What Is Functional Programming? by by Luis Atencio
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Exploring Languages with Interpreters and Functional Programming Chapter 8
Exploring Languages with Interpreters and Functional Programming Chapter 8 H. Conrad Cunningham 24 September 2018 Contents 8 Evaluation Model 2 8.1 Chapter Introduction . .2 8.2 Referential Transparency Revisited . .2 8.3 Substitution Model . .3 8.4 Time and Space Complexity . .6 8.5 Termination . .7 8.6 What Next? . .7 8.7 Exercises . .8 8.8 Acknowledgements . .8 8.9 References . .9 8.10 Terms and Concepts . .9 Copyright (C) 2016, 2017, 2018, H. Conrad Cunningham Professor of Computer and Information Science University of Mississippi 211 Weir Hall P.O. Box 1848 University, MS 38677 (662) 915-5358 Browser Advisory: The HTML version of this textbook requires a browser that supports the display of MathML. A good choice as of September 2018 is a recent version of Firefox from Mozilla. 1 8 Evaluation Model 8.1 Chapter Introduction This chapter introduces an evaluation model applicable to Haskell programs. As in the previous chapters, this chapter focuses on use of first-order functions and primitive data types. A goal of this chapter and the next one is enable students to analyze Haskell functions to determine under what conditions they terminate normally and how efficient they are. This chapter presents the evaluation model and the next chapter informally analyzes simple functions in terms of time and space efficiency and termination. How can we evaluate (i.e. execute) an expression that “calls” a function like the fact1 function from Chapter 4? We do this by rewriting expressions using a substitution model, as we see in this chapter. This process depends upon a property of functional languages called referential transparency. -
Week 3: Scope and Evaluation Order Assignment 1 Has Been Posted!
Week 3: Scope and Evaluation Order CSC324 Principles of Programming Languages David Liu, Department of Computer Science Assignment 1 has been posted! Closures and static scope static (adjective) determined only by the program source code dynamic (adjective) determined only when the program is run E.g., referential transparency is a static property How are closures implemented? Are they static or dynamic? Or both? Function bodies can be processed statically (e.g., Haskell compiler generates code once per lambda). The closure environment (and therefore the closure itself) can only be generated dynamically. The closure depends only on where the function is evaluated, not where that function is called. (define (make-adder n) (lambda (x) (+ x n))) (define adder (make-adder 1)) (adder 100) So we can determine where each free identifier obtains its values statically, based on where its enclosing function is defined. scope (of an identifier) The parts of program code that may refer to that identifier. static (aka lexical) scope The scope of every identifier is determined by the structure of the source code (e.g., by nesting of lambdas and lets). Every identifier obtains its value from the closest enclosing expression that binds it. (define (make-adder n) (lambda (x) (+ x n))) (define adder (make-adder 1)) ; (0x..., {n: 1}) (let* ([n 100]) (adder 2)) Implementing static scope in an interpreter A simple interpreter (define/match (interpret env expr) [(_ (? number?)) expr] [(_ (? symbol?)) (hash-ref env expr)] [(_ (list '+ l r)) (+ (interpret env l) (interpret env r))]) A simple interpreter (define/match (interpret env expr) [(_ (? number?)) expr] [(_ (? symbol?)) (hash-ref env expr)] [(_ (list '+ l r)) (+ (interpret env l) (interpret env r))]) The environment is passed recursively when interpreting each subexpression. -
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. -
SI 413, Unit 3: Advanced Scheme
SI 413, Unit 3: Advanced Scheme Daniel S. Roche ([email protected]) Fall 2018 1 Pure Functional Programming Readings for this section: PLP, Sections 10.7 and 10.8 Remember there are two important characteristics of a “pure” functional programming language: • Referential Transparency. This fancy term just means that, for any expression in our program, the result of evaluating it will always be the same. In fact, any referentially transparent expression could be replaced with its value (that is, the result of evaluating it) without changing the program whatsoever. Notice that imperative programming is about as far away from this as possible. For example, consider the C++ for loop: for ( int i = 0; i < 10;++i) { /∗ some s t u f f ∗/ } What can we say about the “stuff” in the body of the loop? Well, it had better not be referentially transparent. If it is, then there’s no point in running over it 10 times! • Functions are First Class. Another way of saying this is that functions are data, just like any number or list. Functions are values, in fact! The specific privileges that a function earns by virtue of being first class include: 1) Functions can be given names. This is not a big deal; we can name functions in pretty much every programming language. In Scheme this just means we can do (define (f x) (∗ x 3 ) ) 2) Functions can be arguments to other functions. This is what you started to get into at the end of Lab 2. For starters, there’s the basic predicate procedure?: (procedure? +) ; #t (procedure? 