Defining Functions
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Higher-Order Functions 15-150: Principles of Functional Programming – Lecture 13
Higher-order Functions 15-150: Principles of Functional Programming { Lecture 13 Giselle Reis By now you might feel like you have a pretty good idea of what is going on in functional program- ming, but in reality we have used only a fragment of the language. In this lecture we see what more we can do and what gives the name functional to this paradigm. Let's take a step back and look at ML's typing system: we have basic types (such as int, string, etc.), tuples of types (t*t' ) and functions of a type to a type (t ->t' ). In a grammar style (where α is a basic type): τ ::= α j τ ∗ τ j τ ! τ What types allowed by this grammar have we not used so far? Well, we could, for instance, have a function below a tuple. Or even a function within a function, couldn't we? The following are completely valid types: int*(int -> int) int ->(int -> int) (int -> int) -> int The first one is a pair in which the first element is an integer and the second one is a function from integers to integers. The second one is a function from integers to functions (which have type int -> int). The third type is a function from functions to integers. The two last types are examples of higher-order functions1, i.e., a function which: • receives a function as a parameter; or • returns a function. Functions can be used like any other value. They are first-class citizens. Maybe this seems strange at first, but I am sure you have used higher-order functions before without noticing it. -
Typescript Language Specification
TypeScript Language Specification Version 1.8 January, 2016 Microsoft is making this Specification available under the Open Web Foundation Final Specification Agreement Version 1.0 ("OWF 1.0") as of October 1, 2012. The OWF 1.0 is available at http://www.openwebfoundation.org/legal/the-owf-1-0-agreements/owfa-1-0. TypeScript is a trademark of Microsoft Corporation. Table of Contents 1 Introduction ................................................................................................................................................................................... 1 1.1 Ambient Declarations ..................................................................................................................................................... 3 1.2 Function Types .................................................................................................................................................................. 3 1.3 Object Types ...................................................................................................................................................................... 4 1.4 Structural Subtyping ....................................................................................................................................................... 6 1.5 Contextual Typing ............................................................................................................................................................ 7 1.6 Classes ................................................................................................................................................................................. -
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 .......................................................................... -
Smalltalk Smalltalk
3/8/2008 CSE 3302 Programming Languages Smalltalk Everyygthing is obj ect. Obj ects communicate by messages. Chengkai Li Spring 2008 Lecture 14 – Smalltalk, Spring Lecture 14 – Smalltalk, Spring CSE3302 Programming Languages, UT-Arlington 1 CSE3302 Programming Languages, UT-Arlington 2 2008 ©Chengkai Li, 2008 2008 ©Chengkai Li, 2008 Object Hierarchy Object UndefinedObject Boolean Magnitude Collection No Data Type. True False Set … There is only Class. Char Number … Fraction Integer Float Lecture 14 – Smalltalk, Spring Lecture 14 – Smalltalk, Spring CSE3302 Programming Languages, UT-Arlington 3 CSE3302 Programming Languages, UT-Arlington 4 2008 ©Chengkai Li, 2008 2008 ©Chengkai Li, 2008 Syntax • Smalltalk is really “small” – Only 6 keywords (pseudo variables) – Class, object, variable, method names are self explanatory Sma llta lk Syn tax is Simp le. – Only syntax for calling method (messages) and defining method. • No syntax for control structure • No syntax for creating class Lecture 14 – Smalltalk, Spring Lecture 14 – Smalltalk, Spring CSE3302 Programming Languages, UT-Arlington 5 CSE3302 Programming Languages, UT-Arlington 6 2008 ©Chengkai Li, 2008 2008 ©Chengkai Li, 2008 1 3/8/2008 Expressions Literals • Literals • Number: 3 3.5 • Character: $a • Pseudo Variables • String: ‘ ’ (‘Hel’,’lo!’ and ‘Hello!’ are two objects) • Symbol: # (#foo and #foo are the same object) • Variables • Compile-time (literal) array: #(1 $a 1+2) • Assignments • Run-time (dynamic) array: {1. $a. 1+2} • Comment: “This is a comment.” • Blocks • Messages Lecture 14 – Smalltalk, Spring Lecture 14 – Smalltalk, Spring CSE3302 Programming Languages, UT-Arlington 7 CSE3302 Programming Languages, UT-Arlington 8 2008 ©Chengkai Li, 2008 2008 ©Chengkai Li, 2008 Pseudo Variables Variables • Instance variables. -
