NIC) NIC Series Volume 27
Total Page:16
File Type:pdf, Size:1020Kb

Load more
Recommended publications
-
Fuzzy Logic : Introduction
Fuzzy Logic : Introduction Debasis Samanta IIT Kharagpur [email protected] 07.01.2015 Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 1 / 69 What is Fuzzy logic? Fuzzy logic is a mathematical language to express something. This means it has grammar, syntax, semantic like a language for communication. There are some other mathematical languages also known • Relational algebra (operations on sets) • Boolean algebra (operations on Boolean variables) • Predicate logic (operations on well formed formulae (wff), also called predicate propositions) Fuzzy logic deals with Fuzzy set. Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 2 / 69 A brief history of Fuzzy Logic First time introduced by Lotfi Abdelli Zadeh (1965), University of California, Berkley, USA (1965). He is fondly nick-named as LAZ Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 3 / 69 A brief history of Fuzzy logic 1 Dictionary meaning of fuzzy is not clear, noisy etc. Example: Is the picture on this slide is fuzzy? 2 Antonym of fuzzy is crisp Example: Are the chips crisp? Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 4 / 69 Example : Fuzzy logic vs. Crisp logic Yes or No Crisp answer True or False Milk Yes Water A liquid Crisp Coca No Spite Is the liquid colorless? Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 5 / 69 Example : Fuzzy logic vs. Crisp logic May be May not be Fuzzy answer Absolutely Partially etc Debasis Samanta (IIT Kharagpur) Soft Computing Applications -
Mathematics Is Megethology
17 Mathematics is megethology Mereology is the theory of the relation of part to whole, and kindred notions. Megethology is the result of adding plural quantification, as advocated by George Boolos in [1] and [2], to the language of mere ology. It is so-called because it turns out to have enough expressive power to let us express interesting hypotheses about the size of Reality. It also has the power, as John P. Burgess and A. P. Hazen have shown in [3], to simulate quantification over relations. It is generally accepted that mathematics reduces to set theory. In my book Parts of Classes, [6], I argued that set theory in turn reduces, with the aid of mereology, to the theory of singleton functions. I also argued (somewhat reluctantly) for a 'structuralist' approach to the theory of singleton functions. We need not think we have somehow achieved a primitive grasp of some one special singleton function. Rather, we can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. We need only assume, to avoid vacuity, that there exists at least one singleton function. But we need not assume even that. For it now turns out that if the size of Reality is right, there must exist a singleton function. All we need as a foundation for mathematics, apart from the framework of megethology, are some hypotheses about the size of Reality. First published in this form in Philosophia Mathematila 3 (1993), 3--23. This paper consists in part of near-verbatim excerpts from David Lewis, Parts of Classes (Oxford, Blackwell, 1991). -
Definiteness and Determinacy
Linguistics and Philosophy manuscript No. (will be inserted by the editor) Definiteness and Determinacy Elizabeth Coppock · David Beaver the date of receipt and acceptance should be inserted later Abstract This paper distinguishes between definiteness and determinacy. Defi- niteness is seen as a morphological category which, in English, marks a (weak) uniqueness presupposition, while determinacy consists in denoting an individual. Definite descriptions are argued to be fundamentally predicative, presupposing uniqueness but not existence, and to acquire existential import through general type-shifting operations that apply not only to definites, but also indefinites and possessives. Through these shifts, argumental definite descriptions may become either determinate (and thus denote an individual) or indeterminate (functioning as an existential quantifier). The latter option is observed in examples like `Anna didn't give the only invited talk at the conference', which, on its indeterminate reading, implies that there is nothing in the extension of `only invited talk at the conference'. The paper also offers a resolution of the issue of whether posses- sives are inherently indefinite or definite, suggesting that, like indefinites, they do not mark definiteness lexically, but like definites, they typically yield determinate readings due to a general preference for the shifting operation that produces them. Keywords definiteness · descriptions · possessives · predicates · type-shifting We thank Dag Haug, Reinhard Muskens, Luca Crniˇc,Cleo Condoravdi, Lucas -
Introduction Code Reuse
