Daniel Matichuk Makarius Wenzel, Toby Murray
|
|
- Juniper Reed
- 5 years ago
- Views:
Transcription
1 THE UNIVERSITY OF NEW SOUTH WALES Eisbach: An Isabelle Proof Method Language Daniel Matichuk Makarius Wenzel, Toby Murray ITP 2014
2 Proof Engineering average 0 Mar-2004 Size distribution of AFP entries in lines of proof, sorted by submission date Feb
3 Proof Engineering average 0 Mar-2004 Size distribution of AFP entries in lines of proof, sorted by submission date Feb
4 Proof Engineering average 0 Mar-2004 Size distribution of AFP entries in lines of proof, sorted by submission date Feb
5 Proof Engineering average 0 Mar-2004 Size distribution of AFP entries in lines of proof, sorted by submission date Feb
6 Outline = Isabelle = Isabelle Isabelle Concepts - Isar - Proof Methods Eisbach - Easy Custom Proof Methods - Demo Evaluation/Future -Existing method rewritten -Tracing/Debugging 3
7 Isabelle Concepts = Isabelle = Isabelle Isabelle Concepts - Isar - Proof Methods Eisbach - Easy Custom Proof Methods - Demo Evaluation/Future -Existing method rewritten -Tracing/Debugging 4
8 Isabelle/Isar theorem Knaster-Tarski: assumes mono: V xy. x apple y =) fxapple fy shows f ( d {x. fxapple x}) = d {x. fxapple x} (is f?a=?a) proof have : f?aapple?a (is - apple d?h ) proof fix x assume H : x 2?H then have?a apple x.. also from H have f... apple x.. moreover note mono finally show f?aapple x. qed also have?a apple f?a proof from mono and have f (f?a) apple f?a. then show f?a2?h.. qed finally show f?a=?a. qed 5
9 Isabelle/Isar theorem Knaster-Tarski: assumes mono: V xy. x apple y =) fxapple fy shows f ( d {x. fxapple x}) = d {x. fxapple x} (is f?a=?a) proof have : f?aapple?a (is - apple d?h ) proof fix x assume H : x 2?H then have?a apple x.. also from H have f... apple x.. moreover note mono finally show f?aapple x. qed also have?a apple f?a proof from mono and have f (f?a) apple f?a. then show f?a2?h.. qed finally show f?a=?a. qed 5
10 Isabelle/Isar theorem Knaster-Tarski 0 : assumes mono[intro]: V xy. x apple y =) fxapplefy shows f ( d {x. fxapplex}) = d { } ({x. { fxapple x}) } (is f?a=?a) proof have : f?aapple apple?a by (clarsimp,rule order.trans, fastforce) also have?a apple f?aby (fastforce intro: ) finally show f?a=?a. qed 6
11 Isabelle/Isar theorem Knaster-Tarski 0 : assumes mono[intro]: V xy. x apple y =) fxapplefy shows f ( d {x. fxapplex}) = d { } ({x. { fxapple x}) } (is f?a=?a) proof have : f?aapple apple?a by (clarsimp,rule order.trans, fastforce) also have?a apple f?aby (fastforce intro: ) finally show f?a=?a. qed 6
12 Proof Methods V d { apple } d { apple } have : f?aapple?a by (clarsimp,rule order.trans, fastforce) apple Goal Method Combinator d V d apple also have?a apple f?aby (fastforce intro: ) Method Parameter 7
13 Isabelle/ML theorem Knaster-Tarski 0 :( V xy. x apple y =) fxapple fy)=) f ( d {x. fxapple x}) = d ({x. fxapple x}) apply (tactic hh [0 ]@{thms order-eq-i } 1 ) THEN context-conji } 1 ) THEN Inf-greatest} 1 ) THEN Inf-lower} 1 ) THEN 1 ) THEN Inf-lower} 1 ) THEN 1 ) ii) done 8
14 Isabelle s AFP Number of files in AFP ML 50 Isar (.thy) 1,663 9
15 sel4 - our experience Full functional correctness proof Source code and Proof going open source for more info July 29 Isabelle proof methods developed WP/WPC - vcg for monadic hoare logic sep-* - automating separation logic Proof Engineers want more Languages like Ltac show this 10
16 Eisbach = Isabelle = Isabelle Isabelle Concepts - Isar - Proof Methods Eisbach - Easy Custom Proof Methods - Demo Evaluation/Future -Existing method rewritten -Tracing/Debugging 11
17 12
18 Eisbach 12
19 Language Elements Integrates existing/new methods fastforce, simp, auto Abstract over Terms/Facts/Methods Attributes for method hints simp, intro, my_vcg_rules Matching provides control flow Match and bind higher-order patterns against focused subgoal elements 13
20 Eisbach method-definition induct-list facts simp = (match?concl in?p (?x :: 0 a list) ) (induct?x 7 fastforce simp: simp)) lemma length ys) =length xs + length ys by induct-list 14
21 Eisbach - Design goals Easy for beginners and experts Familiar method syntax from Isar Limited functionality - leave complexity to Isabelle/ML Integration with other Isabelle languages Readable proof procedures 15
22 Eisbach - Combinators Standard Isar Method Combinators - alternative composition, - sequential composition? - suppress failure (try) + - repeated application New Combinator 7 - compose with emerging subgoals method-definition prop-solver 1 =((rule impi, (erule conje)?) assumption)+ lemma P ^ Q ^ R P by prop-solver 16
