu Audrey W. Meyer Manager / Science Operations ODP/TAMU Timothy J.G. Francis Deputy Director ODP/TAMU January 1992 This informal report was prepared from the shipboard files by scientists, engineers, and technicians who participated in the cruise. The report was assembled under time constraints and is not considered to be a formal publication that incorporates final works or conclusions of the participants. The material contained herein is privileged proprietary information and cannot be used for publication or quotation. Preliminary Report No. 40 First Printing 1992 Distribution Copies of this publication may be obtained from the Director, Ocean Drilling Program, Texas A&M University Research Park, 1000 Discovery Drive, College Station, Texas 77845-9547, U.S.A. In some cases, orders for copies may require a payment for postage and handling. DISCLAIMER This publication was prepared by the Ocean Drilling Program, Texas A&M University, as an account of the work performed under the international Ocean