Lecture Notes on Types for Part II of the Computer Science Tripos
Q Lecture Notes on Types for Part II of the Computer Science Tripos Prof. Andrew M. Pitts University of Cambridge Computer Laboratory c 2016 A. M. Pitts Contents Learning Guide i 1 Introduction 1 2 ML Polymorphism 6 2.1 Mini-ML type system . 6 2.2 Examples of type inference, by hand . 14 2.3 Principal type schemes . 16 2.4 A type inference algorithm . 18 3 Polymorphic Reference Types 25 3.1 The problem . 25 3.2 Restoring type soundness . 30 4 Polymorphic Lambda Calculus 33 4.1 From type schemes to polymorphic types . 33 4.2 The Polymorphic Lambda Calculus (PLC) type system . 37 4.3 PLC type inference . 42 4.4 Datatypes in PLC . 43 4.5 Existential types . 50 5 Dependent Types 53 5.1 Dependent functions . 53 5.2 Pure Type Systems . 57 5.3 System Fw .............................................. 63 6 Propositions as Types 67 6.1 Intuitionistic logics . 67 6.2 Curry-Howard correspondence . 69 6.3 Calculus of Constructions, lC ................................... 73 6.4 Inductive types . 76 7 Further Topics 81 References 84 Learning Guide These notes and slides are designed to accompany 12 lectures on type systems for Part II of the Cambridge University Computer Science Tripos. The course builds on the techniques intro- duced in the Part IB course on Semantics of Programming Languages for specifying type systems for programming languages and reasoning about their properties. The emphasis here is on type systems for functional languages and their connection to constructive logic. We pay par- ticular attention to the notion of parametric polymorphism (also known as generics), both because it has proven useful in practice and because its theory is quite subtle. -
Python Functions
PPYYTTHHOONN FFUUNNCCTTIIOONNSS http://www.tutorialspoint.com/python/python_functions.htm Copyright © tutorialspoint.com A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions like print, etc. but you can also create your own functions. These functions are called user-defined functions. Defining a Function You can define functions to provide the required functionality. Here are simple rules to define a function in Python. Function blocks begin with the keyword def followed by the function name and parentheses ( ). Any input parameters or arguments should be placed within these parentheses. You can also define parameters inside these parentheses. The first statement of a function can be an optional statement - the documentation string of the function or docstring. The code block within every function starts with a colon : and is indented. The statement return [expression] exits a function, optionally passing back an expression to the caller. A return statement with no arguments is the same as return None. Syntax def functionname( parameters ): "function_docstring" function_suite return [expression] By default, parameters have a positional behavior and you need to inform them in the same order that they were defined. Example The following function takes a string as input parameter and prints it on standard screen. def printme( str ): "This prints a passed string into this function" print str return Calling a Function Defining a function only gives it a name, specifies the parameters that are to be included in the function and structures the blocks of code. -
Open C++ Tutorial∗
Open C++ Tutorial∗ Shigeru Chiba Institute of Information Science and Electronics University of Tsukuba [email protected] Copyright c 1998 by Shigeru Chiba. All Rights Reserved. 1 Introduction OpenC++ is an extensible language based on C++. The extended features of OpenC++ are specified by a meta-level program given at compile time. For dis- tinction, regular programs written in OpenC++ are called base-level programs. If no meta-level program is given, OpenC++ is identical to regular C++. The meta-level program extends OpenC++ through the interface called the OpenC++ MOP. The OpenC++ compiler consists of three stages: preprocessor, source-to-source translator from OpenC++ to C++, and the back-end C++ com- piler. The OpenC++ MOP is an interface to control the translator at the second stage. It allows to specify how an extended feature of OpenC++ is translated into regular C++ code. An extended feature of OpenC++ is supplied as an add-on software for the compiler. The add-on software consists of not only the meta-level program but also runtime support code. The runtime support code provides classes and functions used by the base-level program translated into C++. The base-level program in OpenC++ is first translated into C++ according to the meta-level program. Then it is linked with the runtime support code to be executable code. This flow is illustrated by Figure 1. The meta-level program is also written in OpenC++ since OpenC++ is a self- reflective language. It defines new metaobjects to control source-to-source transla- tion. The metaobjects are the meta-level representation of the base-level program and they perform the translation. -
