Commutative Monads, Diagrams and Knots. Dan Piponi. Industrial Light & Magic, San Francisco [email protected] Abstract. There is certain diverse class of. Commutative monads diagrams and. knots pdf. Commutative monads diagrams and Commutative monads diagrams and knots pdf knots pdf. DOWNLOAD!. Commutative monads diagrams and knots pdf. none ab55cfc. PenIMC. or, if you have already installed an earlier copy from the product CD.
|Published (Last):||25 March 2011|
|PDF File Size:||13.59 Mb|
|ePub File Size:||15.64 Mb|
|Price:||Free* [*Free Regsitration Required]|
You may hide this message. To insert individual citation into a bibliography in a word-processor, you can open the article, select your preferred citation style and drag-and-drop it into the document. The author gives a calculus based on a categorical semantics for computations, which provides diaggams correct basis for proving equivalence of programs, independent from any specific computational model We design and implement a library that solves the long-standing problem of combining effects without imposing restrictions on their interactions such as static ordering.
Effects arise from interactions between a client and an effect handler interpreter ; interactions may vary throughout the program and dynamically adapt to execution conditions. Existing code that relies on monad transformers commmutative be used with our library with minor changes, gaining efficiency over long monad stacks.
In addition, our library has greater expressiveness, allowing for practical idioms The materiality of interactive artifacts concerns, on one hand, design materials and activities, while on the other hand, it is strongly related to commutatove users experiencing the materiality. However, current approaches to investigate the material and the user perspective face several commutafive, as they focus on either the human or the artifact. In our paper, we describe a materiality-centered data analysis approach that puts the user and the artifact equally in the center of attention.
A Neighborhood of Infinity
Based on Actor-Network Theory and Bruno This paper describes the history of Haskell, including its genesis and principles, technical contributions, implementations and tools, and applications and impact. The use of monads to structure functional programs is described.
Monads provide a convenient framework for simulating effects found in other languages, such as global state, exception handling, output, or non-determinism. Three case studies are looked at in detail: Category theorists invented monads commutatiev the ‘s to concisely express certain aspects of universal algebra.
Functional programmers invented list comprehensions in the ‘s to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised to an arbitrary monad, and how the resulting programming feature can concisely express in a pure functional language some programs that manipulate state, handle exceptions, parse text, or invoke continuations In this paper we introduce calculi based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs, As part of the development, we extend Meyer and Wand’s characterization of the relationship between continuation-passing and direct style monafs one for continuation-passing vs.
We further show that the composable-continuations construct can itself be represented using ordinary, non-composable first-class continuations and a single piece of state. Thus, in the presence of two QuickCheck is a previously published random testing tool for Haskell programs.
In this paper we show how to use it for testing monadic code, and in particular imperative code written using the ST monad. QuickCheck tests a program against a specification: Moreover, all these forms of specification can be used directly for testing. We define a new language Moggi’s Computational Monads and Power et al. We present generalisations ccommutative both computational monads and Freyd categories, which we call parameterised monads and parameterised Freyd categories, that also capture computational effects with parameters.
We present new ways of reasoning about a particular class of effectful Haskell programs, namely those expressed as idiomatic traversals.
Starting out with a specific problem about labelling and unlabelling binary trees, we extract a general inversion law, applicable to any monad, relating a traversal over the elements of dkagrams arbitrary traversable type to a traversal that goes in the opposite direction.
This law can be invoked to show that, in a suitable sense, unlabelling is the inverse of labelling. Functional programming may be beautiful, but to write real applications we must grapple with awkward real-world issues: Pleasingly, the arrow interface turned out to be applicable to other kinds of non-monadic library also, for example the fudgets library for graphical user interfaces [CH93], and a new library for programming active web pages. These applications will be described in sections 6 and 9.
While arrows snd a little less convenient to use than monads, they have significantly wider applicability. They can therefore be used to bring the benefits of monad-like programming to a much wider class Monads have become very popular for structuring functional programs since Wadler introduced their use in In particular, libraries of combinators are often based on a monadic type.
Such libraries share in part a common interface, from which numerous benefits flow, such as the possibility to write generic code which works together with any library.
But, several interesting and useful libraries are fundamentally incompatible with the monadic commutativ. In this paper I propose a generalisation of monads, which I call arrows, A tension in language design has been between simple semantics on the one hand, and rich possibilities for side-effects, exception handling and so on on the other.
The introduction of monads has made a large step towards reconciling these alternatives.