The Sather Language: Efficient, Interactive, Object-Oriented Programming Stephen Omohundro Dr. Dobbs Journal Introduction Sather is an object oriented language which aims to be simple, efficient, interactive, safe, and non-proprietary. One way of placing it in the "space of languages" is to say that it aims to be as efficient as C, C++, or Fortran, as elegant and safe as Eiffel or CLU, and to support interactive programming and higher-order functions as well as Common Lisp, Scheme, or Smalltalk. Sather has parameterized classes, object-oriented dispatch, statically-checked strong typing, separate implementation and type inheritance, multiple inheritance, garbage collection, iteration abstraction, higher-order routines and iters, exception handling, constructors for arbitrary data structures, and assertions, preconditions, postconditions, and class invariants. This article describes the first few of these features. The development environment integrates an interpreter, a debugger, and a compiler. Sather programs can be compiled into portable C code and can efficiently link with C object files. Sather has a very unrestrictive license which allows its use in proprietary projects but encourages contribution to the public library. The original 0.2 version of the Sather compiler and tools was made available in June 1991. This article describes version 1.0. By the time the article appears, the combined 1.0 compiler/interpreter/debugger should be available on "ftp.icsi.berkeley.edu" and the newsgroup "comp.lang.sather" should be activated for discussion. Code Reuse The primary benefit promised by object-oriented languages is reuse of code. Sather programs consist of collections of modules called "classes" which encapsulate well-defined abstractions. -
Solutions Are Available
Math 436 Introduction to Topology Spring 2018 Examination 1 1. Define (a) the concept of the closure of a set, and (b) the concept of a basis for a given topology. Solution. The closure of a set A can be defined as the smallest closed set containing A, or as the intersection of all closed sets containing A, or as the union of A with the set of limit points of A. A basis for a given topology is a subset of such that every element of can be obtained as a union of elements of . In alternative language, a basis for a given topology is a collection of open sets such that every open set can be obtained by taking a union of some open sets belonging to the basis. 2. Give an example of a separable Hausdorff topological space .X; / with the property that X has no limit points. Solution. A point x is a limit point of X when every neighborhood of x intersects X ⧵ ^x`. This property evidently holds unless the singleton set ^x` is an open set. Saying that X has no limit points is equivalent to saying that every singleton set is an open set. In other words, the topology on X is the discrete topology. The discrete topology is automatically Hausdorff, for if x and y are distinct points, then the sets ^x` and ^y` are disjoint open sets that separate x from y. A minimal basis for the discrete topology consists of all singletons, so the discrete topology is separable if and only if the space X is countable. -
Design and Implementation of Generics for the .NET Common Language Runtime
Design and Implementation of Generics for the .NET Common Language Runtime Andrew Kennedy Don Syme Microsoft Research, Cambridge, U.K. fakeÒÒ¸d×ÝÑeg@ÑicÖÓ×ÓfغcÓÑ Abstract cally through an interface definition language, or IDL) that is nec- essary for language interoperation. The Microsoft .NET Common Language Runtime provides a This paper describes the design and implementation of support shared type system, intermediate language and dynamic execution for parametric polymorphism in the CLR. In its initial release, the environment for the implementation and inter-operation of multiple CLR has no support for polymorphism, an omission shared by the source languages. In this paper we extend it with direct support for JVM. Of course, it is always possible to “compile away” polymor- parametric polymorphism (also known as generics), describing the phism by translation, as has been demonstrated in a number of ex- design through examples written in an extended version of the C# tensions to Java [14, 4, 6, 13, 2, 16] that require no change to the programming language, and explaining aspects of implementation JVM, and in compilers for polymorphic languages that target the by reference to a prototype extension to the runtime. JVM or CLR (MLj [3], Haskell, Eiffel, Mercury). However, such Our design is very expressive, supporting parameterized types, systems inevitably suffer drawbacks of some kind, whether through polymorphic static, instance and virtual methods, “F-bounded” source language restrictions (disallowing primitive type instanti- type parameters, instantiation at pointer and value types, polymor- ations to enable a simple erasure-based translation, as in GJ and phic recursion, and exact run-time types. -
Parametric Polymorphism Parametric Polymorphism
