Function Programming in Python
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Armadillo C++ Library
Armadillo: a template-based C++ library for linear algebra Conrad Sanderson and Ryan Curtin Abstract The C++ language is often used for implementing functionality that is performance and/or resource sensitive. While the standard C++ library provides many useful algorithms (such as sorting), in its current form it does not provide direct handling of linear algebra (matrix maths). Armadillo is an open source linear algebra library for the C++ language, aiming towards a good balance between speed and ease of use. Its high-level application programming interface (function syntax) is deliberately similar to the widely used Matlab and Octave languages [4], so that mathematical operations can be expressed in a familiar and natural manner. The library is useful for algorithm development directly in C++, or relatively quick conversion of research code into production environments. Armadillo provides efficient objects for vectors, matrices and cubes (third order tensors), as well as over 200 associated functions for manipulating data stored in the objects. Integer, floating point and complex numbers are supported, as well as dense and sparse storage formats. Various matrix factorisations are provided through integration with LAPACK [3], or one of its high performance drop-in replacements such as Intel MKL [6] or OpenBLAS [9]. It is also possible to use Armadillo in conjunction with NVBLAS to obtain GPU-accelerated matrix multiplication [7]. Armadillo is used as a base for other open source projects, such as MLPACK, a C++ library for machine learning and pattern recognition [2], and RcppArmadillo, a bridge between the R language and C++ in order to speed up computations [5]. -
Homework 2: Reflection and Multiple Dispatch in Smalltalk
Com S 541 — Programming Languages 1 October 2, 2002 Homework 2: Reflection and Multiple Dispatch in Smalltalk Due: Problems 1 and 2, September 24, 2002; problems 3 and 4, October 8, 2002. This homework can either be done individually or in teams. Its purpose is to familiarize you with Smalltalk’s reflection facilities and to help learn about other issues in OO language design. Don’t hesitate to contact the staff if you are not clear about what to do. In this homework, you will adapt the “multiple dispatch as dispatch on tuples” approach, origi- nated by Leavens and Millstein [1], to Smalltalk. To do this you will have to read their paper and then do the following. 1. (30 points) In a new category, Tuple-Smalltalk, add a class Tuple, which has indexed instance variables. Design this type to provide the necessary methods for working with dispatch on tuples, for example, we’d like to have access to the tuple of classes of the objects in a given tuple. Some of these methods will depend on what’s below. Also design methods so that tuples can be used as a data structure (e.g., to pass multiple arguments and return multiple results). 2. (50 points) In the category, Tuple-Smalltalk, design other classes to hold the behavior that will be declared for tuples. For example, you might want something analogous to a method dictionary and other things found in the class Behavior or ClassDescription. It’s worth studying those classes to see what can be adapted to our purposes. -
Scala Tutorial
Scala Tutorial SCALA TUTORIAL Simply Easy Learning by tutorialspoint.com tutorialspoint.com i ABOUT THE TUTORIAL Scala Tutorial Scala is a modern multi-paradigm programming language designed to express common programming patterns in a concise, elegant, and type-safe way. Scala has been created by Martin Odersky and he released the first version in 2003. Scala smoothly integrates features of object-oriented and functional languages. This tutorial gives a great understanding on Scala. Audience This tutorial has been prepared for the beginners to help them understand programming Language Scala in simple and easy steps. After completing this tutorial, you will find yourself at a moderate level of expertise in using Scala from where you can take yourself to next levels. Prerequisites Scala Programming is based on Java, so if you are aware of Java syntax, then it's pretty easy to learn Scala. Further if you do not have expertise in Java but you know any other programming language like C, C++ or Python, then it will also help in grasping Scala concepts very quickly. Copyright & Disclaimer Notice All the content and graphics on this tutorial are the property of tutorialspoint.com. Any content from tutorialspoint.com or this tutorial may not be redistributed or reproduced in any way, shape, or form without the written permission of tutorialspoint.com. Failure to do so is a violation of copyright laws. This tutorial may contain inaccuracies or errors and tutorialspoint provides no guarantee regarding the accuracy of the site or its contents including this tutorial. If you discover that the tutorialspoint.com site or this tutorial content contains some errors, please contact us at [email protected] TUTORIALS POINT Simply Easy Learning Table of Content Scala Tutorial .......................................................................... -