First proposed by Moggi as a way of structuring semantic descriptions, they were adopted by Wadler to structure Haskell programs, and now offer a general technique for delimiting the scope of effects, thus reconciling referential We revisit the connection between three notions of computation: Further, idioms embed into arrows and arrows embed into monads.
They can therefore be used to bring the benefits of monad-like programming to a much wider class of Consider this simple Haskell definition, of a function which counts the number of occurrences of a given word in a string: Point-free programming is rightly popular: This paper explores the use monads to structure functional programs.
No prior knowledge of monads or category theory is required.
Monads increase the ease with which programs may be modified. They can mimic the effect of impure features such as commutayive, state, and continuations; and also provide effects not easily achieved with such features. The types of a program reflect which effects occur. The first section is an extended example of the use of monads. A simple interpreter is modified to support various extra features: Without adding any primitives to the language, we define a concurrency monad transformer in Haskell.
This allows us to add a limited form of concurrency to any existing monad. The atomic actions of the new monad are lifted actions of the underlying monad.
Some extra operations, such as forkto initiate new processes, are provided. We discuss the implementation, and use some examples to illustrate the usefulness of this construction. Moggi’s original paper on applying monads to programming, specifically looking at using them for defining denotational semantics. This paper shows how list comprehensions may be generalised to an arbitrary monad, and how the resulting programming feature can concisely express in a pure functional language some programs that manipulate state, handle exceptions, parse text, or invoke continuations.
A new solution to the old problem of destructive array update is Wadler explains how monads can be used for adding impure features to pure languages, and gives a list-comprehension-like system for expressing monads.
dblp: Dan Piponi
One of the appeals of pure functional programming is that it is so amenable to equational reasoning. One of the problems of pure functional programming is that it rules out computational effects. Moggi and Wadler showed how to get round this problem by using monads to encapsulate the effects, leading in essence to a phase distinction – a pure functional evaluation yielding an impure imperative computation.
Still, it has not been clear how to reconcile that phase distinction with the continuing Many useful programming constructions can be jonads as monads. There is certain diverse class of diagram that is found in a variety of branches of mathematics and which all share this property: These diagrams include Knos networks, quantum computer circuits , trace diagrams for multilinear algebra , Feynman diagrams and even knot diagrams .
I will show how a common thread lying behind these diagrams is the presence of a commutative monad and I will VDM descriptions of programming languages differ from the original Scott—Strachey style by making extensive use of combinators which have a fixed operational interpretation.
We also suggest that use of further monadic We present an algebraic treatment of exception handlers and, more generally, introduce handlers for other computational effects representable by an algebraic theory.
A Neighborhood of Infinity: March
Each such handler corresponds to a model of the theory for the effects at hand. The handling construct, which applies a handler to a computation, is based on the one introduced by Benton and Kennedy, The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved.
We make explicit a link between our theory and the theory of Schwartz distributions of compact support. We also discuss ,nots distributions. This is a tutorial for mathematically inclined functional programmers, based on previously published, peered reviewed theoretical work. We discuss a higher-type functional, written here in the functional programming language Haskell, which 1 optimally plays sequential games, 2 implements a computational version of the Tychonoff Theorem from topology, and 3 realizes the Double-Negation Shift from logic and proof theory.
Commutative monads, diagrams and knots
The functional makes sense for finite and infinite lazy lists, and in the binary case it amounts to an operation that is available We explore the logical underpinnings of higher-order, security-typed languages with mutable state.
Our analysis is based on a logic of information flow derived from lax logic and the monadic metalanguage. Thus, our logic deals with mutation explicitly, with impurity reflected in the types, in contrast to most higher-order security-typed languages, which deal with mutation implicitly via side-effects.
More importantly, we also take a store-oriented view of security, wherein security levels are associated with elements of the mutable store.
In functional programming, a popular approach to building recursive descent parsers is to model parsers as functions, and to define higher-order functions or combinators that implement grammar constructions such as sequencing, choice, and repetition.
Such parsers form an instance of a monadan algebraic structure from mathematics that has proved useful for addressing a number of computational problems.
The purpose of this article is to provide a step-by-step tutorial on the monadic approach Locality and non-contextuality are intuitively appealing features of classical physics, which are contradicted by quantum mechanics. The goal of the classic no-go theorems by Bell, Kochen-Specker, et al. We use the mathematics of sheaf theory to analyze the structure of non-locality and contextuality in a very general setting. Starting from a simple experimental scenario, and the kind of probabilistic models familiar from discussions of Bell’s theorem, we show