23 Eisbach - Abstraction Parameterize over facts, terms, and methods Method Signature method-definition prop-solver 2 facts intro elim = ((rule intro, (erule elim)?) assumption)+ lemma P ^ Q P by prop-solver intro impi elim Abstracted Facts 17
24 Eisbach - Abstraction Parameterize over facts, terms, and methods Method Signature method-definition prop-solver 2 facts intro elim = ((rule intro, (erule elim)?) assumption)+ lemma P ^ Q P by prop-solver intro impi elim Abstracted Facts Fact Arguments lemma P ^ Q P by (prop-solver 2 intro: impi elim: conje) 17
25 Eisbach - Attributes New command: declare-attributes Managed with the usual Isar declare command declare-attributes intro elim method-definition prop-solver declare impi [intro] and conje [elim] lemma P ^ Q P by prop-solver Used at run-time by methods method-definition prop-solver 3 facts [intro] [elim] = ((rule intro, (erule elim)?) assumption)+ declare and 18
26 Eisbach - Attributes New command: declare-attributes Managed with the usual Isar declare command declare-attributes intro elim method-definition prop-solver declare impi [intro] and conje [elim] lemma P ^ Q P by prop-solver Used at run-time by methods method-definition prop-solver 3 facts [intro] [elim] = ((rule intro, (erule elim)?) assumption)+ declare and Square brackets indicate fact parameter is managed by attribute 18
27 Eisbach - Attributes New command: declare-attributes Managed with the usual Isar declare command declare-attributes intro elim method-definition prop-solver declare impi [intro] and conje [elim] lemma P ^ Q P by prop-solver Used at run-time by methods method-definition prop-solver 3 facts [intro] [elim] = ((rule intro, (erule elim)?) assumption)+ declare Contains impi ^ and Contains conje Square brackets indicate fact parameter is managed by attribute 18
28 Eisbach - Attributes New command: declare-attributes Managed with the usual Isar declare command declare-attributes intro elim method-definition prop-solver declare impi [intro] and conje [elim] lemma P ^ Q P by prop-solver Used at run-time by methods Square brackets indicate fact parameter is managed by attribute method-definition prop-solver 3 facts [intro] [elim] = ((rule intro, (erule elim)?) assumption)+ declare Contains impi ^ and Contains conje lemma P ^ Q P by prop-solver 3 18
29 Eisbach - Matching Higher-order matching for control flow Bind matched patterns method-definition solve-ex = (match?concl in 9 x.?q x ) (match prems in U: Q?y ) (rule exi [where x = y and P = Q, OF U]))) 9 19
30 Eisbach - Matching Higher-order matching for control flow Bind matched patterns definitio Special term?concl is current subgoal h prems method-definition solve-ex = (match?concl in 9 x.?q x ) (match prems in U: Q?y ) (rule exi [where x = y and P = Q, OF U]))) 9 19
31 Eisbach - Matching Higher-order matching for control flow Bind matched patterns definitio Special term?concl is current subgoal h prems method-definition solve-ex = (match?concl in 9 x.?q x ) (match prems in U: Q?y ) (rule exi [where x = y and P = Q, OF U]))) 9 Matched pattern is bound?q Q?y 19
32 Eisbach - Matching Higher-order matching for control flow Bind matched patterns definitio Special term?concl is current subgoal h prems method-definition solve-ex = (match?concl in 9 x.?q x ) (match prems in U: Q?y ) (rule exi [where x = y and P = Q, OF U]))) 9 Matched pattern is bound?q Q?y Special fact prems is current premises 19
33 Eisbach - Matching Higher-order matching for control flow Bind matched patterns definitio Special term?concl is current subgoal h prems method-definition solve-ex = (match?concl in 9 x.?q x ) (match prems in U: Q?y ) (rule exi [where x = y and P = Q, OF U]))) 9 Matched pattern is bound?q Q?y Special fact prems is current premises Matching singleton fact is bound 9 U: 19
34 Focus/Matching Problem: Raw subgoals are unstructured V x. Ax=) Bx=) Ax^ Bx V 20
35 Focus/Matching Problem: Raw subgoals are unstructured V V x. Ax=) Bx=) Ax^ Bx lemma V assumes A: A and B: B show by (rule conji [OF assms(1 ) assms(2 )]) V 20
36 Focus/Matching Problem: Raw subgoals are unstructured V V x. Ax=) Bx=) Ax^ Bx lemma V assumes A: A and B: B show by (rule conji [OF assms(1 ) assms(2 )]) V 20
37 Focus/Matching Problem: Raw subgoals are unstructured V V x. Ax=) Bx=) Ax^ Bx lemma V assumes A: A and B: B show by (rule conji [OF assms(1 ) assms(2 )]) Goal: V method-definition solve-conj = (match?concl in?p ^?Q ) (match prems in U : P and U 0 : Q ) (rule conji [OF U U 0 ]))) V 20
38 Focus/Matching Problem: Raw subgoals are unstructured V V x. Ax=) Bx=) Ax^ Bx lemma V assumes A: A and B: B show by (rule conji [OF assms(1 ) assms(2 )]) Goal: method-definition solve-conj = (match?concl in?p ^?Q ) (match prems in U : P and U 0 : Q ) (rule conji [OF U U 0 ]))) V V Find and name assumptions through matching 20
