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Reversible Programming with Negative and Fractional Types
9 A Computational Interpretation of Compact Closed Categories: Reversible Programming with Negative and Fractional Types CHAO-HONG CHEN, Indiana University, USA AMR SABRY, Indiana University, USA Compact closed categories include objects representing higher-order functions and are well-established as models of linear logic, concurrency, and quantum computing. We show that it is possible to construct such compact closed categories for conventional sum and product types by defining a dual to sum types, a negative type, and a dual to product types, a fractional type. Inspired by the categorical semantics, we define a sound operational semantics for negative and fractional types in which a negative type represents a computational effect that “reverses execution flow” and a fractional type represents a computational effect that“garbage collects” particular values or throws exceptions. Specifically, we extend a first-order reversible language of type isomorphisms with negative and fractional types, specify an operational semantics for each extension, and prove that each extension forms a compact closed category. We furthermore show that both operational semantics can be merged using the standard combination of backtracking and exceptions resulting in a smooth interoperability of negative and fractional types. We illustrate the expressiveness of this combination by writing a reversible SAT solver that uses back- tracking search along freshly allocated and de-allocated locations. The operational semantics, most of its meta-theoretic properties, and all examples are formalized in a supplementary Agda package. CCS Concepts: • Theory of computation → Type theory; Abstract machines; Operational semantics. Additional Key Words and Phrases: Abstract Machines, Duality of Computation, Higher-Order Reversible Programming, Termination Proofs, Type Isomorphisms ACM Reference Format: Chao-Hong Chen and Amr Sabry. -
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. -
Dependency Injection with Unity
D EPEN DEPENDENCY INJECTION WITH UNITY Over the years software systems have evolutionarily become more and more patterns & practices D ENCY complex. One of the techniques for dealing with this inherent complexity Proven practices for predictable results of software systems is dependency injection – a design pattern that I allows the removal of hard-coded dependencies and makes it possible to Save time and reduce risk on your NJECT assemble a service by changing dependencies easily, whether at run-time software development projects by or compile-time. It promotes code reuse and loosely-coupled design which incorporating patterns & practices, I leads to more easily maintainable and flexible code. Microsoft’s applied engineering ON guidance that includes both production The guide you are holding in your hands is a primer on using dependency quality source code and documentation. W I injection with Unity – a lightweight extensible dependency injection TH DEPENDENCY INJECTION container built by the Microsoft patterns & practices team. It covers The guidance is designed to help U software development teams: various styles of dependency injection and also additional capabilities N I of Unity container, such as object lifetime management, interception, Make critical design and technology TY and registration by convention. It also discusses the advanced topics of selection decisions by highlighting WITH UNITY enhancing Unity with your custom extensions. the appropriate solution architectures, technologies, and Microsoft products The guide contains plenty of trade-off discussions and tips and tricks for for common scenarios managing your application cross-cutting concerns and making the most out of both dependency injection and Unity. These are accompanied by a Understand the most important Dominic Betts real world example that will help you master the techniques. -
Notes on Functional Programming with Haskell
Notes on Functional Programming with Haskell H. Conrad Cunningham [email protected] Multiparadigm Software Architecture Group Department of Computer and Information Science University of Mississippi 201 Weir Hall University, Mississippi 38677 USA Fall Semester 2014 Copyright c 1994, 1995, 1997, 2003, 2007, 2010, 2014 by H. Conrad Cunningham Permission to copy and use this document for educational or research purposes of a non-commercial nature is hereby granted provided that this copyright notice is retained on all copies. All other rights are reserved by the author. H. Conrad Cunningham, D.Sc. Professor and Chair Department of Computer and Information Science University of Mississippi 201 Weir Hall University, Mississippi 38677 USA [email protected] PREFACE TO 1995 EDITION I wrote this set of lecture notes for use in the course Functional Programming (CSCI 555) that I teach in the Department of Computer and Information Science at the Uni- versity of Mississippi. The course is open to advanced undergraduates and beginning graduate students. The first version of these notes were written as a part of my preparation for the fall semester 1993 offering of the course. This version reflects some restructuring and revision done for the fall 1994 offering of the course|or after completion of the class. For these classes, I used the following resources: Textbook { Richard Bird and Philip Wadler. Introduction to Functional Program- ming, Prentice Hall International, 1988 [2]. These notes more or less cover the material from chapters 1 through 6 plus selected material from chapters 7 through 9. Software { Gofer interpreter version 2.30 (2.28 in 1993) written by Mark P. -
Designpatternsphp Documentation Release 1.0
