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Metaobject Protocols: Why We Want Them and What Else They Can Do
Metaobject protocols: Why we want them and what else they can do Gregor Kiczales, J.Michael Ashley, Luis Rodriguez, Amin Vahdat, and Daniel G. Bobrow Published in A. Paepcke, editor, Object-Oriented Programming: The CLOS Perspective, pages 101 ¾ 118. The MIT Press, Cambridge, MA, 1993. © Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. Metaob ject Proto cols WhyWeWant Them and What Else They Can Do App ears in Object OrientedProgramming: The CLOS Perspective c Copyright 1993 MIT Press Gregor Kiczales, J. Michael Ashley, Luis Ro driguez, Amin Vahdat and Daniel G. Bobrow Original ly conceivedasaneat idea that could help solve problems in the design and implementation of CLOS, the metaobject protocol framework now appears to have applicability to a wide range of problems that come up in high-level languages. This chapter sketches this wider potential, by drawing an analogy to ordinary language design, by presenting some early design principles, and by presenting an overview of three new metaobject protcols we have designed that, respectively, control the semantics of Scheme, the compilation of Scheme, and the static paral lelization of Scheme programs. Intro duction The CLOS Metaob ject Proto col MOP was motivated by the tension b etween, what at the time, seemed liketwo con icting desires. The rst was to have a relatively small but p owerful language for doing ob ject-oriented programming in Lisp. The second was to satisfy what seemed to b e a large numb er of user demands, including: compatibility with previous languages, p erformance compara- ble to or b etter than previous implementations and extensibility to allow further exp erimentation with ob ject-oriented concepts see Chapter 2 for examples of directions in which ob ject-oriented techniques might b e pushed. -
Chapter 2 Basics of Scanning And
Chapter 2 Basics of Scanning and Conventional Programming in Java In this chapter, we will introduce you to an initial set of Java features, the equivalent of which you should have seen in your CS-1 class; the separation of problem, representation, algorithm and program – four concepts you have probably seen in your CS-1 class; style rules with which you are probably familiar, and scanning - a general class of problems we see in both computer science and other fields. Each chapter is associated with an animating recorded PowerPoint presentation and a YouTube video created from the presentation. It is meant to be a transcript of the associated presentation that contains little graphics and thus can be read even on a small device. You should refer to the associated material if you feel the need for a different instruction medium. Also associated with each chapter is hyperlinked code examples presented here. References to previously presented code modules are links that can be traversed to remind you of the details. The resources for this chapter are: PowerPoint Presentation YouTube Video Code Examples Algorithms and Representation Four concepts we explicitly or implicitly encounter while programming are problems, representations, algorithms and programs. Programs, of course, are instructions executed by the computer. Problems are what we try to solve when we write programs. Usually we do not go directly from problems to programs. Two intermediate steps are creating algorithms and identifying representations. Algorithms are sequences of steps to solve problems. So are programs. Thus, all programs are algorithms but the reverse is not true. -
Variables in Mathematics Education
Variables in Mathematics Education Susanna S. Epp DePaul University, Department of Mathematical Sciences, Chicago, IL 60614, USA http://www.springer.com/lncs Abstract. This paper suggests that consistently referring to variables as placeholders is an effective countermeasure for addressing a number of the difficulties students’ encounter in learning mathematics. The sug- gestion is supported by examples discussing ways in which variables are used to express unknown quantities, define functions and express other universal statements, and serve as generic elements in mathematical dis- course. In addition, making greater use of the term “dummy variable” and phrasing statements both with and without variables may help stu- dents avoid mistakes that result from misinterpreting the scope of a bound variable. Keywords: variable, bound variable, mathematics education, placeholder. 1 Introduction Variables are of critical importance in mathematics. For instance, Felix Klein wrote in 1908 that “one may well declare that real mathematics begins with operations with letters,”[3] and Alfred Tarski wrote in 1941 that “the invention of variables constitutes a turning point in the history of mathematics.”[5] In 1911, A. N. Whitehead expressly linked the concepts of variables and quantification to their expressions in informal English when he wrote: “The ideas of ‘any’ and ‘some’ are introduced to algebra by the use of letters. it was not till within the last few years that it has been realized how fundamental any and some are to the very nature of mathematics.”[6] There is a question, however, about how to describe the use of variables in mathematics instruction and even what word to use for them. -