10) ; #f (procedure? procedure?) ; #t 1 And then there are “higher-order functions” like map and apply: (apply max (list 5 3 10 4)) ; 10 (map sqrt (list 16 9 64)) ; '(4 3 8) What makes the functions “higher-order” is that one of their arguments is itself another function. -
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. -
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. -
Purity in Erlang
Purity in Erlang Mihalis Pitidis1 and Konstantinos Sagonas1,2 1 School of Electrical and Computer Engineering, National Technical University of Athens, Greece 2 Department of Information Technology, Uppsala University, Sweden [email protected], [email protected] Abstract. Motivated by a concrete goal, namely to extend Erlang with the abil- ity to employ user-defined guards, we developed a parameterized static analysis tool called PURITY, that classifies functions as referentially transparent (i.e., side- effect free with no dependency on the execution environment and never raising an exception), side-effect free with no dependencies but possibly raising excep- tions, or side-effect free but with possible dependencies and possibly raising ex- ceptions. We have applied PURITY on a large corpus of Erlang code bases and report experimental results showing the percentage of functions that the analysis definitely classifies in each category. Moreover, we discuss how our analysis has been incorporated on a development branch of the Erlang/OTP compiler in order to allow extending the language with user-defined guards. 1 Introduction Purity plays an important role in functional programming languages as it is a corner- stone of referential transparency, namely that the same language expression produces the same value when evaluated twice. Referential transparency helps in writing easy to test, robust and comprehensible code, makes equational reasoning possible, and aids program analysis and optimisation. In pure functional languages like Clean or Haskell, any side-effect or dependency on the state is captured by the type system and is reflected in the types of functions. In a language like ERLANG, which has been developed pri- marily with concurrency in mind, pure functions are not the norm and impure functions can freely be used interchangeably with pure ones. -
Scala by Example (2009)
Scala By Example DRAFT January 13, 2009 Martin Odersky PROGRAMMING METHODS LABORATORY EPFL SWITZERLAND Contents 1 Introduction1 2 A First Example3 3 Programming with Actors and Messages7 4 Expressions and Simple Functions 11 4.1 Expressions And Simple Functions...................... 11 4.2 Parameters.................................... 12 4.3 Conditional Expressions............................ 15 4.4 Example: Square Roots by Newton’s Method................ 15 4.5 Nested Functions................................ 16 4.6 Tail Recursion.................................. 18 5 First-Class Functions 21 5.1 Anonymous Functions............................. 22 5.2 Currying..................................... 23 5.3 Example: Finding Fixed Points of Functions................ 25 5.4 Summary..................................... 28 5.5 Language Elements Seen So Far....................... 28 6 Classes and Objects 31 7 Case Classes and Pattern Matching 43 7.1 Case Classes and Case Objects........................ 46 7.2 Pattern Matching................................ 47 8 Generic Types and Methods 51 8.1 Type Parameter Bounds............................ 53 8.2 Variance Annotations.............................. 56 iv CONTENTS 8.3 Lower Bounds.................................. 58 8.4 Least Types.................................... 58 8.5 Tuples....................................... 60 8.6 Functions.................................... 61 9 Lists 63 9.1 Using Lists.................................... 63 9.2 Definition of class List I: First Order Methods.............. -
Lambda Expressions
