What Is Functional Programming
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Causal Commutative Arrows Revisited
Causal Commutative Arrows Revisited Jeremy Yallop Hai Liu University of Cambridge, UK Intel Labs, USA [email protected] [email protected] Abstract init which construct terms of an overloaded type arr. Most of the Causal commutative arrows (CCA) extend arrows with additional code listings in this paper uses these combinators, which are more constructs and laws that make them suitable for modelling domains convenient for defining instances, in place of the notation; we refer such as functional reactive programming, differential equations and the reader to Paterson (2001) for the details of the desugaring. synchronous dataflow. Earlier work has revealed that a syntactic Unfortunately, speed does not always follow succinctness. Al- transformation of CCA computations into normal form can result in though arrows in poetry are a byword for swiftness, arrows in pro- significant performance improvements, sometimes increasing the grams can introduce significant overhead. Continuing with the ex- speed of programs by orders of magnitude. In this work we refor- ample above, in order to run exp, we must instantiate the abstract mulate the normalization as a type class instance and derive op- arrow with a concrete implementation, such as the causal stream timized observation functions via a specialization to stream trans- transformer SF (Liu et al. 2009) that forms the basis of signal func- formers to demonstrate that the same dramatic improvements can tions in the Yampa domain-specific language for functional reactive be achieved without leaving the language. programming (Hudak et al. 2003): newtype SF a b = SF {unSF :: a → (b, SF a b)} Categories and Subject Descriptors D.1.1 [Programming tech- niques]: Applicative (Functional) Programming (The accompanying instances for SF , which define the arrow operators, appear on page 6.) Keywords arrows, stream transformers, optimization, equational Instantiating exp with SF brings an unpleasant surprise: the reasoning, type classes program runs orders of magnitude slower than an equivalent pro- gram that does not use arrows. -
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. -
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. -
An Exploration of the Effects of Enhanced Compiler Error Messages for Computer Programming Novices
Technological University Dublin ARROW@TU Dublin Theses LTTC Programme Outputs 2015-11 An Exploration Of The Effects Of Enhanced Compiler Error Messages For Computer Programming Novices Brett A. Becker Technological University Dublin Follow this and additional works at: https://arrow.tudublin.ie/ltcdis Part of the Computer and Systems Architecture Commons, and the Educational Methods Commons Recommended Citation Becker, B. (2015) An exploration of the effects of enhanced compiler error messages for computer programming novices. Thesis submitted to Technologicl University Dublin in part fulfilment of the requirements for the award of Masters (M.A.) in Higher Education, November 2015. This Theses, Masters is brought to you for free and open access by the LTTC Programme Outputs at ARROW@TU Dublin. It has been accepted for inclusion in Theses by an authorized administrator of ARROW@TU Dublin. For more information, please contact [email protected], [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License An Exploration of the Effects of Enhanced Compiler Error Messages for Computer Programming Novices A thesis submitted to Dublin Institute of Technology in part fulfilment of the requirements for the award of Masters (M.A.) in Higher Education by Brett A. Becker November 2015 Supervisor: Dr Claire McDonnell Learning Teaching and Technology Centre, Dublin Institute of Technology Declaration I certify that this thesis which I now submit for examination for the award of Masters (M.A.) in Higher Education is entirely my own work and has not been taken from the work of others, save and to the extent that such work has been cited and acknowledged within the text of my own work. -
Directing Javascript with Arrows
Directing JavaScript with Arrows Khoo Yit Phang Michael Hicks Jeffrey S. Foster Vibha Sazawal University of Maryland, College Park {khooyp,mwh,jfoster,vibha}@cs.umd.edu Abstract callback with a (short) timeout. Unfortunately, this style of event- JavaScript programmers make extensive use of event-driven pro- driven programming is tedious, error-prone, and hampers reuse. gramming to help build responsive web applications. However, The callback sequencing code is strewn throughout the program, standard approaches to sequencing events are messy, and often and very often each callback must hard-code the names of the next lead to code that is difficult to understand and maintain. We have events and callbacks in the chain. found that arrows, a generalization of monads, are an elegant solu- To combat this problem, many researchers and practitioners tion to this problem. Arrows allow us to easily write asynchronous have developed libraries to ease the construction of rich and highly programs in small, modular units of code, and flexibly compose interactive web applications. Examples include jQuery (jquery. them in many different ways, while nicely abstracting the details of com), Prototype (prototypejs.org), YUI (developer.yahoo. asynchronous program composition. In this paper, we present Ar- com/yui), MochiKit (mochikit.com), and Dojo (dojotoolkit. rowlets, a new JavaScript library that offers arrows to the everyday org). These libraries generally provide high-level APIs for com- JavaScript programmer. We show how to use Arrowlets to construct mon features, e.g., drag-and-drop, animation, and network resource a variety of state machines, including state machines that branch loading, as well as to handle API differences between browsers. -