39 Focus Solution: Focusing Based on existing work V x. Ax=) Bx=) Ax^ Bx V 21
40 Focus Solution: Focusing Based on existing work V x. Ax=) Bx=) Ax^ Bx V V emma V x. fixes x assumes Axand Bx shows Ax^ Bx V Ax Ax^ Bx Bx 21
41 Focus Solution: Focusing Based on existing work V x. Ax=) Bx=) Ax^ Bx V V emma V x. fixes x assumes Axand Bx shows Ax^ Bx V Ax Ax^ Bx Bx prems definiti?concl h prems 21
42 Demo 22
43 Evaluation/Future work = Isabelle = Isabelle Isabelle Concepts - Isar - Proof Methods Eisbach - Easy Custom Proof Methods - Demo Evaluation/Future -Existing method rewritten -Tracing/Debugging 23
44 Tactic Languages are not new Ltac Untyped High-level tactic language for Coq Goal matching, iteration, recursion VeriML Dependently typed tactic language Provides strong static guarantees Mtac Typed tactic language for Coq Leverages built-in Coq notion of computation Strong static guarantees 24
45 Current Results Eisbach Extension of Isar, Isabelle s proof language Integrates with existing Isar syntax methods attributes Evaluation Existing methods rewritten in Eisbach WP, WPC: l4.verified invariant proof successfully checked Future Work Tracing/Debugging Optimisations 25
46 Conclusion Proof Engineers need tools to write proofs at scale Isar provides structure/syntax for proofs Most Isabelle users most familiar with Isar Eisbach provides easy mechanisms for writing automation abstraction matching backtracking recursion Coming soon 26
47 Thank You 27
CS Lecture 5. Vidroha debroy. Material adapted courtesy of Prof. Xiangnan Kong and Prof. Carolina Ruiz at Worcester Polytechnic Institute
CS 3353 Lecture 5 Vidroha debroy Material adapted courtesy of Prof. Xiangnan Kong and Prof. Carolina Ruiz at Worcester Polytechnic Institute Searching for a number Find a specific number 91-3 26 54 73
More informationCSE 3402: Intro to Artificial Intelligence Uninformed Search II
CSE 3402: Intro to Artificial Intelligence Uninformed Search II Required Readings: Chapter 3, Sec. 1-4. 1 {Arad}, {Zerind, Timisoara, Sibiu}, {Zerind, Timisoara, Arad, Oradea, Fagaras, RimnicuVilcea },
More informationIntroduction to Alloy
Introduction to Alloy L. Dillon CSE 814 Overview of Alloy 1 Acknowledgements Excerpted (mostly) and adapted from:! One day tutorial at http://alloy.mit.edu/fm06/! SBMF/ICGT 2006 keynote at http:// people.csail.mit.edu/dnj/talks/brazil06/brazil06.pdf!
More informationBachelor of Computer Applications (Semester-2) Subject Name: Project in C Subject Code: BCA 205. General Guidelines for Project in C
DR. BABASAHEB AMBEDKAR OPEN UNIVERSITY (Established by Government of Gujarat) 'Jyotirmay' Parisar, Opp. Shri Balaji Temple, Sarkhej-Gandhinagar Highway, Chharodi, Ahmedabad - 382 481. Tel. (079) 27663748
More informationCSE 3401: Intro to AI & LP Uninformed Search II
CSE 3401: Intro to AI & LP Uninformed Search II Required Readings: R & N Chapter 3, Sec. 1-4. 1 {Arad}, {Zerind, Timisoara, Sibiu}, {Zerind, Timisoara, Arad, Oradea, Fagaras, RimnicuVilcea }, {Zerind,
More informationPolynomial DC decompositions
Polynomial DC decompositions Georgina Hall Princeton, ORFE Joint work with Amir Ali Ahmadi Princeton, ORFE 7/31/16 DIMACS Distance geometry workshop 1 Difference of convex (dc) programming Problems of
More informationTaking Your Class for a Walk, Randomly
Taking Your Class for a Walk, Randomly Daniel Kaplan Macalester College Oct. 27, 2009 Overview of the Activity You are going to turn your students into an ensemble of random walkers. They will start at
More informationBetter Search Improved Uninformed Search CIS 32
Better Search Improved Uninformed Search CIS 32 Functionally PROJECT 1: Lunar Lander Game - Demo + Concept - Open-Ended: No One Solution - Menu of Point Options - Get Started NOW!!! - Demo After Spring
More informationRobust Task Execution: Procedural and Model-based. Outline. Desiderata: Robust Task-level Execution
Robust Task Execution: Procedural and Model-based Mission Goals and Environment Constraints Temporal Planner Temporal Network Solver Projective Task Expansion Initial Conditions Temporal Plan Dynamic Scheduling
More informationCOMP 406 Lecture 05. Artificial. Fiona Yan Liu Department of Computing The Hong Kong Polytechnic University
COMP 406 Lecture 05 Artificial Intelligence Fiona Yan Liu Department of Computing The Hong Kong Polytechnic University Learning Outcomes of Intelligent Agents Search agents Uninformed search Informed search
More informationif all agents follow RSS s interpretation then there will be zero accidents.
