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Hindley–Milner Type System
A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis. Among HM's more notable properties are its completeness and its ability to infer the most general type of a given program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice and has been successfully applied on large code bases, although it has a high theoretical complexity.Hindley–Milner type inference is DEXPTIME-complete. In fact, merely deciding whether an ML program is typeable (without having to infer a type) is itself DEXPTIME-complete. Non-linear behaviour does manifest itself, yet mostly on pathological inputs. Thus the complexity theoretic proofs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type System
In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a ''type'' (for example, integer, floating point, string) to every '' term'' (a word, phrase, or other set of symbols). Usually the terms are various language constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term. Type systems formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other data types, such as "string", "array of float", "function returning boolean". Type systems are often specified as part of programming languages and built into interpreters and compilers, although the type system of a language can be extended by optional tools that perform added checks using the language's original type synta ... [...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 \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Grammar
A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabet. A grammar does not describe the semantics, meaning of the strings — only their form. In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, Formal semantics (logic), formal semantics, mathematical logic, and other areas. A formal grammar is a Set_(mathematics), set of rules for rewriting strings, along with a "start symbol" from which rewriting starts. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a "recognizer"—a function in computing that determines whether a given string belongs to the language or is grammatical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System F
System F (also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of universal quantification over types. System F formalizes parametric polymorphism in programming languages, thus forming a theoretical basis for languages such as Haskell and ML. It was discovered independently by logician Jean-Yves Girard (1972) and computer scientist John C. Reynolds. Whereas simply typed lambda calculus has variables ranging over terms, and binders for them, System F additionally has variables ranging over ''types'', and binders for them. As an example, the fact that the identity function can have any type of the form ''A'' → ''A'' would be formalized in System F as the judgement :\vdash \Lambda\alpha. \lambda x^\alpha.x: \forall\alpha.\alpha \to \alpha where \alpha is a type variable. The upper-case \Lambda is traditionally used to denote type-level functions, as opposed to the lower-ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object-oriented Programming
Object-oriented programming (OOP) is a programming paradigm based on the concept of '' objects''. Objects can contain data (called fields, attributes or properties) and have actions they can perform (called procedures or methods and implemented in code). In OOP, computer programs are designed by making them out of objects that interact with one another. Many of the most widely used programming languages (such as C++, Java, and Python) support object-oriented programming to a greater or lesser degree, typically as part of multiple paradigms in combination with others such as imperative programming and declarative programming. Significant object-oriented languages include Ada, ActionScript, C++, Common Lisp, C#, Dart, Eiffel, Fortran 2003, Haxe, Java, JavaScript, Kotlin, Logo, MATLAB, Objective-C, Object Pascal, Perl, PHP, Python, R, Raku, Ruby, Scala, SIMSCRIPT, Simula, Smalltalk, Swift, Vala and Visual Basic.NET. History The idea of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymorphism (computer Science)
In programming language theory and type theory, polymorphism is the use of one symbol to represent multiple different types.: "Polymorphic types are types whose operations are applicable to values of more than one type." In object-oriented programming, polymorphism is the provision of one Interface (object-oriented programming), interface to entities of different data types. The concept is borrowed from a principle in biology where an organism or species can have many different forms or stages. The most commonly recognized major forms of polymorphism are: * ''Ad hoc polymorphism'': defines a common interface for an arbitrary set of individually specified types. * ''Parametric polymorphism'': not specifying concrete types and instead use abstract symbols that can substitute for any type. * ''Subtyping'' (also called ''subtype polymorphism'' or ''inclusion polymorphism''): when a name denotes instances of many different classes related by some common superclass. History Interest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced'' '' – like the letter c'') is a general-purpose programming language. It was created in the 1970s by Dennis Ritchie and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted Central processing unit, CPUs. It has found lasting use in operating systems code (especially in Kernel (operating system), kernels), device drivers, and protocol stacks, but its use in application software has been decreasing. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the most widely used programming langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascal (programming Language)