TAMING the MERGE OPERATOR a Type-Directed Operational Semantics Approach
Technical Report, Department of Computer Science, the University of Hong Kong, Jan 2021. 1 TAMING THE MERGE OPERATOR A Type-directed Operational Semantics Approach XUEJING HUANG JINXU ZHAO BRUNO C. D. S. OLIVEIRA The University of Hong Kong (e-mail: fxjhuang, jxzhao, [email protected]) Abstract Calculi with disjoint intersection types support a symmetric merge operator with subtyping. The merge operator generalizes record concatenation to any type, enabling expressive forms of object composition, and simple solutions to hard modularity problems. Unfortunately, recent calculi with disjoint intersection types and the merge operator lack a (direct) operational semantics with expected properties such as determinism and subject reduction, and only account for terminating programs. This paper proposes a type-directed operational semantics (TDOS) for calculi with intersection types and a merge operator. We study two variants of calculi in the literature. The first calculus, called li, is a variant of a calculus presented by Oliveira et al. (2016) and closely related to another calculus by Dunfield (2014). Although Dunfield proposes a direct small-step semantics for her calcu- lus, her semantics lacks both determinism and subject reduction. Using our TDOS we obtain a direct + semantics for li that has both properties. The second calculus, called li , employs the well-known + subtyping relation of Barendregt, Coppo and Dezani-Ciancaglini (BCD). Therefore, li extends the more basic subtyping relation of li, and also adds support for record types and nested composition (which enables recursive composition of merged components). To fully obtain determinism, both li + and li employ a disjointness restriction proposed in the original li calculus. -
Cmsc 132: Object-Oriented Programming Ii
© Department of Computer Science UMD CMSC 132: OBJECT-ORIENTED PROGRAMMING II Iterator, Marker, Observer Design Patterns Department of Computer Science University of Maryland, College Park © Department of Computer Science UMD Design Patterns • Descriptions of reusable solutions to common software design problems (e.g, Iterator pattern) • Captures the experience of experts • Goals • Solve common programming challenges • Improve reliability of solution • Aid rapid software development • Useful for real-world applications • Design patterns are like recipes – generic solutions to expected situations • Design patterns are language independent • Recognizing when and where to use design patterns requires familiarity & experience • Design pattern libraries serve as a glossary of idioms for understanding common, but complex solutions • Design patterns are used throughout the Java Class Libraries © Department of Computer Science UMD Iterator Pattern • Definition • Move through collection of objects without knowing its internal representation • Where to use & benefits • Use a standard interface to represent data objects • Uses standard iterator built in each standard collection, like List • Need to distinguish variations in the traversal of an aggregate • Example • Iterator for collection • Original • Examine elements of collection directly • Using pattern • Collection provides Iterator class for examining elements in collection © Department of Computer Science UMD Iterator Example public interface Iterator<V> { bool hasNext(); V next(); void remove(); -
Iterators in C++ C 2016 All Rights Reserved
Software Design Lecture Notes Prof. Stewart Weiss Iterators in C++ c 2016 All rights reserved. Iterators in C++ 1 Introduction When a program needs to visit all of the elements of a vector named myvec starting with the rst and ending with the last, you could use an iterative loop such as the following: for ( int i = 0; i < myvec.size(); i++ ) // the visit, i.e., do something with myvec[i] This code works and is a perfectly ne solution. This same type of iterative loop can visit each character in a C++ string. But what if you need code that visits all elements of a C++ list object? Is there a way to use an iterative loop to do this? To be clear, an iterative loop is one that has the form for var = start value; var compared to end value; update var; {do something with node at specic index} In other words, an iterative loop is a counting loop, as opposed to one that tests an arbitrary condition, like a while loop. The short answer to the question is that, in C++, without iterators, you cannot do this. Iterators make it possible to iterate through arbitrary containers. This set of notes answers the question, What is an iterator, and how do you use it? Iterators are a generalization of pointers in C++ and have similar semantics. They allow a program to navigate through dierent types of containers in a uniform manner. Just as pointers can be used to traverse a linked list or a binary tree, and subscripts can be used to traverse the elements of a vector, iterators can be used to sequence through the elements of any standard C++ container class. -
Pattern Matching