RSS Concept RSS - Mobileye SFF - Nvidia Safety Goal Guaranteeing that an agent will never be involved in an accident is impossible. Hence, our ultimate goal is to guarantee that an agent will be careful
More informationBoyle s Law: Pressure-Volume Relationship in Gases. PRELAB QUESTIONS (Answer on your own notebook paper)
Boyle s Law: Pressure-Volume Relationship in Gases Experiment 18 GRADE LEVEL INDICATORS Construct, interpret and apply physical and conceptual models that represent or explain systems, objects, events
More informationExperiences with Area Assessment Materials
Experiences with Area Assessment Materials 1. Jenny bought a rectangular rug that had an area of 24 square feet and a perimeter of 20 feet. Which model shows the correct dimensions of the rug? A. 8 feet
More informationNeural Network in Computer Vision for RoboCup Middle Size League
Journal of Software Engineering and Applications, 2016, *,** Neural Network in Computer Vision for RoboCup Middle Size League Paulo Rogério de Almeida Ribeiro 1, Gil Lopes 1, Fernando Ribeiro 1 1 Department
More informationCommunication Amid Uncertainty
Communication Amid Uncertainty Madhu Sudan Harvard University Based on joint works with Brendan Juba, Oded Goldreich, Adam Kalai, Sanjeev Khanna, Elad Haramaty, Jacob Leshno, Clement Canonne, Venkatesan
More informationGenerating None-Plans in Order to Find Plans 1
Generating None-Plans in Order to Find Plans 1 Wojciech Penczek a joint work with Michał Knapik and Artur Niewiadomski Institute of Computer Sciences, PAS, Warsaw, and Siedlce University, Poland MINI PW,
More informationFlyweight Pattern. Flyweight: Intent. Use sharing to support large numbers of fine-grained objects efficiently. CSIE Department, NTUT Chien-Hung Liu
Flyweight Pattern CSIE Department, NTUT Chien-Hung Liu Flyweight: Intent Use sharing to support large numbers of fine-grained objects efficiently 1 Flyweight: Motivation (1) Some applications could benefit
More informationTHE MLU PLAYER DEVELOPMENT CURRICULUM
THE MLU PLAYER DEVELOPMENT CURRICULUM U9 INTRODUCTION The mission of the MLU Player Development Curriculum is to enhance the soccer experience of young players and coaches within our club. The game is
More informationIteration: while, for, do while, Reading Input with Sentinels and User-defined Functions
Iteration: while, for, do while, Reading Input with Sentinels and User-defined Functions This programming assignment uses many of the ideas presented in sections 6 and 7 of the course notes. You are advised
More informationFirst-Server Advantage in Tennis Matches
First-Server Advantage in Tennis Matches Iain MacPhee and Jonathan Rougier Department of Mathematical Sciences University of Durham, U.K. Abstract We show that the advantage that can accrue to the server
More informationDESIGN AND ANALYSIS OF ALGORITHMS (DAA 2017)
DESIGN AND ANALYSIS OF ALGORITHMS (DAA 2017) Veli Mäkinen 12/05/2017 1 COURSE STRUCTURE 7 weeks: video lecture -> demo lecture -> study group -> exercise Video lecture: Overview, main concepts, algorithm
More informationThree New Methods to Find Initial Basic Feasible. Solution of Transportation Problems
Applied Mathematical Sciences, Vol. 11, 2017, no. 37, 1803-1814 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.75178 Three New Methods to Find Initial Basic Feasible Solution of Transportation
More informationShot-by-shot directional source deghosting and directional designature using near-gun measurements
H1-1-3 Shot-by-shot directional source deghosting and directional designature using near-gun measurements Neil Hargreaves, Rob Telling, Sergio Grion Dolphin Geophysical, London, UK Introduction In this
More informationLanguage Marathon Rules
Language Marathon Rules GENERAL TERMS 1. The Promoter is: Lingoda GmbH whose registered office is at Charlottenstraße 18 10117 Germany. 2. By entering this promotion, the Participant is indicating their
More informationBFH/HTA Biel/DUE/Course 355/ Software Engineering 2. Suppose you ll write an application that displays a large number of icons:
Flyweight [GoF] Intent Object sharing to support large set of objects. Motivation Suppose you ll write an application that displays a large number of icons: Design Patterns Flyweight [GoF] 1 To manipulation
More informationarxiv: v1 [math.co] 11 Apr 2018
arxiv:1804.04504v1 [math.co] 11 Apr 2018 Scheduling Asynchronous Round-Robin Tournaments Warut Suksompong Abstract. We study the problem of scheduling asynchronous round-robin tournaments. We consider
More informationBreaking Up is Hard to Do: An Investigation of Decomposition for Assume-Guarantee Reasoning
Breaking Up is Hard to Do: An Investigation of Decomposition for Assume-Guarantee Reasoning Jamieson M. Cobleigh Dept. of Computer Science University of Massachusetts Amherst, MA 01003, USA jcobleig@cs.umass.edu
More informationDEVELOPING YOUTH FOOTBALL PLAYERS BY HORST WEIN DOWNLOAD EBOOK : DEVELOPING YOUTH FOOTBALL PLAYERS BY HORST WEIN PDF
Read Online and Download Ebook DEVELOPING YOUTH FOOTBALL PLAYERS BY HORST WEIN DOWNLOAD EBOOK : DEVELOPING YOUTH FOOTBALL PLAYERS BY HORST WEIN PDF Click link bellow and free register to download ebook:
More informationCoaching Your Best in Competitions. Wade Gilbert, PhD
Coaching Your Best in Competitions Wade Gilbert, PhD wgilbert@csufresno.edu @WadeWgilbert Last webinar Winning the game before the game *Today* Winning the game within the game Insights from recent competition