Back to Basics Lambda Expressions Barbara Geller & Ansel Sermersheim CppCon September 2020 Introduction ● Prologue ● History ● Function Pointer ● Function Object ● Definition of a Lambda Expression ● Capture Clause ● Generalized Capture ● This ● Full Syntax as of C++20 ● What is the Big Deal ● Generic Lambda 2 Prologue ● Credentials ○ every library and application is open source ○ development using cutting edge C++ technology ○ source code hosted on github ○ prebuilt binaries are available on our download site ○ all documentation is generated by DoxyPress ○ youtube channel with over 50 videos ○ frequent speakers at multiple conferences ■ CppCon, CppNow, emBO++, MeetingC++, code::dive ○ numerous presentations for C++ user groups ■ United States, Germany, Netherlands, England 3 Prologue ● Maintainers and Co-Founders ○ CopperSpice ■ cross platform C++ libraries ○ DoxyPress ■ documentation generator for C++ and other languages ○ CsString ■ support for UTF-8 and UTF-16, extensible to other encodings ○ CsSignal ■ thread aware signal / slot library ○ CsLibGuarded ■ library for managing access to data shared between threads 4 Lambda Expressions ● History ○ lambda calculus is a branch of mathematics ■ introduced in the 1930’s to prove if “something” can be solved ■ used to construct a model where all functions are anonymous ■ some of the first items lambda calculus was used to address ● if a sequence of steps can be defined which solves a problem, then can a program be written which implements the steps ○ yes, always ● can any computer hardware -
PHP Advanced and Object-Oriented Programming
VISUAL QUICKPRO GUIDE PHP Advanced and Object-Oriented Programming LARRY ULLMAN Peachpit Press Visual QuickPro Guide PHP Advanced and Object-Oriented Programming Larry Ullman Peachpit Press 1249 Eighth Street Berkeley, CA 94710 Find us on the Web at: www.peachpit.com To report errors, please send a note to: [email protected] Peachpit Press is a division of Pearson Education. Copyright © 2013 by Larry Ullman Acquisitions Editor: Rebecca Gulick Production Coordinator: Myrna Vladic Copy Editor: Liz Welch Technical Reviewer: Alan Solis Compositor: Danielle Foster Proofreader: Patricia Pane Indexer: Valerie Haynes Perry Cover Design: RHDG / Riezebos Holzbaur Design Group, Peachpit Press Interior Design: Peachpit Press Logo Design: MINE™ www.minesf.com Notice of Rights All rights reserved. No part of this book may be reproduced or transmitted in any form by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. For information on getting permission for reprints and excerpts, contact [email protected]. Notice of Liability The information in this book is distributed on an “As Is” basis, without warranty. While every precaution has been taken in the preparation of the book, neither the author nor Peachpit Press shall have any liability to any person or entity with respect to any loss or damage caused or alleged to be caused directly or indirectly by the instructions contained in this book or by the computer software and hardware products described in it. Trademarks Visual QuickPro Guide is a registered trademark of Peachpit Press, a division of Pearson Education. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. -
Functional Programming Functional Vs. Imperative Referential
Functional vs. Imperative Referential transparency Imperative programming concerned with “how.” The main (good) property of functional programming is Functional Programming referential transparency. Functional programming concerned with “what.” COMS W4115 Every expression denotes a single value. Based on the mathematics of the lambda calculus Prof. Stephen A. Edwards (Church as opposed to Turing). The value cannot be changed by evaluating an expression Spring 2003 or by sharing it between different parts of the program. “Programming without variables” Columbia University No references to global data; there is no global data. Department of Computer Science It is inherently concise, elegant, and difficult to create subtle bugs in. There are no side-effects, unlike in referentially opaque Original version by Prof. Simon Parsons languages. It’s a cult: once you catch the functional bug, you never escape. The Joy of Pascal Strange behavior Variables program example(output) This prints 5 then 4. At the heart of the “problem” is fact that the global data var flag: boolean; flag affects the value of f. Odd since you expect function f(n:int): int In particular begin f (1) + f (2) = f (2) + f (1) if flag then f := n flag := not flag else f := 2*n; gives the offending behavior flag := not flag Mathematical functions only depend on their inputs end They have no memory Eliminating assignments eliminates such problems. begin In functional languages, variables not names for storage. flag := true; What does this print? Instead, they’re names that refer to particular values. writeln(f(1) + f(2)); writeln(f(2) + f(1)); Think of them as not very variables.