Functional Programming Steven Lau March 2015 before function programming... https://www.youtube.com/watch?v=92WHN-pAFCs Models of computation ● Turing machine ○ invented by Alan Turing in 1936 ● Lambda calculus ○ invented by Alonzo Church in 1930 ● more... Turing machine ● A machine operates on an infinite tape (memory) and execute a program stored ● It may ○ read a symbol ○ write a symbol ○ move to the left cell ○ move to the right cell ○ change the machine’s state ○ halt Turing machine Have some fun http://www.google.com/logos/2012/turing-doodle-static.html http://www.ioi2012.org/wp-content/uploads/2011/12/Odometer.pdf http://wcipeg.com/problems/desc/ioi1211 Turing machine incrementer state symbol action next_state _____ state 0 __1__ state 1 0 _ or 0 write 1 1 _10__ state 2 __1__ state 1 0 1 write 0 2 _10__ state 0 __1__ state 0 _00__ state 2 1 _ left 0 __0__ state 2 _00__ state 0 __0__ state 0 1 0 or 1 right 1 100__ state 1 _10__ state 1 2 0 left 0 100__ state 1 _10__ state 1 100__ state 1 _10__ state 1 100__ state 1 _10__ state 0 100__ state 0 _11__ state 1 101__ state 1 _11__ state 1 101__ state 1 _11__ state 0 101__ state 0 λ-calculus Beware! ● think mathematical, not C++/Pascal ● (parentheses) are for grouping ● variables cannot be mutated ○ x = 1 OK ○ x = 2 NO ○ x = x + 1 NO λ-calculus Simplification 1 of 2: ● Only anonymous functions are used ○ f(x) = x2+1 f(1) = 12+1 = 2 is written as ○ (λx.x2+1)(1) = 12+1 = 2 note that f = λx.x2+1 λ-calculus Simplification 2 of 2: ● Only unary functions are used ○ a binary function can be written as a unary function that return another unary function ○ (λ(x,y).x+y)(1,2) = 1+2 = 3 is written as [(λx.(λy.x+y))(1)](2) = [(λy.1+y)](2) = 1+2 = 3 ○ this technique is known as Currying Haskell Curry λ-calculus ● A lambda term has 3 forms: ○ x ○ λx.A ○ AB where x is a variable, A and B are lambda terms. -
Julia: a Fresh Approach to Numerical Computing
RSDG @ UCL Julia: A Fresh Approach to Numerical Computing Mosè Giordano @giordano [email protected] Knowledge Quarter Codes Tech Social October 16, 2019 Julia’s Facts v1.0.0 released in 2018 at UCL • Development started in 2009 at MIT, first • public release in 2012 Julia co-creators won the 2019 James H. • Wilkinson Prize for Numerical Software Julia adoption is growing rapidly in • numerical optimisation, differential equations, machine learning, differentiable programming It is used and taught in several universities • (https://julialang.org/teaching/) Mosè Giordano (RSDG @ UCL) Julia: A Fresh Approach to Numerical Computing October 16, 2019 2 / 29 Julia on Nature Nature 572, 141-142 (2019). doi: 10.1038/d41586-019-02310-3 Mosè Giordano (RSDG @ UCL) Julia: A Fresh Approach to Numerical Computing October 16, 2019 3 / 29 Solving the Two-Language Problem: Julia Multiple dispatch • Dynamic type system • Good performance, approaching that of statically-compiled languages • JIT-compiled scripts • User-defined types are as fast and compact as built-ins • Lisp-like macros and other metaprogramming facilities • No need to vectorise: for loops are fast • Garbage collection: no manual memory management • Interactive shell (REPL) for exploratory work • Call C and Fortran functions directly: no wrappers or special APIs • Call Python functions: use the PyCall package • Designed for parallelism and distributed computation • Mosè Giordano (RSDG @ UCL) Julia: A Fresh Approach to Numerical Computing October 16, 2019 4 / 29 Multiple Dispatch using DifferentialEquations -
From Perl to Python
From Perl to Python Fernando Pineda 140.636 Oct. 11, 2017 version 0.1 3. Strong/Weak Dynamic typing The notion of strong and weak typing is a little murky, but I will provide some examples that provide insight most. Strong vs Weak typing To be strongly typed means that the type of data that a variable can hold is fixed and cannot be changed. To be weakly typed means that a variable can hold different types of data, e.g. at one point in the code it might hold an int at another point in the code it might hold a float . Static vs Dynamic typing To be statically typed means that the type of a variable is determined at compile time . Type checking is done by the compiler prior to execution of any code. To be dynamically typed means that the type of variable is determined at run-time. Type checking (if there is any) is done when the statement is executed. C is a strongly and statically language. float x; int y; # you can define your own types with the typedef statement typedef mytype int; mytype z; typedef struct Books { int book_id; char book_name[256] } Perl is a weakly and dynamically typed language. The type of a variable is set when it's value is first set Type checking is performed at run-time. Here is an example from stackoverflow.com that shows how the type of a variable is set to 'integer' at run-time (hence dynamically typed). $value is subsequently cast back and forth between string and a numeric types (hence weakly typed). -
Declare New Function Javascript