More informationCOMP Intro to Logic for Computer Scientists. Lecture 13
COMP 1002 Intro to Logic for Computer Scientists Lecture 13 B 5 2 J Admin stuff Assignments schedule? Split a2 and a3 in two (A2,3,4,5), 5% each. A2 due Feb 17 th. Midterm date? March 2 nd. No office hour
More informationTHE REFEREEING IN BASKETBALL- TRENDS AND OPTIMIZATION STRATEGIES OF THE TRAINING AND PERFORMANCE OF REFEREES IN A DIVISION
THE MINISTRY OF NATIONAL EDUCATION THE NATIONAL UNIVERSITY OF PHYSICAL EDUCATION AND SPORTS THE REFEREEING IN BASKETBALL- TRENDS AND OPTIMIZATION STRATEGIES OF THE TRAINING AND PERFORMANCE OF REFEREES
More informationIntroduction to Pattern Recognition
Introduction to Pattern Recognition Jason Corso SUNY at Buffalo 12 January 2009 J. Corso (SUNY at Buffalo) Introduction to Pattern Recognition 12 January 2009 1 / 28 Pattern Recognition By Example Example:
More information1 SE/P-02. Experimental and Analytical Studies on Thermal-Hydraulic Performance of a Vacuum Vessel Pressure Suppression System in ITER
1 SE/P-2 Experimental and Analytical Studies on Thermal-Hydraulic Performance of a Vacuum Vessel Pressure Suppression System in ITER K. Takase 1), H. Akimoto 1) 1) Japan Atomic Energy Research Institute,
More informationBulgarian Olympiad in Informatics: Excellence over a Long Period of Time
Olympiads in Informatics, 2017, Vol. 11, 151 158 2017 IOI, Vilnius University DOI: 10.15388/ioi.2017.12 151 Bulgarian Olympiad in Informatics: Excellence over a Long Period of Time Emil KELEVEDJIEV 1,
More informationCMIMC 2018 Official Contest Information
CMIMC 2018 Official Contest Information CMIMC Staff Latest version: January 14, 2018 1 Introduction 1. This document is the official contest information packet for the 2018 Carnegie Mellon Informatics
More informationWind Flow Model of Area Surrounding the Case Western Reserve University Wind Turbine
Wind Flow Model of Area Surrounding the Case Western Reserve University Wind Turbine Matheus C. Fernandes 1, David H. Matthiesen PhD *2 1 Case Western Reserve University Dept. of Mechanical Engineering,
More informationTransform Your Classroom and Construct Learning with Geometry Golf
Transform Your Classroom and Construct Learning with Geometry Golf Nancy Norem Powell nancynpowell@gmail.com 2012 Conference Common Core State Standards for Mathematics Practice Standards: This lesson
More information- 2 - Companion Web Site. Back Cover. Synopsis
Companion Web Site A Programmer's Introduction to C# by Eric Gunnerson ISBN: 1893115860 Apress 2000, 358 pages This book takes the C programmer through the all the details from basic to advanced-- of the
More informationAC : A LABORATORY EXERCISE TO DEMONSTRATE HOW TO EXPERIMENTALLY DETERMINE THE OPERATING POINT FOR A FAN
AC 2007-206: A LABORATORY EXERCISE TO DEMONSTRATE HOW TO EXPERIMENTALLY DETERMINE THE OPERATING POINT FOR A FAN Robert Edwards, Pennsylvania State University-Erie Robert Edwards is currently a Lecturer
More informationTRINITY COLLEGE DUBLIN
TRINITY COLLEGE DUBLIN COLÁISTE NA TRÍONÓIDE, BAILE ÁTHA CLIATH On the Semantics of Markov Automata Yuxin Deng 1 Matthew Hennessy 21 1 Shanghai Jiao Tong University 2 Trinity College Dublin Computer Science
More informationFlies and a Frog. Flies and a Frog. 1 of 11. Copyright 2007, Exemplars, Inc. All rights reserved.
Fran the frog loves to catch flies and is a good fly catcher. On Sunday she ate 3 yummy flies. On Monday she ate 6 yummy flies. On Tuesday she ate 9 yummy flies, and on Wednesday she ate 12 yummy flies!
More informationA Message from Phil Capelle. Capelle s Course on Pool
essage from Phil apelle This sneak peek into my new book, Practicing Pool, will provide you with some lessons to work on. e sure to check back in a week to 10 days and I ll have some more exercises that
More informationOptimal Weather Routing Using Ensemble Weather Forecasts
Optimal Weather Routing Using Ensemble Weather Forecasts Asher Treby Department of Engineering Science University of Auckland New Zealand Abstract In the United States and the United Kingdom it is commonplace
More informationSwimming Program 2018
Swimming Program 2018 Strongman International Sports Training Centre, established since 1998, is well known for running excellent basic swimming programs and grooming excellent athletes. We are the exclusive
More informationGrade 6 Lesson 1. Lesson Plan. Page 2. Guided Practice Handout. Page 4. Student Activity Handout Page 5
Grade 6 Lesson 1 Item Lesson Plan Page Page 2 Guided Practice Handout Page 4 Activity Handout Page 5 Marlins Think Tank: Sixth Grade Math Lesson Plan #1 VISION-SETTING OBJECTIVE. What is your objective?
More informationKey Concept Culture. Related Concepts expression, structure. Global Context Personal and Cultural Expression
Key Concept Culture Related Concepts expression, structure Global Context Personal and Cultural Expression The arts have developed in different parts of the world as a result of many factors. The beliefs,
More informationREPORT ON RED-LIGHT MONITORING SYSTEMS
REPORT ON RED-LIGHT TRAFFIC CONTROL SIGNAL MONITORING SYSTEMS Prepared by the New Jersey Department of Transportation November 2011 Executive Summary Public Law 2007, Chapter 348 (P.L. 2007, c.348), signed
More informationAssignment A7 BREAKOUT CS1110 Fall 2011 Due Sat 3 December 1
Assignment A7 BREAKOUT CS1110 Fall 2011 Due Sat 3 December 1 This assignment, including much of the wording of this document, is taken from an assignment from Stanford University, by Professor Eric Roberts.