Lecture 2: Variables and Primitive Data Types
Lecture 2: Variables and Primitive Data Types MIT-AITI Kenya 2005 1 In this lecture, you will learn… • What a variable is – Types of variables – Naming of variables – Variable assignment • What a primitive data type is • Other data types (ex. String) MIT-Africa Internet Technology Initiative 2 ©2005 What is a Variable? • In basic algebra, variables are symbols that can represent values in formulas. • For example the variable x in the formula f(x)=x2+2 can represent any number value. • Similarly, variables in computer program are symbols for arbitrary data. MIT-Africa Internet Technology Initiative 3 ©2005 A Variable Analogy • Think of variables as an empty box that you can put values in. • We can label the box with a name like “Box X” and re-use it many times. • Can perform tasks on the box without caring about what’s inside: – “Move Box X to Shelf A” – “Put item Z in box” – “Open Box X” – “Remove contents from Box X” MIT-Africa Internet Technology Initiative 4 ©2005 Variables Types in Java • Variables in Java have a type. • The type defines what kinds of values a variable is allowed to store. • Think of a variable’s type as the size or shape of the empty box. • The variable x in f(x)=x2+2 is implicitly a number. • If x is a symbol representing the word “Fish”, the formula doesn’t make sense. MIT-Africa Internet Technology Initiative 5 ©2005 Java Types • Integer Types: – int: Most numbers you’ll deal with. – long: Big integers; science, finance, computing. – short: Small integers. -
Subtyping, Declaratively an Exercise in Mixed Induction and Coinduction
Subtyping, Declaratively An Exercise in Mixed Induction and Coinduction Nils Anders Danielsson and Thorsten Altenkirch University of Nottingham Abstract. It is natural to present subtyping for recursive types coin- ductively. However, Gapeyev, Levin and Pierce have noted that there is a problem with coinductive definitions of non-trivial transitive inference systems: they cannot be \declarative"|as opposed to \algorithmic" or syntax-directed|because coinductive inference systems with an explicit rule of transitivity are trivial. We propose a solution to this problem. By using mixed induction and coinduction we define an inference system for subtyping which combines the advantages of coinduction with the convenience of an explicit rule of transitivity. The definition uses coinduction for the structural rules, and induction for the rule of transitivity. We also discuss under what condi- tions this technique can be used when defining other inference systems. The developments presented in the paper have been mechanised using Agda, a dependently typed programming language and proof assistant. 1 Introduction Coinduction and corecursion are useful techniques for defining and reasoning about things which are potentially infinite, including streams and other (poten- tially) infinite data types (Coquand 1994; Gim´enez1996; Turner 2004), process congruences (Milner 1990), congruences for functional programs (Gordon 1999), closures (Milner and Tofte 1991), semantics for divergence of programs (Cousot and Cousot 1992; Hughes and Moran 1995; Leroy and Grall 2009; Nakata and Uustalu 2009), and subtyping relations for recursive types (Brandt and Henglein 1998; Gapeyev et al. 2002). However, the use of coinduction can lead to values which are \too infinite”. For instance, a non-trivial binary relation defined as a coinductive inference sys- tem cannot include the rule of transitivity, because a coinductive reading of transitivity would imply that every element is related to every other (to see this, build an infinite derivation consisting solely of uses of transitivity). -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
PDF (Dissertation.Pdf)
