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Zipper (data Structure)
A zipper is a technique of representing an aggregate data structure so that it is convenient for writing programs that traverse the structure arbitrarily and update its contents, especially in purely functional programming languages. The zipper was described by Gérard Huet in 1997. It includes and generalizes the gap buffer technique sometimes used with arrays. The zipper technique is general in the sense that it can be adapted to List (computing), lists, Tree (data structure), trees, and other Recursive data type, recursively defined data structures. Such modified data structures are usually referred to as "a tree with zipper" or "a list with zipper" to emphasize that the structure is conceptually a tree or list, while the zipper is a detail of the implementation. A layperson's explanation for a tree with zipper would be an ordinary computer filesystem with operations to go to parent (often cd (command), cd ..), and the possibility to go downwards (cd subdirectory). The zipper is ...
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Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ...
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Sum Type
In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type or coproduct, is a data structure used to hold a value that could take on several different, but fixed, types. Only one of the types can be in use at any one time, and a tag field explicitly indicates which one is in use. It can be thought of as a type that has several "cases", each of which should be handled correctly when that type is manipulated. This is critical in defining recursive datatypes, in which some component of a value may have the same type as the value itself, for example in defining a type for representing trees, where it is necessary to distinguish multi-node subtrees and leaves. Like ordinary unions, tagged unions can save storage by overlapping storage areas for each type, since only one is in use at a time. Description Tagged unions are most important in functional languages such as ML and Haskell, where they are called dataty ...
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Filesystem
In computing, file system or filesystem (often abbreviated to fs) is a method and data structure that the operating system uses to control how data is stored and retrieved. Without a file system, data placed in a storage medium would be one large body of data with no way to tell where one piece of data stopped and the next began, or where any piece of data was located when it was time to retrieve it. By separating the data into pieces and giving each piece a name, the data are easily isolated and identified. Taking its name from the way a paper-based data management system is named, each group of data is called a "file". The structure and logic rules used to manage the groups of data and their names is called a "file system." There are many kinds of file systems, each with unique structure and logic, properties of speed, flexibility, security, size and more. Some file systems have been designed to be used for specific applications. For example, the ISO 9660 file system is designe ...
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Automated Theorem Prover
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. Logical foundations While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics. Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His ''Foundations of Arithmetic'', published 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential ''Principia Mathematica'', first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms and inference ...
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Structural Editor
A structure editor, also structured editor or projectional editor, is any document editor that is cognizant of the document's underlying structure. Structure editors can be used to edit hierarchical or marked up text, computer programs, diagrams, chemical formulas, and any other type of content with clear and well-defined structure. In contrast, a text editor is any document editor used for editing plain text files. Typically, the benefits of text and structure editing are combined in the user interface of a single hybrid tool. For example, Emacs is fundamentally a text editor, but supports the manipulation of words, sentences, and paragraphs as structures that are inferred from the text. Conversely, Dreamweaver is fundamentally a structure editor for marked up web documents, but supports the display and manipulation of raw HTML text as well. Similarly, molecule editors typically support both graphical and textual input. Structure editing predominates when content is graphical a ...
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Window (computing)
In computing, a window is a graphical control element. It consists of a visual area containing some of the graphical user interface of the program it belongs to and is framed by a window decoration. It usually has a rectangular shape that can overlap with the area of other windows. It displays the ''output'' of and may allow ''input'' to one or more processes. Windows are primarily associated with graphical displays, where they can be manipulated with a pointer by employing some kind of pointing device. Text-only displays can also support windowing, as a way to maintain multiple independent display areas, such as multiple buffers in Emacs. Text windows are usually controlled by keyboard, though some also respond to the mouse. A graphical user interface (GUI) using windows as one of its main "metaphors" is called a windowing system, whose main components are the display server and the window manager. History The idea was developed at the Stanford Research Institute (led by D ...