Let's Get Functional
5 LET’S GET FUNCTIONAL I’ve mentioned several times that F# is a functional language, but as you’ve learned from previous chapters you can build rich applications in F# without using any functional techniques. Does that mean that F# isn’t really a functional language? No. F# is a general-purpose, multi paradigm language that allows you to program in the style most suited to your task. It is considered a functional-first lan- guage, meaning that its constructs encourage a functional style. In other words, when developing in F# you should favor functional approaches whenever possible and switch to other styles as appropriate. In this chapter, we’ll see what functional programming really is and how functions in F# differ from those in other languages. Once we’ve estab- lished that foundation, we’ll explore several data types commonly used with functional programming and take a brief side trip into lazy evaluation. The Book of F# © 2014 by Dave Fancher What Is Functional Programming? Functional programming takes a fundamentally different approach toward developing software than object-oriented programming. While object-oriented programming is primarily concerned with managing an ever-changing system state, functional programming emphasizes immutability and the application of deterministic functions. This difference drastically changes the way you build software, because in object-oriented programming you’re mostly concerned with defining classes (or structs), whereas in functional programming your focus is on defining functions with particular emphasis on their input and output. F# is an impure functional language where data is immutable by default, though you can still define mutable data or cause other side effects in your functions. -
An Overview of the Scala Programming Language
An Overview of the Scala Programming Language Second Edition Martin Odersky, Philippe Altherr, Vincent Cremet, Iulian Dragos Gilles Dubochet, Burak Emir, Sean McDirmid, Stéphane Micheloud, Nikolay Mihaylov, Michel Schinz, Erik Stenman, Lex Spoon, Matthias Zenger École Polytechnique Fédérale de Lausanne (EPFL) 1015 Lausanne, Switzerland Technical Report LAMP-REPORT-2006-001 Abstract guage for component software needs to be scalable in the sense that the same concepts can describe small as well as Scala fuses object-oriented and functional programming in large parts. Therefore, we concentrate on mechanisms for a statically typed programming language. It is aimed at the abstraction, composition, and decomposition rather than construction of components and component systems. This adding a large set of primitives which might be useful for paper gives an overview of the Scala language for readers components at some level of scale, but not at other lev- who are familar with programming methods and program- els. Second, we postulate that scalable support for compo- ming language design. nents can be provided by a programming language which unies and generalizes object-oriented and functional pro- gramming. For statically typed languages, of which Scala 1 Introduction is an instance, these two paradigms were up to now largely separate. True component systems have been an elusive goal of the To validate our hypotheses, Scala needs to be applied software industry. Ideally, software should be assembled in the design of components and component systems. Only from libraries of pre-written components, just as hardware is serious application by a user community can tell whether the assembled from pre-fabricated chips. -
Scala Is an Object Functional Programming and Scripting Language for General Software Applications Designed to Express Solutions in a Concise Manner
