Ad hoc polymorphismIn programming languages, ad hoc polymorphism 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.
Parametric polymorphismIn 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.
Generic programmingGeneric programming is a style of computer programming in which algorithms are written in terms of data types to-be-specified-later that are then instantiated when needed for specific types provided as parameters. This approach, pioneered by the ML programming language in 1973, permits writing common functions or types that differ only in the set of types on which they operate when used, thus reducing duplicate code. Generics was introduced to the main-stream programming with Ada in 1977 and then with templates in C++ it became part of the repertoire of professional library design.
Polymorphism (computer science)In programming language theory and type theory, polymorphism is the provision of a single interface to entities of different types or the use of a single symbol to represent multiple different 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 classes of polymorphism are: Ad hoc polymorphism: defines a common interface for an arbitrary set of individually specified types.
Operator overloadingIn computer programming, operator overloading, sometimes termed operator ad hoc polymorphism, is a specific case of polymorphism, where different operators have different implementations depending on their arguments. Operator overloading is generally defined by a programming language, a programmer, or both. Operator overloading is syntactic sugar, and is used because it allows programming using notation nearer to the target domain and allows user-defined types a similar level of syntactic support as types built into a language.
F Sharp (programming language)F# (pronounced F sharp) is a functional-first, general-purpose, strongly typed, multi-paradigm programming language that encompasses functional, imperative, and object-oriented programming methods. It is most often used as a cross-platform Common Language Infrastructure (CLI) language on .NET, but can also generate JavaScript and graphics processing unit (GPU) code. F# is developed by the F# Software Foundation, Microsoft and open contributors. An open source, cross-platform compiler for F# is available from the F# Software Foundation.
Scala (programming language)Scala (ˈskɑːlə ) is a strong statically typed high-level general-purpose programming language that supports both object-oriented programming and functional programming. Designed to be concise, many of Scala's design decisions are aimed to address criticisms of Java. Scala source code can be compiled to Java bytecode and run on a Java virtual machine (JVM). Scala can also be compiled to JavaScript to run in a browser, or directly to a native executable.
Chisel (programming language)The Constructing Hardware in a Scala Embedded Language (Chisel) is an open-source hardware description language (HDL) used to describe digital electronics and circuits at the register-transfer level. Chisel is based on Scala as an embedded domain-specific language (DSL). Chisel inherits the object-oriented and functional programming aspects of Scala for describing digital hardware. Using Scala as a basis allows describing circuit generators. High quality, free access documentation exists in several languages.
Rust (programming language)Rust is a multi-paradigm, general-purpose programming language that emphasizes performance, type safety, and concurrency. It enforces memory safety—ensuring that all references point to valid memory—without requiring the use of a garbage collector or reference counting present in other memory-safe languages. To simultaneously enforce memory safety and prevent data races, its "borrow checker" tracks the object lifetime of all references in a program during compilation.
MixinIn object-oriented programming languages, a mixin (or mix-in) is a class that contains methods for use by other classes without having to be the parent class of those other classes. How those other classes gain access to the mixin's methods depends on the language. Mixins are sometimes described as being "included" rather than "inherited". Mixins encourage code reuse and can be used to avoid the inheritance ambiguity that multiple inheritance can cause (the "diamond problem"), or to work around lack of support for multiple inheritance in a language.
Extension methodIn object-oriented computer programming, an extension method is a method added to an object after the original object was compiled. The modified object is often a class, a prototype or a type. Extension methods are features of some object-oriented programming languages. There is no syntactic difference between calling an extension method and calling a method declared in the type definition. Not all languages implement extension methods in an equally safe manner, however.
C++C++ ('si:_plVs_plVs, pronounced "C plus plus" and sometimes abbreviated as CPP) is a high-level, general-purpose programming language created by Danish computer scientist Bjarne Stroustrup. First released in 1985 as an extension of the C programming language, it has since expanded significantly over time; modern C++ currently has object-oriented, generic, and functional features, in addition to facilities for low-level memory manipulation.
Counterfactual conditionalCounterfactual conditionals (also subjunctive or X-marked) are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives, which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of fake tense morphology, which some languages use in combination with other kinds of morphology including aspect and mood.
Material conditionalThe material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics.
Well-orderIn mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the well-order relation is then called a well-ordered set. In some academic articles and textbooks these terms are instead written as wellorder, wellordered, and wellordering or well order, well ordered, and well ordering. Every non-empty well-ordered set has a least element.
Indicative conditionalIn natural languages, an indicative conditional is a conditional sentence such as "If Leona is at home, she isn't in Paris", whose grammatical form restricts it to discussing what could be true. Indicatives are typically defined in opposition to counterfactual conditionals, which have extra grammatical marking which allows them to discuss eventualities which are no longer possible. Indicatives are a major topic of research in philosophy of language, philosophical logic, and linguistics.
Type classIn computer science, a type class is a type system construct that supports ad hoc polymorphism. This is achieved by adding constraints to type variables in parametrically polymorphic types. Such a constraint typically involves a type class T and a type variable a, and means that a can only be instantiated to a type whose members support the overloaded operations associated with T.
Weak orderingIn mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders.
Well-ordering theoremIn mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. The well-ordering theorem together with Zorn's lemma are the most important mathematical statements that are equivalent to the axiom of choice (often called AC, see also ). Ernst Zermelo introduced the axiom of choice as an "unobjectionable logical principle" to prove the well-ordering theorem.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
