|
Parametricity
In programming language theory, parametricity is an abstract uniformity property enjoyed by parametrically polymorphic functions, which captures the intuition that all instances of a polymorphic function act the same way. Idea Consider this example, based on a set ''X'' and the type ''T''(''X'') = 'X'' → ''X''of functions from ''X'' to itself. The higher-order function ''twice''''X'' : ''T''(''X'') → ''T''(''X'') given by ''twice''''X''(''f'') = ''f'' ∘ ''f'', is intuitively independent of the set ''X''. The family of all such functions ''twice''''X'', parametrized by sets ''X'', is called a " parametrically polymorphic function". We simply write twice for the entire family of these functions and write its type as \forall''X''. ''T''(''X'') → ''T''(''X''). The individual functions ''twice''''X'' are called the ''components'' or ''instances'' of the polymorphic function. Notice that all the component functions ''twice''''X'' act "the same way" because they are given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language Theory
Programming language theory (PLT) is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of formal languages known as programming languages. Programming language theory is closely related to other fields including mathematics, software engineering, and linguistics. There are a number of academic conferences and journals in the area. History In some ways, the history of programming language theory predates even the development of programming languages themselves. The lambda calculus, developed by Alonzo Church and Stephen Cole Kleene in the 1930s, is considered by some to be the world's first programming language, even though it was intended to ''model'' computation rather than being a means for programmers to ''describe'' algorithms to a computer system. Many modern functional programming languages have been described as providing a "thin veneer" over the lambda calculus, and many are easily described in te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Polymorphism
In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism. Parametrically polymorphic definitions are ''uniform'': they behave identically regardless of the type they are instantiated at. In contrast, ad hoc polymorphic definitions are given a distinct definition for each type. Thus, ad hoc polymorphism can generally only support a limited number of such distinct types, since a separate implementation has to be provided for each type. Basic definition It is possible to write functions that do not depend on the types of their arguments. For example, the identity function \math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ad Hoc Polymorphism
In programming languages, ad hoc polymorphismC. StracheyFundamental concepts in programming languages Lecture notes for International Summer School in Computer Programming, Copenhagen, August 1967 is a kind of polymorphism in which polymorphic functions can be applied to arguments of different types, because a polymorphic function can denote a number of distinct and potentially heterogeneous implementations depending on the type of argument(s) to which it is applied. When applied to object-oriented or procedural concepts, it is also known as function overloading or operator overloading. The term ad hoc in this context is not intended to be pejorative; it refers simply to the fact that this type of polymorphism is not a fundamental feature of the type system. This is in contrast to parametric polymorphism, in which polymorphic functions are written without mention of any specific type, and can thus apply a single abstract implementation to any number of types in a transparent way. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Church Encoding
In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way. Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function. Use A straightforward implementation of Church encoding slows some access operations from O(1) to O(n), where n is the size of the data structure, making Church encoding impractical. Research has shown that this can be addressed by targeted optimizations, but most functional programming languages instead expand their in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John C
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip Wadler
Philip Lee Wadler (born April 8, 1956) is an American computer scientist known for his contributions to programming language design and type theory. He is the chair of Theoretical Computer Science at the Laboratory for Foundations of Computer Science at School of Informatics, University of Edinburgh. He has contributed to the theory behind functional programming and the use of monads in functional programming, the design of the purely functional language Haskell, and the XQuery declarative query language. In 1984, he created the Orwell programming language. Wadler was involved in adding generic types to Java 5.0. He is also author of the paper ''Theorems for free!'' that gave rise to much research on functional language optimization (see also Parametricity). Education Wadler received a Bachelor of Science degree in mathematics from Stanford University in 1977, and a Master of Science degree in Computer Science from Carnegie Mellon University in 1979. He completed his Doctor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Program Transformation
A program transformation is any operation that takes a computer program and generates another program. In many cases the transformed program is required to be semantically equivalent to the original, relative to a particular formal semantics and in fewer cases the transformations result in programs that semantically differ from the original in predictable ways. While the transformations can be performed manually, it is often more practical to use a program transformation system that applies specifications of the required transformations. Program transformations may be specified as automated procedures that modify compiler data structures (e.g. abstract syntax trees) representing the program text, or may be specified more conveniently using patterns or templates representing parameterized source code fragments. A practical requirement for source code transformation systems is that they be able to effectively process programs written in a programming language. This usually require ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell Programming Language
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strict Function
In computer science and computer programming, a function f is said to be strict if, when applied to a non-terminating expression, it also fails to terminate. A strict function in the denotational semantics of programming languages is a function ''f'' where f\left(\perp\right) = \perp. The entity \perp, called ''bottom'', denotes an expression that does not return a normal value, either because it loops endlessly or because it aborts due to an error such as division by zero. A function that is not strict is called non-strict. A strict programming language is one in which user-defined functions are always strict. Intuitively, non-strict functions correspond to control structures. Operationally, a strict function is one that always evaluates its argument; a non-strict function is one that might not evaluate some of its arguments. Functions having more than one parameter can be strict or non-strict in each parameter independently, as well as ''jointly strict'' in several parameters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lazy Evaluation
In programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which also avoids repeated evaluations (sharing). The benefits of lazy evaluation include: * The ability to define control flow (structures) as abstractions instead of primitives. * The ability to define potentially infinite data structures. This allows for more straightforward implementation of some algorithms. * The ability to define partially-defined data structures where some elements are errors. This allows for rapid prototyping. Lazy evaluation is often combined with memoization, as described in Jon Bentley's ''Writing Efficient Programs''. After a function's value is computed for that parameter or set of parameters, the result is stored in a lookup table that is indexed by the values of those parameters; the next time the function is called, the table is consulted to determine whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patricia Johann
Patricia is a female given name of Latin origin. Derived from the Latin word ''patrician'', meaning "noble"; it is the feminine form of the masculine given name Patrick. The name Patricia was the second most common female name in the United States according to the 1990 US Census. Another well-known variant of this is "Patrice". According to the US Social Security Administration records, the use of the name for newborns peaked at #3 from 1937 to 1943 in the United States, after which it dropped in popularity, sliding to #745 in 2016.Popularity of a NameSocial Security Administration''ssa.gov'', accessed June 26, 2017 From 1928 to 1967, the name was ranked among the top 11 female names. In Portuguese and Spanish-speaking Latin-American countries, the name Patrícia/Patricia is common as well, pronounced . In Catalan and Portuguese it is written Patrícia, while in Italy, Germany and Austria Patrizia is the form, pronounced . In Polish, the variant is Patrycja. It is also used in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