More informationSTARTING OUT WITH VISUAL C# (4TH EDITION) BY TONY GADDIS DOWNLOAD EBOOK : STARTING OUT WITH VISUAL C# (4TH EDITION) BY TONY GADDIS PDF
Read Online and Download Ebook STARTING OUT WITH VISUAL C# (4TH EDITION) BY TONY GADDIS DOWNLOAD EBOOK : STARTING OUT WITH VISUAL C# (4TH EDITION) BY TONY Click link bellow and free register to download
More informationLecture 5. Optimisation. Regularisation
Lecture 5. Optimisation. Regularisation COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne Iterative optimisation Loss functions Coordinate
More informationWalking up Scenic Hills: Towards a GIS Based Typology of Crowd Sourced Walking Routes
Walking up Scenic Hills: Towards a GIS Based Typology of Crowd Sourced Walking Routes Liam Bratley 1, Alex D. Singleton 2, Chris Brunsdon 3 1 Department of Geography and Planning, School of Environmental
More information6.RP Speed Conversions
6.RP Speed Conversions Alignments to Content Standards: 6.RP.A.3.d Task Jessica sees the following speed limit sign while visiting Australia where the units for speed are kilometers per hour: a. A conversion
More informationBlocking time reduction for level crossings using the genetic algorithm
Computers in Railways X 299 Blocking time reduction for level crossings using the genetic algorithm Y. Noguchi 1, H. Mochizuki 1, S. Takahashi 1, H. Nakamura 1, S. Kaneko 1 & M. Sakai 2 1 Nihon University,
More informationOptimizing Cyclist Parking in a Closed System
Optimizing Cyclist Parking in a Closed System Letu Qingge, Killian Smith Gianforte School of Computing, Montana State University, Bozeman, MT 59717, USA Abstract. In this paper, we consider the two different
More informationImperfectly Shared Randomness in Communication
Imperfectly Shared Randomness in Communication Madhu Sudan Harvard Joint work with Clément Canonne (Columbia), Venkatesan Guruswami (CMU) and Raghu Meka (UCLA). 11/16/2016 UofT: ISR in Communication 1
More informationOPTIMAL FLOWSHOP SCHEDULING WITH DUE DATES AND PENALTY COSTS
J. Operation Research Soc. of Japan VoJ. 1, No., June 1971. 1971 The Operations Research Society of Japan OPTMAL FLOWSHOP SCHEDULNG WTH DUE DATES AND PENALTY COSTS JATNDER N.D. GUPTA Assistant Professor,
More informationCritical Systems Validation
Critical Systems Validation Objectives To explain how system reliability can be measured and how reliability growth models can be used for reliability prediction To describe safety arguments and how these
More informationTERMINATION FOR HYBRID TABLEAUS
TERMINATION FOR HYBRID TABLEAUS THOMAS BOLANDER AND PATRICK BLACKBURN Abstract. This article extends and improves work on tableau-based decision methods for hybrid logic by Bolander and Braüner [5]. Their
More information2015 GENERAL INFORMATION
2015 GENERAL INFORMATION CMH Heli-Skiing is the world s most comprehensive and spectacular wilderness skiing experience available to Heli-Skiers and Snowboarders. Prices include: From 11,500 to 43,570
More informationINSTRUMENT INSTRUMENTAL ERROR (of full scale) INSTRUMENTAL RESOLUTION. Tutorial simulation. Tutorial simulation
Lab 1 Standing Waves on a String Learning Goals: To distinguish between traveling and standing waves To recognize how the wavelength of a standing wave is measured To recognize the necessary conditions
More informationModelling Today for the Future. Advanced Modelling Control Techniques
CwMAG 1 st Autumn Conference 2012 Modelling Today for the Future Advanced Modelling Control Techniques What are advanced modelling controls? Why do we have them? How can we use them? What are the differences
More informationD-Case Modeling Guide for Target System
D-Case Modeling Guide for Target System 1/32 Table of Contents 1 Scope...4 2 Overview of D-Case and SysML Modeling Guide...4 2.1 Background and Purpose...4 2.2 Target System of Modeling Guide...5 2.3 Constitution
More informationA CONCISE HISTORY OF THEATRE BY JIM A. PATTERSON, TIM DONOHUE DOWNLOAD EBOOK : A CONCISE HISTORY OF THEATRE BY JIM A. PATTERSON, TIM DONOHUE PDF
Read Online and Download Ebook A CONCISE HISTORY OF THEATRE BY JIM A. PATTERSON, TIM DONOHUE DOWNLOAD EBOOK : A CONCISE HISTORY OF THEATRE BY JIM A. PATTERSON, Click link bellow and free register to download
More informationA quantitative software testing method for hardware and software integrated systems in safety critical applications
A quantitative software testing method for hardware and software integrated systems in safety critical applications Hai ang a, Lixuan Lu* a a University of Ontario Institute of echnology, Oshawa, ON, Canada
More information1 8 Practice Perimeter Circumference And Area Answers Form G
1 8 Practice Perimeter Circumference And Area Answers Form G We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer,
More informationJapan AWS Summit Sponsorship Opportunities
2018 Japan AWS Summit Sponsorship Opportunities T o k y o AWS Summit Overview AWS Global Summits are free events designed to bring together the cloud computing community to connect, collaborate, and learn
More informationMechanical Design Patterns
Mechanical Design Patterns Jonathan Hey BiD lunch :: April 27 th 2005 What this is Sharing Interesting Multi-way with a caveat or two What I ll talk about What are they A little evolution Architectural
More informationStudent Outcomes. Lesson Notes. Classwork. Discussion (20 minutes)
Student Outcomes Students explain a proof of the converse of the Pythagorean Theorem. Students apply the theorem and its converse to solve problems. Lesson Notes Students had their first experience with
More informationPresented by. Mr.Danish.D.R. M.Tech Coastal Management Institute for Ocean Management Anna University, Chennai Tamil Nadu, India.