Kind Theory Thesis by Joseph R. Kiniry In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2002 (Defended 10 May 2002) ii © 2002 Joseph R. Kiniry All Rights Reserved iii Preface This thesis describes a theory for representing, manipulating, and reasoning about structured pieces of knowledge in open collaborative systems. The theory's design is motivated by both its general model as well as its target user commu- nity. Its model is structured information, with emphasis on classification, relative structure, equivalence, and interpretation. Its user community is meant to be non-mathematicians and non-computer scientists that might use the theory via computational tool support once inte- grated with modern design and development tools. This thesis discusses a new logic called kind theory that meets these challenges. The core of the work is based in logic, type theory, and universal algebras. The theory is shown to be efficiently implementable, and several parts of a full realization have already been constructed and are reviewed. Additionally, several software engineering concepts, tools, and technologies have been con- structed that take advantage of this theoretical framework. These constructs are discussed as well, from the perspectives of general software engineering and applied formal methods. iv Acknowledgements I am grateful to my initial primary adviser, Prof. K. Mani Chandy, for bringing me to Caltech and his willingness to let me explore many unfamiliar research fields of my own choosing. I am also appreciative of my second adviser, Prof. Jason Hickey, for his support, encouragement, feedback, and patience through the later years of my work. -
OMG Meta Object Facility (MOF) Core Specification
Date : October 2019 OMG Meta Object Facility (MOF) Core Specification Version 2.5.1 OMG Document Number: formal/2019-10-01 Standard document URL: https://www.omg.org/spec/MOF/2.5.1 Normative Machine-Readable Files: https://www.omg.org/spec/MOF/20131001/MOF.xmi Informative Machine-Readable Files: https://www.omg.org/spec/MOF/20131001/CMOFConstraints.ocl https://www.omg.org/spec/MOF/20131001/EMOFConstraints.ocl Copyright © 2003, Adaptive Copyright © 2003, Ceira Technologies, Inc. Copyright © 2003, Compuware Corporation Copyright © 2003, Data Access Technologies, Inc. Copyright © 2003, DSTC Copyright © 2003, Gentleware Copyright © 2003, Hewlett-Packard Copyright © 2003, International Business Machines Copyright © 2003, IONA Copyright © 2003, MetaMatrix Copyright © 2015, Object Management Group Copyright © 2003, Softeam Copyright © 2003, SUN Copyright © 2003, Telelogic AB Copyright © 2003, Unisys USE OF SPECIFICATION - TERMS, CONDITIONS & NOTICES The material in this document details an Object Management Group specification in accordance with the terms, conditions and notices set forth below. This document does not represent a commitment to implement any portion of this specification in any company's products. The information contained in this document is subject to change without notice. LICENSES The companies listed above have granted to the Object Management Group, Inc. (OMG) a nonexclusive, royalty-free, paid up, worldwide license to copy and distribute this document and to modify this document and distribute copies of the modified version. Each of the copyright holders listed above has agreed that no person shall be deemed to have infringed the copyright in the included material of any such copyright holder by reason of having used the specification set forth herein or having conformed any computer software to the specification. -
Scalars and Vectors
1 CHAPTER ONE VECTOR GEOMETRY 1.1 INTRODUCTION In this chapter vectors are first introduced as geometric objects, namely as directed line segments, or arrows. The operations of addition, subtraction, and multiplication by a scalar (real number) are defined for these directed line segments. Two and three dimensional Rectangular Cartesian coordinate systems are then introduced and used to give an algebraic representation for the directed line segments (or vectors). Two new operations on vectors called the dot product and the cross product are introduced. Some familiar theorems from Euclidean geometry are proved using vector methods. 1.2 SCALARS AND VECTORS Some physical quantities such as length, area, volume and mass can be completely described by a single real number. Because these quantities are describable by giving only a magnitude, they are called scalars. [The word scalar means representable by position on a line; having only magnitude.] On the other hand physical quantities such as displacement, velocity, force and acceleration require both a magnitude and a direction to completely describe them. Such quantities are called vectors. If you say that a car is traveling at 90 km/hr, you are using a scalar quantity, namely the number 90 with no direction attached, to describe the speed of the car. On the other hand, if you say that the car is traveling due north at 90 km/hr, your description of the car©s velocity is a vector quantity since it includes both magnitude and direction. To distinguish between scalars and vectors we will denote scalars by lower case italic type such as a, b, c etc. -
Outline of Mathematics