Parametric Polymorphism Parametric Polymorphism • is a way to make a language more expressive, while still maintaining full static type-safety (every Haskell expression has a type, and types are all checked at compile-time; programs with type errors will not even compile) • using parametric polymorphism, a function or a data type can be written generically so that it can handle values identically without depending on their type • such functions and data types are called generic functions and generic datatypes Polymorphism in Haskell • Two kinds of polymorphism in Haskell – parametric and ad hoc (coming later!) • Both kinds involve type variables, standing for arbitrary types. • Easy to spot because they start with lower case letters • Usually we just use one letter on its own, e.g. a, b, c • When we use a polymorphic function we will usually do so at a specific type, called an instance. The process is called instantiation. Identity function Consider the identity function: id x = x Prelude> :t id id :: a -> a It does not do anything with the input other than returning it, therefore it places no constraints on the input's type. Prelude> :t id id :: a -> a Prelude> id 3 3 Prelude> id "hello" "hello" Prelude> id 'c' 'c' Polymorphic datatypes • The identity function is the simplest possible polymorphic function but not very interesting • Most useful polymorphic functions involve polymorphic types • Notation – write the name(s) of the type variable(s) used to the left of the = symbol Maybe data Maybe a = Nothing | Just a • a is the type variable • When we instantiate a to something, e.g. -
CSE 307: Principles of Programming Languages Classes and Inheritance
OOP Introduction Type & Subtype Inheritance Overloading and Overriding CSE 307: Principles of Programming Languages Classes and Inheritance R. Sekar 1 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Topics 1. OOP Introduction 3. Inheritance 2. Type & Subtype 4. Overloading and Overriding 2 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Section 1 OOP Introduction 3 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding OOP (Object Oriented Programming) So far the languages that we encountered treat data and computation separately. In OOP, the data and computation are combined into an “object”. 4 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Benefits of OOP more convenient: collects related information together, rather than distributing it. Example: C++ iostream class collects all I/O related operations together into one central place. Contrast with C I/O library, which consists of many distinct functions such as getchar, printf, scanf, sscanf, etc. centralizes and regulates access to data. If there is an error that corrupts object data, we need to look for the error only within its class Contrast with C programs, where access/modification code is distributed throughout the program 5 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Benefits of OOP (Continued) Promotes reuse. by separating interface from implementation. We can replace the implementation of an object without changing client code. Contrast with C, where the implementation of a data structure such as a linked list is integrated into the client code by permitting extension of new objects via inheritance. Inheritance allows a new class to reuse the features of an existing class. -
INF 102 CONCEPTS of PROG. LANGS Type Systems
INF 102 CONCEPTS OF PROG. LANGS Type Systems Instructors: James Jones Copyright © Instructors. What is a Data Type? • A type is a collection of computational entities that share some common property • Programming languages are designed to help programmers organize computational constructs and use them correctly. Many programming languages organize data and computations into collections called types. • Some examples of types are: o the type Int of integers o the type (Int→Int) of functions from integers to integers Why do we need them? • Consider “untyped” universes: • Bit string in computer memory • λ-expressions in λ calculus • Sets in set theory • “untyped” = there’s only 1 type • Types arise naturally to categorize objects according to patterns of use • E.g. all integer numbers have same set of applicable operations Use of Types • Identifying and preventing meaningless errors in the program o Compile-time checking o Run-time checking • Program Organization and documentation o Separate types for separate concepts o Indicates intended use declared identifiers • Supports Optimization o Short integers require fewer bits o Access record component by known offset Type Errors • A type error occurs when a computational entity, such as a function or a data value, is used in a manner that is inconsistent with the concept it represents • Languages represent values as sequences of bits. A "type error" occurs when a bit sequence written for one type is used as a bit sequence for another type • A simple example can be assigning a string to an integer -
CLOS, Eiffel, and Sather: a Comparison