MATHEMATICAL MODEL STUDY OF THE EFFLUENT DISPOSAL FROM A DESALINATION PLANT IN THE MARINE ENVIRONMENT AT TUTICORIN Presented by Mr.Danish.D.R M.Tech Coastal Management Institute for Ocean Management Anna
More informationBID APPLICATION QUESTIONNAIRE FOR THE CANDIDATES TO ORGANISE A UNITED WORLD WRESTLING EVENT
BID APPLICATION QUESTIONNAIRE FOR THE CANDIDATES TO ORGANISE A UNITED WORLD WRESTLING EVENT OBJECTIVES The aim of this bid application questionnaire is to assess the candidate s existing and future capability
More informationOpen Research Online The Open University s repository of research publications and other research outputs
Open Research Online The Open University s repository of research publications and other research outputs Developing an intelligent table tennis umpiring system Conference or Workshop Item How to cite:
More informationCommunication Amid Uncertainty
Communication Amid Uncertainty Madhu Sudan Harvard University Based on joint works with Brendan Juba, Oded Goldreich, Adam Kalai, Sanjeev Khanna, Elad Haramaty, Jacob Leshno, Clement Canonne, Venkatesan
More informationOn Almost Feebly Totally Continuous Functions in Topological Spaces
On Almost Feebly Totally Continuous Functions in Topological Spaces A.P.DhanaBalan 1, R.Buvaneswari 2 1,2 Department of Mathematics, Alagappa Govt. Arts college, Karaikudi-3, Tamil Nadu, India Abstract:
More informationAlpine Certification Standards 2014
Professional Ski Instructors of America Alpine Certification Standards 2014 National Standards: Level One, Level Two, Level Three Updated Jan 1, 2014 ASEA and ASEA-EF Alpine Contributors and Developers:
More informationEstimating Paratransit Demand Forecasting Models Using ACS Disability and Income Data
Estimating Paratransit Demand Forecasting Models Using ACS Disability and Income Data Presenter: Daniel Rodríguez Román University of Puerto Rico, Mayagüez Co-author: Sarah V. Hernandez University of Arkansas,
More informationEQ: GPE.4 How do I calculate distance, midpoint, and slope?
EQ: GPE.4 How do I calculate distance, midpoint, and slope? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 3,
More informationDecision of the Dispute Resolution Chamber
Decision of the Dispute Resolution Chamber passed in Zurich, Switzerland, on 23 March 2006, in the following composition: Slim Aloulou (Tunisia), Chairman Mario Gallavotti (Italy), Member Peter Friend
More informationStatistics Unit Statistics 1A
Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Statistics 1A Statistics Unit Statistics 1A Friday 14 January 2011 General
More informationATHLETE INFORMATION FORM
ATHLETE INFORMATION FORM School Birth Age (On 8/31/17) Athlete s Name Gender Last First MI M / F Guardian Name Gender Last First MI M / F Relationship to Athlete Address Street City State Zip Cell Phone
More informationDesign Project 2 Sizing of a Bicycle Chain Ring Bolt Set ENGR 0135 Sangyeop Lee November 16, 2016 Jordan Gittleman Noah Sargent Seth Strayer Desmond
1 Design Project 2 Sizing of a Bicycle Chain Ring Bolt Set ENGR 0135 Sangyeop Lee November 16, 2016 Jordan Gittleman Noah Sargent Seth Strayer Desmond Zheng 2 Abstract This report will analyze our calculations,
More informationCOMPARISON OF FIXED & VARIABLE RATES (25 YEARS) CHARTERED BANK ADMINISTERED INTEREST RATES - PRIME BUSINESS*
COMPARISON OF FIXED & VARIABLE RATES (25 YEARS) Fixed Rates Variable Rates FIXED RATES OF THE PAST 25 YEARS AVERAGE RESIDENTIAL MORTGAGE LENDING RATE - 5 YEAR* (Per cent) Year Jan Feb Mar Apr May Jun Jul
More informationMANUFACTURE OF SUBSTRUCTURE BY AUTOMATED FIBER PLACEMENT
MANUFACTURE OF SUBSTRUCTURE BY AUTOMATED FIBER PLACEMENT Trevor S. Angell Spirit AeroSystems 3365 S. Oliver St. Wichita, KS 67278 Todd Rudberg Electroimpact 4413 Chennault Beach Rd. Mukilteo, WA 98275
More informationThree-position-jacquard machine
( 1 of 27264 ) United States Patent 6,581,646 Dewispelaere June 24, 2003 Three-position-jacquard machine Abstract A three-position shed-forming device with a shed-forming element (10);(60,70) in connection
More informationToday. Last update: 5 June Structural Adapter Bridge Composite Decorator Façade Flyweight Proxy APPLICATION_1 APPLICATION_2. class APPLICATION_1
Software Architecture Bertrand Meyer ETH Zurich, March-July 2007 Last update: 5 June 2007 Lecture 11: More patterns: bridge, composite, decorator, facade, flyweight Today Creational Abstract Factory Builder
More informationFixedWingLib CGF. Realistic CGF Aircraft Entities ware-in-the-loop Simulations
