Concept

Subtyping

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Type conversion

In computer science, type conversion, type casting, type coercion, and type juggling are different ways of changing an expression from one data type to another. An example would be the conversion of an integer value into a floating point value or its textual representation as a string, and vice versa. Type conversions can take advantage of certain features of type hierarchies or data representations.

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.

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 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.

Abstract type

In programming languages, an abstract type is a type in a nominative type system that cannot be instantiated directly; a type that is not abstract – which can be instantiated – is called a concrete type. Every instance of an abstract type is an instance of some concrete subtype. Abstract types are also known as existential types. An abstract type may provide no implementation, or an incomplete implementation. In some languages, abstract types with no implementation (rather than an incomplete implementation) are known as protocols, interfaces, signatures, or class types.

Tagged union

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.

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.

Liskov substitution principle

The Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called strong behavioral subtyping, that was initially introduced by Barbara Liskov in a 1987 conference keynote address titled Data abstraction and hierarchy. It is based on the concept of "substitutability" a principle in object-oriented programming stating that an object (such as a class) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program.

Class-based programming

Class-based programming, or more commonly class-orientation, is a style of object-oriented programming (OOP) in which inheritance occurs via defining classes of objects, instead of inheritance occurring via the objects alone (compare prototype-based programming). The most popular and developed model of OOP is a class-based model, instead of an object-based model. In this model, objects are entities that combine state (i.e., data), behavior (i.e., procedures, or methods) and identity (unique existence among all other objects).

Ad hoc polymorphism

In 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.

Object composition

In computer science, object composition and object aggregation are closely related ways to combine objects or data types into more complex ones. In conversation the distinction between composition and aggregation is often ignored. Common kinds of compositions are objects used in object-oriented programming, tagged unions, sets, sequences, and various graph structures. Object compositions relate to, but are not the same as, data structures.