Declare New Function Javascript Piggy or embowed, Levon never stalemating any punctuality! Bipartite Amory wets no blackcurrants flagged anes after Hercules supinate methodically, quite aspirant. Estival Stanleigh bettings, his perspicaciousness exfoliating sopped enforcedly. How a javascript objects for mistakes to retain the closure syntax and maintainability of course, written by reading our customers and line? Everything looks very useful. These values or at first things without warranty that which to declare new function javascript? You declare a new class and news to a function expressions? Explore an implementation defined in new row with a function has a gas range. If it allows you probably work, regular expression evaluation but mostly warszawa, and to retain the explanation of. Reimagine your namespaces alone relate to declare new function javascript objects for arrow functions should be governed by programmers avoid purity. Js library in the different product topic and zip archives are. Why is selected, and declare a superclass method decorators need them into functions defined by allocating local time. It makes more sense to handle work in which support optional, only people want to preserve type to be very short term, but easier to! String type variable side effects and declarations take a more situations than or leading white list of merchantability or a way as explicit. You declare many types to prevent any ecmascript program is not have two categories by any of parameters the ecmascript is one argument we expect. It often derived from the new knowledge within the string, news and error if the function expression that their prototype. -
Generic Programming
Generic Programming July 21, 1998 A Dagstuhl Seminar on the topic of Generic Programming was held April 27– May 1, 1998, with forty seven participants from ten countries. During the meeting there were thirty seven lectures, a panel session, and several problem sessions. The outcomes of the meeting include • A collection of abstracts of the lectures, made publicly available via this booklet and a web site at http://www-ca.informatik.uni-tuebingen.de/dagstuhl/gpdag.html. • Plans for a proceedings volume of papers submitted after the seminar that present (possibly extended) discussions of the topics covered in the lectures, problem sessions, and the panel session. • A list of generic programming projects and open problems, which will be maintained publicly on the World Wide Web at http://www-ca.informatik.uni-tuebingen.de/people/musser/gp/pop/index.html http://www.cs.rpi.edu/˜musser/gp/pop/index.html. 1 Contents 1 Motivation 3 2 Standards Panel 4 3 Lectures 4 3.1 Foundations and Methodology Comparisons ........ 4 Fundamentals of Generic Programming.................. 4 Jim Dehnert and Alex Stepanov Automatic Program Specialization by Partial Evaluation........ 4 Robert Gl¨uck Evaluating Generic Programming in Practice............... 6 Mehdi Jazayeri Polytypic Programming........................... 6 Johan Jeuring Recasting Algorithms As Objects: AnAlternativetoIterators . 7 Murali Sitaraman Using Genericity to Improve OO Designs................. 8 Karsten Weihe Inheritance, Genericity, and Class Hierarchies.............. 8 Wolf Zimmermann 3.2 Programming Methodology ................... 9 Hierarchical Iterators and Algorithms................... 9 Matt Austern Generic Programming in C++: Matrix Case Study........... 9 Krzysztof Czarnecki Generative Programming: Beyond Generic Programming........ 10 Ulrich Eisenecker Generic Programming Using Adaptive and Aspect-Oriented Programming . -
Lambda Calculus and Functional Programming
Global Journal of Researches in Engineering Vol. 10 Issue 2 (Ver 1.0) June 2010 P a g e | 47 Lambda Calculus and Functional Programming Anahid Bassiri1Mohammad Reza. Malek2 GJRE Classification (FOR) 080299, 010199, 010203, Pouria Amirian3 010109 Abstract-The lambda calculus can be thought of as an idealized, Basis concept of a Turing machine is the present day Von minimalistic programming language. It is capable of expressing Neumann computers. Conceptually these are Turing any algorithm, and it is this fact that makes the model of machines with random access registers. Imperative functional programming an important one. This paper is programming languages such as FORTRAN, Pascal etcetera focused on introducing lambda calculus and its application. As as well as all the assembler languages are based on the way an application dikjestra algorithm is implemented using a Turing machine is instructed by a sequence of statements. lambda calculus. As program shows algorithm is more understandable using lambda calculus in comparison with In addition functional programming languages, like other imperative languages. Miranda, ML etcetera, are based on the lambda calculus. Functional programming is a programming paradigm that I. INTRODUCTION treats computation as the evaluation of mathematical ambda calculus (λ-calculus) is a useful device to make functions and avoids state and mutable data. It emphasizes L the theories realizable. Lambda calculus, introduced by the application of functions, in contrast with the imperative Alonzo Church and Stephen Cole Kleene in the 1930s is a programming style that emphasizes changes in state. formal system designed to investigate function definition, Lambda calculus provides a theoretical framework for function application and recursion in mathematical logic and describing functions and their evaluation.