FixedWingLib CGF FixedWingLib CGF offers high-fidelity maneuvers for air combat, close air support and other real-world military and civil manned and unmanned fixed wing operations. Developers can use
More informationUniversity Moot Court Selections (UMCS)
University Moot Court Selections (UMCS) Organised by Moot Court Committee Dr. Ram Manohar Lohiya National Law University Lucknow Rules & Guidelines Introduction The Moot court committee shall be organising
More informationThe Cooperative Cleaners Case Study: Modelling and Analysis in Real-Time ABS
: Modelling and Analysis in Real-Time ABS Silvia Lizeth Tapia Tarifa Precise Modelling and Analysis University of Oslo sltarifa@ifi.uio.no 29.11.2013 S. Lizeth Tapia Tarifa Outline Motivation 1 Motivation
More informationOPTIMIZATION OF SINGLE STAGE AXIAL FLOW COMPRESSOR FOR DIFFERENT ROTATIONAL SPEED USING CFD
http:// OPTIMIZATION OF SINGLE STAGE AXIAL FLOW COMPRESSOR FOR DIFFERENT ROTATIONAL SPEED USING CFD Anand Kumar S malipatil 1, Anantharaja M.H 2 1,2 Department of Thermal Power Engineering, VTU-RO Gulbarga,
More informationAGA Swiss McMahon Pairing Protocol Standards
AGA Swiss McMahon Pairing Protocol Standards Final Version 1: 2009-04-30 This document describes the Swiss McMahon pairing system used by the American Go Association (AGA). For questions related to user
More informationitalian language SERVICES at the italian cultural institute LONDON telephone: september 2017-july 2018
italian language SERVICES at the italian cultural institute LONDON courses@icilondon.uk telephone: 02078231887 september 2017-july 2018 The place to learn Italian The place to learn Italian is the Italian
More informationTHE CANDU 9 DISTRffiUTED CONTROL SYSTEM DESIGN PROCESS
THE CANDU 9 DISTRffiUTED CONTROL SYSTEM DESIGN PROCESS J.E. HARBER, M.K. KATTAN Atomic Energy of Canada Limited 2251 Speakman Drive, Mississauga, Ont., L5K 1B2 CA9900006 and M.J. MACBETH Institute for
More informationIntroduction to Pattern Recognition
Introduction to Pattern Recognition Jason Corso SUNY at Buffalo 19 January 2011 J. Corso (SUNY at Buffalo) Introduction to Pattern Recognition 19 January 2011 1 / 32 Examples of Pattern Recognition in
More informationPrincess Nora University Faculty of Computer & Information Systems ARTIFICIAL INTELLIGENCE (CS 370D) Computer Science Department
Princess Nora University Faculty of Computer & Information Systems 1 ARTIFICIAL INTELLIGENCE (CS 370D) Computer Science Department (CHAPTER-3-PART2) PROBLEM SOLVING AND SEARCH (Course coordinator) Searching
More informationInternational olympiads in Informatics in Kazakhstan. A. Iglikov Z. Gamezardashvili B. Matkarimov
International olympiads in Informatics in Kazakhstan A. Iglikov Z. Gamezardashvili B. Matkarimov Olympiads overview Till 2003: - National Olympiad in Informatics for secondary school students (organized
More informationStandard Rules Competition Reference Guide
Standard Rules Competition Reference Guide Start Position: Standing Match length: Up to 6 minutes. In the event that the score is tied at the end of regulation time, the match will continue until the next
More informationA Complete Practice Manual for Beginner to Advanced coaches U10-U12
Practice Plan Manual A Complete Practice Manual for Beginner to Advanced coaches U10-U12 U10 Introduction 4 U10 Practice Plans 5-24 U10 Conclusion 25 U12 Introduction 26 U12 Practice Plans 27-50 U12 Conclusion
More informationNETBALL AUSTRALIA HIGH PERFORMANCE UMPIRE PATHWAY
NETBALL AUSTRALIA HIGH PERFORMANCE UMPIRE PATHWAY VERSION 5 APRIL 2018 CONTENTS GLOSSARY OF TERMS 3 INTRODUCTION 4 WHAT DOES IT TAKE TO BE THE BEST? 5 ALL AUSTRALIA UMPIRE SUCCESS PROFILE 5 NETBALL AUSTRALIA
More informationCprE 288 Final Project Description
CprE 288 Final Project Description Parts of the Project: Communication with the VORTEX Manually Traversing Treacherous Terrain for Retrieval Positioning the Rover for Retrieval Code and Documentation Story
More informationLEVEL I INDIVIDUAL TACTICS TACTICAL. September 2007 Page 1
INDIVIDUAL TACTICS September 2007 Page 1 Page 2 September 2007 Within the subject area of tactics, the IIHF Coach Development Program presents individual t ac t ic s for coaches to provide their players
More informationCOP CHANGE LOG
Introduction Categories Pre-Novice (Female/Male) Introduction Categories Categories divided into male/female Introduction Categories Doubles (Novice/Junior/Mixed) Introduction Categories Doubles Senior
More information