DesignPatternsPHP Documentation Release 1.0 Dominik Liebler and contributors Jul 18, 2021 Contents 1 Patterns 3 1.1 Creational................................................3 1.1.1 Abstract Factory........................................3 1.1.2 Builder.............................................8 1.1.3 Factory Method......................................... 13 1.1.4 Pool............................................... 18 1.1.5 Prototype............................................ 21 1.1.6 Simple Factory......................................... 24 1.1.7 Singleton............................................ 26 1.1.8 Static Factory.......................................... 28 1.2 Structural................................................. 30 1.2.1 Adapter / Wrapper....................................... 31 1.2.2 Bridge.............................................. 35 1.2.3 Composite............................................ 39 1.2.4 Data Mapper.......................................... 42 1.2.5 Decorator............................................ 46 1.2.6 Dependency Injection...................................... 50 1.2.7 Facade.............................................. 53 1.2.8 Fluent Interface......................................... 56 1.2.9 Flyweight............................................ 59 1.2.10 Proxy.............................................. 62 1.2.11 Registry............................................. 66 1.3 Behavioral................................................ 69 1.3.1 Chain Of Responsibilities................................... -
Design Patterns in Ocaml
Design Patterns in OCaml Antonio Vicente [email protected] Earl Wagner [email protected] Abstract The GOF Design Patterns book is an important piece of any professional programmer's library. These patterns are generally considered to be an indication of good design and development practices. By giving an implementation of these patterns in OCaml we expected to better understand the importance of OCaml's advanced language features and provide other developers with an implementation of these familiar concepts in order to reduce the effort required to learn this language. As in the case of Smalltalk and Scheme+GLOS, OCaml's higher order features allows for simple elegant implementation of some of the patterns while others were much harder due to the OCaml's restrictive type system. 1 Contents 1 Background and Motivation 3 2 Results and Evaluation 3 3 Lessons Learned and Conclusions 4 4 Creational Patterns 5 4.1 Abstract Factory . 5 4.2 Builder . 6 4.3 Factory Method . 6 4.4 Prototype . 7 4.5 Singleton . 8 5 Structural Patterns 8 5.1 Adapter . 8 5.2 Bridge . 8 5.3 Composite . 8 5.4 Decorator . 9 5.5 Facade . 10 5.6 Flyweight . 10 5.7 Proxy . 10 6 Behavior Patterns 11 6.1 Chain of Responsibility . 11 6.2 Command . 12 6.3 Interpreter . 13 6.4 Iterator . 13 6.5 Mediator . 13 6.6 Memento . 13 6.7 Observer . 13 6.8 State . 14 6.9 Strategy . 15 6.10 Template Method . 15 6.11 Visitor . 15 7 References 18 2 1 Background and Motivation Throughout this course we have seen many examples of methodologies and tools that can be used to reduce the burden of working in a software project. -
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.............. -
Simple Injector Documentation Release 5
Simple Injector Documentation Release 5 Simple Injector Contributors Jul 27, 2021 Contents 1 Quick Start 3 1.1 Overview.................................................3 1.2 Getting started..............................................3 1.3 A Quick Example............................................4 1.3.1 Dependency Injection......................................4 1.3.2 Introducing Simple Injector...................................5 1.4 More information.............................................6 2 Using Simple Injector 7 2.1 Resolving instances...........................................9 2.2 Configuring Simple Injector....................................... 10 2.2.1 Auto-Registration/Batch-registration.............................. 13 2.3 Collections................................................ 14 2.3.1 Collection types......................................... 16 2.3.2 Auto-registering collections.................................. 16 2.3.3 Adding registrations to an existing collection......................... 17 2.4 Verifying the container’s configuration................................. 17 2.5 Automatic constructor injection / auto-wiring.............................. 18 2.6 More information............................................. 19 3 Object Lifetime Management 21 3.1 Transient Lifestyle............................................ 22 3.2 Singleton Lifestyle............................................ 22 3.3 Scoped Lifestyle............................................. 23 3.3.1 Disposing a Scope...................................... -
61A Lecture 6 Lambda Expressions VS Currying
Announcements • Homework 2 due Tuesday 9/17 @ 11:59pm • Project 2 due Thursday 9/19 @ 11:59pm • Optional Guerrilla section next Monday for students to master higher-order functions . Organized by Andrew Huang and the readers 61A Lecture 6 . Work in a group on a problem until everyone in the group understands the solution • Midterm 1 on Monday 9/23 from 7pm to 9pm Friday, September 13 . Details and review materials will be posted early next week . There will be a web form for students who cannot attend due to a conflict 2 Lambda Expressions >>> ten = 10 An expression: this one evaluates to a number >>> square = x * x Also an expression: evaluates to a function Lambda Expressions >>> square = lambda x: x * x Important: No "return" keyword! A function with formal parameter x that returns the value of "x * x" >>> square(4) 16 Must be a single expression Lambda expressions are not common in Python, but important in general (Demo) Lambda expressions in Python cannot contain statements at all! 4 Lambda Expressions Versus Def Statements def square(x): square = lambda x: x * x VS return x * x • Both create a function with the same domain, range, and behavior. • Both functions have as their parent the environment in which they were defined. Currying • Both bind that function to the name square. • Only the def statement gives the function an intrinsic name. The Greek letter lambda Example: http://goo.gl/XH54uE 5 Function Currying def make_adder(n): return lambda k: n + k >>> make_adder(2)(3) There's a general 5 relationship between (Demo) >>> add(2, 3) these functions 5 Newton's Method Currying: Transforming a multi-argument function into a single-argument, higher-order function. -