https://www.guru99.com/ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1) Explain what is Scala? Scala is an object functional programming and scripting language for general software applications designed to express solutions in a concise manner. 2) What is a ‘Scala set’? What are methods through which operation sets are expressed? Scala set is a collection of pairwise elements of the same type. Scala set does not contain any duplicate elements. There are two kinds of sets, mutable and immutable. 3) What is a ‘Scala map’? Scala map is a collection of key or value pairs. Based on its key any value can be retrieved. Values are not unique but keys are unique in the Map. 4) What is the advantage of Scala? • Less error prone functional style • High maintainability and productivity • High scalability • High testability • Provides features of concurrent programming 5) In what ways Scala is better than other programming language? • The arrays uses regular generics, while in other language, generics are bolted on as an afterthought and are completely separate but have overlapping behaviours with arrays. • Scala has immutable “val” as a first class language feature. The “val” of scala is similar to Java final variables. Contents may mutate but top reference is immutable. • Scala lets ‘if blocks’, ‘for-yield loops’, and ‘code’ in braces to return a value. It is more preferable, and eliminates the need for a separate ternary -
Run-Time Type Information and Incremental Loading in C++
Run-time Type Information and Incremental Loading in C++ Murali Vemulapati Sriram Duvvuru Amar Gupta WP #3772 September 1993 PROFIT #93-11 Productivity From Information Technology "PROFIT" Research Initiative Sloan School of Management Massachusetts Institute of Technology Cambridge, MA 02139 USA (617)253-8584 Fax: (617)258-7579 Copyright Massachusetts Institute of Technology 1993. The research described herein has been supported (in whole or in part) by the Productivity From Information Technology (PROFIT) Research Initiative at MIT. This copy is for the exclusive use of PROFIT sponsor firms. Productivity From Information Technology (PROFIT) The Productivity From Information Technology (PROFIT) Initiative was established on October 23, 1992 by MIT President Charles Vest and Provost Mark Wrighton "to study the use of information technology in both the private and public sectors and to enhance productivity in areas ranging from finance to transportation, and from manufacturing to telecommunications." At the time of its inception, PROFIT took over the Composite Information Systems Laboratory and Handwritten Character Recognition Laboratory. These two laboratories are now involved in research re- lated to context mediation and imaging respectively. LABORATORY FOR ELEC RONICS A CENTERCFORENTER COORDINATION LABORATORY ) INFORMATION S RESEARCH RESE CH E53-310, MITAL"Room Cambridge, MA 02M142-1247 Tel: (617) 253-8584 E-Mail: [email protected] Run-time Type Information and Incremental Loading in C++ September 13, 1993 Abstract We present the design and implementation strategy for an integrated programming environment which facilitates specification, implementation and execution of persistent C++ programs. Our system is implemented in E, a persistent programming language based on C++. The environment provides type identity and type persistence, i.e., each user-defined class has a unique identity and persistence across compilations. -
Functional Programming for Imperative Programmers
Functional Programming for Imperative Programmers R. Sekar This document introduces functional programming for those that are used to imperative languages, but are trying to come to terms with recursion and other techniques used in functional programming. We use OCaml as the primary language, and we assume that the reader has been introduced to its basic syntax and features. The goal of this document is to help these programmers get more comfortable with functional programming techniques, while addressing the following topics: • Understanding and visualizing recursion • Iteration as a special case of recursion { Imperative programming in functional languages by \threading" state through functions • Higher-order functions and iteration • Writing efficient functional code • Functional programming in imperative languages 1 Simple Vs Mutual Recursion Recursion can be simple recursion, which means that a function f is recursive with itself. In other words, f is defined in terms of f and h1; : : : ; hn, where h1; : : : ; hn have no dependence on f. In OCaml, such a function f can be defined using a single let rec. The factorial function defined below is one such example: let rec fact n = i f n=0 then 1 else n ∗ ( fact ( n−1)) In this case, fact is defined in terms of itself and two other functions, if and the subtraction function on integers. As a second example, consider the Fibonacci function, where each invocation of fib makes two recursive invoca- tions of fib. let rec fib n = i f n=0 then 0 else i f n=1 then 1 else ( fib ( n−1)) + ( fib ( n−2)) In a more complex case of recursion, functions can be mutually recursive, i.e., f is defined in terms of another function g, which is in turn defined in terms of f.