Outline of mathematics The following outline is provided as an overview of and 1.2.2 Reference databases topical guide to mathematics: • Mathematical Reviews – journal and online database Mathematics is a field of study that investigates topics published by the American Mathematical Society such as number, space, structure, and change. For more (AMS) that contains brief synopses (and occasion- on the relationship between mathematics and science, re- ally evaluations) of many articles in mathematics, fer to the article on science. statistics and theoretical computer science. • Zentralblatt MATH – service providing reviews and 1 Nature of mathematics abstracts for articles in pure and applied mathemat- ics, published by Springer Science+Business Media. • Definitions of mathematics – Mathematics has no It is a major international reviewing service which generally accepted definition. Different schools of covers the entire field of mathematics. It uses the thought, particularly in philosophy, have put forth Mathematics Subject Classification codes for orga- radically different definitions, all of which are con- nizing their reviews by topic. troversial. • Philosophy of mathematics – its aim is to provide an account of the nature and methodology of math- 2 Subjects ematics and to understand the place of mathematics in people’s lives. 2.1 Quantity Quantity – 1.1 Mathematics is • an academic discipline – branch of knowledge that • Arithmetic – is taught at all levels of education and researched • Natural numbers – typically at the college or university level. Disci- plines are defined (in part), and recognized by the • Integers – academic journals in which research is published, and the learned societies and academic departments • Rational numbers – or faculties to which their practitioners belong. -
Software II: Principles of Programming Languages
Software II: Principles of Programming Languages Lecture 6 – Data Types Some Basic Definitions • A data type defines a collection of data objects and a set of predefined operations on those objects • A descriptor is the collection of the attributes of a variable • An object represents an instance of a user- defined (abstract data) type • One design issue for all data types: What operations are defined and how are they specified? Primitive Data Types • Almost all programming languages provide a set of primitive data types • Primitive data types: Those not defined in terms of other data types • Some primitive data types are merely reflections of the hardware • Others require only a little non-hardware support for their implementation The Integer Data Type • Almost always an exact reflection of the hardware so the mapping is trivial • There may be as many as eight different integer types in a language • Java’s signed integer sizes: byte , short , int , long The Floating Point Data Type • Model real numbers, but only as approximations • Languages for scientific use support at least two floating-point types (e.g., float and double ; sometimes more • Usually exactly like the hardware, but not always • IEEE Floating-Point Standard 754 Complex Data Type • Some languages support a complex type, e.g., C99, Fortran, and Python • Each value consists of two floats, the real part and the imaginary part • Literal form real component – (in Fortran: (7, 3) imaginary – (in Python): (7 + 3j) component The Decimal Data Type • For business applications (money) -
Java Primitive Numeric Types, Assignment, and Expressions: Data
Java Primitive Numeric Types, Assignment, and Expressions: Data Types, Variables, and Declarations • A data type refers to a kind of value that a language recognizes { For example, integers, real numbers, characters, Booleans (true/false), etc. • Primitive data types represent single values and are built into a language; i.e., they are given • Java primitive numeric data types: 1. Integral types (a) byte (b) int (c) short (d) long 2. Real types (NOTE: The text calls these decimal types) (a) float (b) double • What distinguishes the various data types of a given group is the amount of storage allocated for storage { The greater the amount of storage, the greater the precision and magnitude of the value { Precision refers to the accuracy with which a value can be represented { Magnitude refers to the largest (and smallest) value that can be represented • A variable represents a storage location in memory for a value { Identifiers are used to represent variables { By convention, user-defined Java variables start with a lower case letter 1 Java Primitive Numeric Types, Assignment, and Expressions: Data Types, Variables, and Declarations (2) • Variable declarations { Java is a strongly typed language ∗ This means that a variable can only store values of a single data type { Semantics: A variable declaration tells the compiler how much storage to set aside for the variable, and how values in that memory location are to be interpreted ∗ Remember: Everything stored in memory is binary - zeroes and ones ∗ How the binary code is interpreted depends