CSE 341 : Programming Languages
CSE 341 : Programming Languages Lecture 10 Closure Idioms Zach Tatlock Spring 2014 More idioms • We know the rule for lexical scope and function closures – Now what is it good for A partial but wide-ranging list: • Pass functions with private data to iterators: Done • Combine functions (e.g., composition) • Currying (multi-arg functions and partial application) • Callbacks (e.g., in reactive programming) • Implementing an ADT with a record of functions (optional) 2 Combine functions Canonical example is function composition: fun compose (f,g) = fn x => f (g x) • Creates a closure that “remembers” what f and g are bound to • Type ('b -> 'c) * ('a -> 'b) -> ('a -> 'c) but the REPL prints something equivalent • ML standard library provides this as infix operator o • Example (third version best): fun sqrt_of_abs i = Math.sqrt(Real.fromInt(abs i)) fun sqrt_of_abs i = (Math.sqrt o Real.fromInt o abs) i val sqrt_of_abs = Math.sqrt o Real.fromInt o abs 3 Left-to-right or right-to-left val sqrt_of_abs = Math.sqrt o Real.fromInt o abs As in math, function composition is “right to left” – “take absolute value, convert to real, and take square root” – “square root of the conversion to real of absolute value” “Pipelines” of functions are common in functional programming and many programmers prefer left-to-right – Can define our own infix operator – This one is very popular (and predefined) in F# infix |> fun x |> f = f x fun sqrt_of_abs i = i |> abs |> Real.fromInt |> Math.sqrt 4 Another example • “Backup function” fun backup1 (f,g) = fn x => case -
1. Difference Between Factory Pattern and Abstract Factory Pattern S.No
1. Difference between Factory Pattern and Abstract Factory Pattern S.No Factory Pattern Abstract Factory Pattern 1 Create object through inheritance Create object through composition 2 Produce only one product Produce families of products 3 Implements code in the abstract creator Concrete factories implements factory that make use of the concrete type that method to create product sub class produces 2.Difference between Abstract Factory Pattern And Builder Pattern S.No Builder Pattern Abstract Factory Pattern 1 In Builder Pattern, there will be one Abstract Factory Pattern will return the Director class which will instruct Builder instance directly. class to build the different parts/properties of our object and finally retrieve the object. 2 It will have reference to the created It does not keep the track of it's created object. object. 3.Difference between Builder Pattern And Composite Pattern S.No Builder Pattern Composite Pattern 1 It is used to create group of objects of It creates Parent - Child relations between predefined types. our objects. 4.Difference between MVC and MVP S.No MVP MVC 1 MVP is a bit more complex to MVC is easier to implement than MVP. implement than MVC .Also, it has additional layer for view interfaces. 2 The request is always received by the The request is received by the controller View and delegated to the presenter which in turn gets the required data and which in turn gets the data does the loads up the appropriate view processing 3 The presentation and view logic an be The controller logic can be unit tested. -
CS 3101-2 - Programming Languages: Scala Lecture 3: Fun with Functions
CS 3101-2 - Programming Languages: Scala Lecture 3: Fun with Functions Daniel Bauer ([email protected]) October 29, 2014 Daniel Bauer CS3101-2 Scala - 03 - Fun with Functions 1/37 Contents 1 Defining and Calling Functions 2 Higher Order Functions 3 Function Literals 4 Closures 5 Partially Applied Functions and Currying 6 By-Name Parameters Daniel Bauer CS3101-2 Scala - 03 - Fun with Functions 2/37 1 Defining and Calling Functions 2 Higher Order Functions 3 Function Literals 4 Closures 5 Partially Applied Functions and Currying 6 By-Name Parameters Daniel Bauer CS3101-2 Scala - 03 - Fun with Functions 3/37 Functions and Methods Functions that are members of some object (class instance or singleton) are called methods. private keyword makes method visible only within this object. import scala.io.Source object LongLines { def processFile(filename: String, width: Int) { val source = Source.fromFile(filename) for (l <- source.getLines) procLine(filename, width, l) } private def procLine(filename: String, l: String) { if (l.length > 79) println(filename +": "+ l.trim) } } Daniel Bauer CS3101-2 Scala - 03 - Fun with Functions 4/37 Local Functions Functions can be defined within other functions. Functions are only visible in surrounding scope. Inner function can access namespace of surrounding function. import scala.io.Source object LongLines { def processFile(filename: String, width: Int) { def procLine(l: String) { if (l.length > 79) println(filename +": "+ l.trim) } val source = Source.fromFile(filename) for (l <- source.getLines) procLine(filename, width, l) } } Daniel Bauer CS3101-2 Scala - 03 - Fun with Functions 5/37 Repeated Parameters The last parameter of a function may be repeated.