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Xmonad
xmonad is a dynamic window manager (tiling) for the X Window System, noted for being written in the functional programming language Haskell. Window manager Begun in March 2007, version 0.1 was announced in April 2007 as 500 lines of Haskell. xmonad is a tiling window manager—akin to dwm, larswm, and StumpWM. It arranges windows in a non-overlapping pattern, and enables managing windows without using the mouse. xmonad is packaged and distributed on a wide range of Unix-like operating systems, such as a large number of Linux distributions, and BSD systems. While originally a clone of dwm (derivative in areas such as default keybindings), xmonad now supports features not available to dwm users such as per-workspace layout, tiling reflection, state preservation, layout mirroring, GNOME support and per-screen status bars; it can be customised by modifying an external configuration file and 'reloaded' while running. xmonad features have begun to influence other tiling window m ...
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Focus (computing)
In computing, focus indicates the act of selecting an element of a graphical user interface. Text entered at the keyboard or pasted from a clipboard is sent to the component which has the focus. Moving the focus away from a specific user interface element is known as a blur event in relation to this element. Typically, the focus is withdrawn from an element by giving another element the focus. This means that focus and blur events typically both occur virtually simultaneously, but in relation to different user interface elements, one that gets the focus and one that gets blurred. The concept is similar to a cursor in a text-based environment. However, when considering a graphical interface, there is also a mouse pointer involved. Moving the mouse will typically move the mouse pointer without changing the focus. The focus can usually be changed by clicking on a component that can receive focus with the mouse. Many desktops also allow the focus to be changed with the keyboard. By co ...
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Boolean Data Type
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted ''true'' and ''false'') which is intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in ..., who first defined an algebraic system of logic in the mid 19th century. The Boolean data type is primarily associated with Conditional (computer programming), conditional statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean ''condition'' evaluates to true or false. It is a special case of a more general ''logical data type—''logic does not always need to be Boolean (see probabilistic logic). Generali ...
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Sentinel Node
In computer programming, a sentinel node is a specifically designated node used with linked lists and trees as a traversal path terminator. This type of node does not hold or reference any data managed by the data structure. Benefits Sentinels are used as an alternative over using NULL as the path terminator in order to get one or more of the following benefits: * Marginally increased speed of operations * Increased data structure robustness (arguably) Drawbacks * Marginally increased algorithmic complexity and code size. * If the data structure is accessed concurrently (which means that all nodes being accessed have to be protected at least for “read-only”), for a sentinel-based implementation the sentinel node has to be protected for “read-write” by a mutex. This extra mutex in quite a few use scenarios can cause severe performance degradation. One way to avoid it is to protect the list structure as a whole for “read-write”, whereas in the version with NULL i ...
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Conor McBride
Conor McBride (born 18 February 1973) is a Reader in the department of Computer and Information Sciences at the University of Strathclyde. In 1999, he completed a Doctor of Philosophy (Ph.D.) in ''Dependently Typed Functional Programs and their Proofs'' at the University of Edinburgh for his work in type theory. He formerly worked at Durham University and briefly at Royal Holloway, University of London before joining the academic staff at the University of Strathclyde. He was involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He favors and often uses the language Haskell. Research His most notable research is in the field of type theory. He cocreated the programming language Epigram with James McKinna. Several of his art ...
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Power Rule
In calculus, the power rule is used to differentiate functions of the form f(x) = x^r, whenever r is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function's derivatives. Statement of the power rule Let f be a function satisfying f(x)=x^r for all x, where r \in \mathbb. Then, :f'(x) = rx^ \, . The power rule for integration states that :\int\! x^r \, dx=\frac+C for any real number r \neq -1. It can be derived by inverting the power rule for differentiation. In this equation C is any constant. Proofs Proof for real exponents To start, we should choose a working definition of the value of f(x) = x^r, where r is any real number. Although it is feasible to define the value as the limit of a sequence of rational powers that approach the irrational power whenever we encounter such a power, or ...
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