The Glasgow Haskell Compiler User's Guide, Version 4.08
The Glasgow Haskell Compiler User's Guide, Version 4.08 The GHC Team The Glasgow Haskell Compiler User's Guide, Version 4.08 by The GHC Team Table of Contents The Glasgow Haskell Compiler License ........................................................................................... 9 1. Introduction to GHC ....................................................................................................................10 1.1. The (batch) compilation system components.....................................................................10 1.2. What really happens when I “compile” a Haskell program? .............................................11 1.3. Meta-information: Web sites, mailing lists, etc. ................................................................11 1.4. GHC version numbering policy .........................................................................................12 1.5. Release notes for version 4.08 (July 2000) ........................................................................13 1.5.1. User-visible compiler changes...............................................................................13 1.5.2. User-visible library changes ..................................................................................14 1.5.3. Internal changes.....................................................................................................14 2. Installing from binary distributions............................................................................................16 2.1. Installing on Unix-a-likes...................................................................................................16 -
SOME USEFUL STRUCTURES for CATEGORICAL APPROACH for PROGRAM BEHAVIOR in Computer Science, Where We Often Use More Complex Structures Not Expressible by Sets
JIOS, VOL. 35, NO. 1 (2011) SUBMITTED 02/11; ACCEPTED 03/11 UDC 004.423.45 [ SomeSome useful Useful structures Structures for categorical for Categorical approach Approach for program for Programbehavior Behavior Viliam Slodicákˇ [email protected] Department of Computers and Informatics Faculty of Electrical Engineering and Informatics Technical university of Košice Letná 9, 042 00 Košice Slovak Republic Abstract Using of category theory in computer science has extremely grown in the last decade. Categories allow us to express mathematical structures in unified way. Algebras are used for constructing basic structures used in computer programs. A program can be considered as an element of the initial algebra arising from the used programming language. In our contribution we formulate two ways of expressing algebras in categories. We also construct the codomain functor from the arrow category of algebras into the base category of sets which objects are also the carrier-sets of the algebras. This functor expresses the relation between algebras and carrier-sets. Keywords: Algebra, arrow category, monad, Kleisli category, codomain functor 1. Introduction Knowing and proving of the expected behavior of complex program systems is very important and actual rôle. It carries the time and cost savings: in mathematics [8] or in practical applications of economical character. The aim of programming is to construct such correct programs and program systems that during their execution provide expected behavior [7]. A program can be considered as an element of the initial algebra arising from the used programming language [14]. Algebraic structures and number systems are widely used in computer science. -
The Bluej Environment Reference Manual
The BlueJ Environment Reference Manual Version 2.0 for BlueJ Version 2.0 Kasper Fisker Michael Kölling Mærsk Mc-Kinney Moller Institute University of Southern Denmark HOW DO I ... ? – INTRODUCTION ........................................................................................................ 1 ABOUT THIS DOCUMENT................................................................................................................................. 1 RELATED DOCUMENTS.................................................................................................................................... 1 REPORT AN ERROR.......................................................................................................................................... 1 USING THE CONTEXT MENU........................................................................................................................... 1 1 PROJECTS.......................................................................................................................................... 2 1.1 CREATE A NEW PROJECT................................................................................................................... 2 1.2 OPEN A PROJECT ............................................................................................................................... 2 1.3 FIND OUT WHAT A PROJECT DOES .................................................................................................... 2 1.4 COPY A PROJECT .............................................................................................................................. -
