Type theory

pair of mathematical objects; tuple of specific length (tuple length n=2)

storage location paired with a name, which contains a value

in programming languages and type theory, accessing different types using a common interface

In mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".

combination of a set and an extra structure on it; more precisely, an object of a concrete category

set of rules that assign a property called type to various constructs a computer program consists of, such as variables, expressions, functions or modules

mathematical model for data types

style of dynamic, structural typing with lazy checking of objects' attributes

study of type systems in mathematical logic and computer science

style of object-oriented programming

changing an expression from one data type to another

expression in computer science which cannot be evaluated further

automatic detection of the data type of an expression in a programming language

algorithmic process of solving equations between symbolic expressions

a computer-programming principle that states that software entities (classes, modules, functions, etc.) should be open for extension, but closed for modification

object-oriented programming principle stating that, in a computer program, if S is a subtype of T, then objects of type T may be replaced with objects of type S without altering any of the desirable properties of the program (correctness, etc.)

the direct relationship between computer programs and mathematical proofs

data type consisting of an unordered set of named values

property of a type system that prevents certain erroneous or undesirable program behaviours

in programming languages, a keyword indicating the absence of data

in computer programming, a type formed by combining other types

computer programming

relationship between a generic type or a function and a component type on subtyping

type in a nominative type system that cannot be instantiated directly

data type whose definition depends on a value

typed lambda calculus

In programming language theory, subtyping (also called subtype polymorphism or inclusion polymorphism) is a form of type polymorphism. A subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements (typically subroutines or functions), written to operate on elements of the supertype, can also operate on elements of the subtype.

defines the inputs and outputs for a function, subroutine or method

axiomatic set theory permitting set comprehension by stratified formulae, hence with a universal set, but in which the singleton map 𝑥↦{𝑥} fails to exist

alternative foundation of mathematics

data type that refers to itself in its definition

typed formalism that uses the lambda-symbol (λ) to denote anonymous function abstraction

encapsulation of an optional value in programming or type theory

variant of type theory incorporating the univalence axiom of Voevodsky

data structure used to hold a value that could take on several different, but fixed, types

basis of generic programming

type system construct for ad-hoc polymorphism

interpretation of intuitionistic logic

formal system in mathematical logic

process by which explicit type annotations are removed from a program

any data type which can be constructed in a program using the programming language's primitive data types and other composite types

a framework

formal system

applying polymorphic functions to arguments of different types

type allowing only one value in type theory

type of types in a type system

feature of a typed formal language that builds new types from old ones

grammar formalism based on combinatory logic

type system supporting type inference

Concept in functional programming

type that is the subtype of all other types; equivalent to the empty type if uninhabited

algebraic term to describe the result of multiplying data types in type theory

family of formalisms in natural language syntax motivated by the principle of compositionality and organized according to the view that syntactic constituents should generally combine as functions or according to a function-argument relationship