Pascal is an imperative and procedural programming language, designed by Niklaus Wirth as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named after French mathematician, philosopher and physicist Blaise Pascal. Pascal was developed on the pattern of the ALGOL 60 language. Wirth was involved in the process to improve the language as part of the ALGOL X efforts and proposed a version named ALGOL W. This was not accepted, and the ALGOL X process bogged down. In 1968, Wirth decided to abandon the ALGOL X process and further improve ALGOL W, releasing this as Pascal in 1970. On top of ALGOL's scalars and arrays, Pascal enables defining complex datatypes and building dynamic and recursive data structures such as lists, trees and graphs. Pascal has strong typing on all objects, which means that one type of data cannot be converted to or interpreted as another without explicit conversions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List (computer Science)
In computer science, a list or sequence is a collection of items that are finite in number and in a particular order. An instance of a list is a computer representation of the mathematical concept of a tuple or finite sequence. A list may contain the same value more than once, and each occurrence is considered a distinct item. The term ''list'' is also used for several concrete data structures that can be used to implement abstract lists, especially linked lists and arrays. In some contexts, such as in Lisp programming, the term ''list'' may refer specifically to a linked list rather than an array. In class-based programming, lists are usually provided as instances of subclasses of a generic "list" class, and traversed via separate iterators. Many programming languages provide support for list data types, and have special syntax and semantics for lists and list operations. A list can often be constructed by writing the items in sequence, separated by commas, semicolons, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luis Damas
Luis is a given name. It is the Spanish form of the originally Germanic name or . Other Iberian Romance languages have comparable forms: (with an accent mark on the i) in Portuguese and Galician, in Aragonese and Catalan, while is archaic in Portugal, but common in Brazil. Origins The Germanic name (and its variants) is usually said to be composed of the words for "fame" () and "warrior" () and hence may be translated to ''famous warrior'' or "famous in battle". According to Dutch onomatologists however, it is more likely that the first stem was , meaning fame, which would give the meaning 'warrior for the gods' (or: 'warrior who captured stability') for the full name.J. van der Schaar, ''Woordenboek van voornamen'' (Prisma Voornamenboek), 4e druk 1990; see also thLodewijs in the Dutch given names database Modern forms of the name are the German name Ludwig and the Dutch form Lodewijk. and the other Iberian forms more closely resemble the French name Louis, a deriva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Inference
Type inference, sometimes called type reconstruction, refers to the automatic detection of the type of an expression in a formal language. These include programming languages and mathematical type systems, but also natural languages in some branches of computer science and linguistics. Nontechnical explanation In a typed language, a term's type determines the ways it can and cannot be used in that language. For example, consider the English language and terms that could fill in the blank in the phrase "sing _." The term "a song" is of singable type, so it could be placed in the blank to form a meaningful phrase: "sing a song." On the other hand, the term "a friend" does not have the singable type, so "sing a friend" is nonsense. At best it might be metaphor; bending type rules is a feature of poetic language. A term's type can also affect the interpretation of operations involving that term. For instance, "a song" is of composable type, so we interpret it as the thing created ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Feys
Robert Feys (19 December 1889 – 13 April 1961) was a Belgian logician and philosopher, who worked at the University of Leuven (Belgium).De Raeymaeker, Louis.In memoriam le chanoine Robert Feys" ''Revue Philosophique de Louvain'' 59.62 (1961): 371-374. Feys was born in Mechelen, and received his PhD in 1909 from the Institute of Philosophy, University of Leuven. In 1913 he was appointed Professor at the Université Saint-Louis, Brussels. But due to the War he enlisted in the Army. In 1919 he was appointed Professor at the Institute St. Gertrude in Nivelles. In 1929 he returned to the Université Saint-Louis, Brussels, and in 1944 he was appointed Professor at the University of Leuven. In 1958 Feys and Haskell B. Curry devised the type inference algorithm for the simply typed lambda calculus The simply typed lambda calculus (), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor () that builds function types. It is the can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