Companion Object
1. Functional Programming Functional Programming What is functional programming? What is it good for? Why to learn it? Functional Programming Programs as a composition of pure functions. Pure function? Deterministic. Same result for the same inputs. Produces no observable side eects. fun mergeAccounts(acc1: Account, acc2: Account): Account = Account(acc1.balance + acc2.balance) val mergedAcc = mergeAccounts(Account(500), Account(1000)) Target platform: JVM Running on Arrow v. 0.11.0-SNAPSHOT Running on Kotlin v. 1.3.50 Referential Transparency Function can be replaced with its corresponding value without changing the program's behavior. Based on the substitution model. Referential Transparency Better reasoning about program behavior. Pure functions referentially transparent. Substitution model Replace a named reference (function) by its value. Based on equational reasoning. Unlocks local reasoning. fun add(a: Int, b: Int): Int = a + b val two = add(1, 1) // could be replaced by 2 everywhere in the program val equal = (two == 1 + 1) Target platform: JVM Running on Arrow v. 0.11.0-SNAPSHOT Running on Kotlin v. 1.3.50 Substitution model Same example, but with two Accounts. fun mergeAccounts(acc1: Account, acc2: Account): Account = Account(acc1.balance + acc2.balance) val mergedAcc = mergeAccounts(Account(100), Account(200)) // could be replaced by Account(300) everywhere // in the program val equal = (mergedAcc == Account(300)) Target platform: JVM Running on Arrow v. 0.11.0-SNAPSHOT Running on Kotlin v. 1.3.50 Side eect? Function tries to access or modify the external world. val accountDB = AccountDB() fun mergeAccounts(acc1: Account, acc2: Account): Account { val merged = Account(acc1.balance + acc2.balance) accountDB.remove(listOf(acc1, acc2)) // side effect! accountDB.save(merged) // side effect! return merged } val merged = mergeAccounts(Account(100), Account(400)) Target platform: JVM Running on Arrow v. -
It's All About Morphisms
It’s All About Morphisms Uberto Barbini @ramtop https://medium.com/@ramtop About me OOP programmer Agile TDD Functional PRogramming Finance Kotlin Industry Blog: https://medium.com/@ ramtop Twitter: @ramtop #morphisms#VoxxedVienna @ramtop Map of this presentation Monoid Category Monad Functor Natural Transformation Yoneda Applicative Morphisms all the way down... #morphisms#VoxxedVienna @ramtop I don’t care about Monads, why should I? Neither do I what I care about is y el is to define system behaviour ec Pr #morphisms#VoxxedVienna @ramtop This presentation will be a success if most of you will not fall asleep #morphisms#VoxxedVienna @ramtop This presentation will be a success if You will consider that Functional Programming is about transformations and preserving properties. Not (only) lambdas and flatmap #morphisms#VoxxedVienna @ramtop What is this Category thingy? Invented in 1940s “with the goal of understanding the processes that preserve mathematical structure.” “Category Theory is about relation between things” “General abstract nonsense” #morphisms#VoxxedVienna @ramtop Once upon a time there was a Category of Stuffed Toys and a Category of Tigers... #morphisms#VoxxedVienna @ramtop A Category is defined in 5 steps: 1) A collection of Objects #morphisms#VoxxedVienna @ramtop A Category is defined in 5 steps: 2) A collection of Arrows #morphisms#VoxxedVienna @ramtop A Category is defined in 5 steps: 3) Each Arrow works on 2 Objects #morphisms#VoxxedVienna @ramtop A Category is defined in 5 steps: 4) Arrows can be combined #morphisms#VoxxedVienna -
Mechanized Reasoning During Compilation in the Glasgow Haskell Compiler
HERMIT: Mechanized Reasoning during Compilation in the Glasgow Haskell Compiler By Andrew Farmer Submitted to the graduate degree program in Electrical Engineering and Computer Science and the Graduate Faculty of the University of Kansas in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Chairperson Dr. Andy Gill Dr. Perry Alexander Dr. Prasad Kulkarni Dr. James Miller Dr. Christopher Depcik Date Defended: April 30, 2015 The Dissertation Committee for Andrew Farmer certifies that this is the approved version of the following dissertation: HERMIT: Mechanized Reasoning during Compilation in the Glasgow Haskell Compiler Chairperson Dr. Andy Gill Date approved: ii Abstract It is difficult to write programs which are both correct and fast. A promising approach, functional programming, is based on the idea of using pure, mathematical functions to construct programs. With effort, it is possible to establish a connection between a specification written in a functional language, which has been proven correct, and a fast implementation, via program transformation. When practiced in the functional programming community, this style of reasoning is still typ- ically performed by hand, by either modifying the source code or using pen-and-paper. Unfortu- nately, performing such semi-formal reasoning by directly modifying the source code often obfus- cates the program, and pen-and-paper reasoning becomes outdated as the program changes over time. Even so, this semi-formal reasoning prevails because formal reasoning is time-consuming, and requires considerable expertise. Formal reasoning tools often only work for a subset of the target language, or require programs to be implemented in a custom language for reasoning.