CLOS, Eiffel, and Sather: A Comparison Heinz W. Schmidt-, Stephen M. Omohundrot " September, 1991 li ____________T_R_._91_-0_47____________~ INTERNATIONAL COMPUTER SCIENCE INSTITUTE 1947 Center Street, Suite 600 Berkeley, California 94704-1105 CLOS, Eiffel, and Sather: A Comparison Heinz W. Schmidt-, Stephen M. Omohundrot September, 1991 Abstract The Common Lisp Object System defines a powerful and flexible type system that builds on more than fifteen years of experience with object-oriented programming. Most current implementations include a comfortable suite of Lisp support tools in cluding an Emacs Lisp editor, an interpreter, an incremental compiler, a debugger, and an inspector that together promote rapid prototyping and design. What else might one want from a system? We argue that static typing yields earlier error detec tion, greater robustness, and higher efficiency and that greater simplicity and more orthogonality in the language constructs leads to a shorter learning curve and more in tuitive programming. These elements can be found in Eiffel and a new object-oriented language, Sather, that we are developing at leS!. Language simplicity and static typ ing are not for free,·though. Programmers have to pay with loss of polymorphism and flexibility in prototyping. We give a short comparison of CLOS, Eiffel and Sather, addressing both language and environment issues. The different approaches taken by the languages described in this paper have evolved to fulfill different needs. While we have only touched on the essential differ ences, we hope that this discussion will be helpful in understanding the advantages and disadvantages of each language. -ICSI, on leave from: Inst. f. Systemtechnik, GMD, Germany tICSI 1 Introduction Common Lisp [25] was developed to consolidate the best ideas from a long line of Lisp systems and has become an important standard. -
The Power of Interoperability: Why Objects Are Inevitable
The Power of Interoperability: Why Objects Are Inevitable Jonathan Aldrich Carnegie Mellon University Pittsburgh, PA, USA [email protected] Abstract 1. Introduction Three years ago in this venue, Cook argued that in Object-oriented programming has been highly suc- their essence, objects are what Reynolds called proce- cessful in practice, and has arguably become the dom- dural data structures. His observation raises a natural inant programming paradigm for writing applications question: if procedural data structures are the essence software in industry. This success can be documented of objects, has this contributed to the empirical success in many ways. For example, of the top ten program- of objects, and if so, how? ming languages at the LangPop.com index, six are pri- This essay attempts to answer that question. After marily object-oriented, and an additional two (PHP reviewing Cook’s definition, I propose the term ser- and Perl) have object-oriented features.1 The equiva- vice abstractions to capture the essential nature of ob- lent numbers for the top ten languages in the TIOBE in- jects. This terminology emphasizes, following Kay, that dex are six and three.2 SourceForge’s most popular lan- objects are not primarily about representing and ma- guages are Java and C++;3 GitHub’s are JavaScript and nipulating data, but are more about providing ser- Ruby.4 Furthermore, objects’ influence is not limited vices in support of higher-level goals. Using examples to object-oriented languages; Cook [8] argues that Mi- taken from object-oriented frameworks, I illustrate the crosoft’s Component Object Model (COM), which has unique design leverage that service abstractions pro- a C language interface, is “one of the most pure object- vide: the ability to define abstractions that can be ex- oriented programming models yet defined.” Academ- tended, and whose extensions are interoperable in a ically, object-oriented programming is a primary focus first-class way. -
Iterable Abstract Pattern Matching for Java
JMatch: Iterable Abstract Pattern Matching for Java Jed Liu and Andrew C. Myers Computer Science Department Cornell University, Ithaca, New York Abstract. The JMatch language extends Java with iterable abstract pattern match- ing, pattern matching that is compatible with the data abstraction features of Java and makes iteration abstractions convenient. JMatch has ML-style deep pattern matching, but patterns can be abstract; they are not tied to algebraic data con- structors. A single JMatch method may be used in several modes; modes may share a single implementation as a boolean formula. Modal abstraction simplifies specification and implementation of abstract data types. This paper describes the JMatch language and its implementation. 1 Introduction Object-oriented languages have become a dominant programming paradigm, yet they still lack features considered useful in other languages. Functional languages offer expressive pattern matching. Logic programming languages provide powerful mech- anisms for iteration and backtracking. However, these useful features interact poorly with the data abstraction mechanisms central to object-oriented languages. Thus, ex- pressing some computations is awkward in object-oriented languages. In this paper we present the design and implementation of JMatch, a new object- oriented language that extends Java [GJS96] with support for iterable abstract pattern matching—a mechanism for pattern matching that is compatible with the data abstrac- tion features of Java and that makes iteration abstractions more convenient.