In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Coq, F*, Epigram, Idris, and Lean, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations.
Two common examples of dependent types are dependent functions and dependent pairs. The return type of a dependent function may depend on the value (not just type) of one of its arguments. For instance, a function that takes a positive integer may return an array of length , where the array length is part of the type of the array. (Note that this is different from polymorphism and generic programming, both of which include the type as an argument.) A dependent pair may have a second value the type of which depends on the first value. Sticking with the array example, a dependent pair may be used to pair an array with its length in a type-safe way.
Dependent types add complexity to a type system. Deciding the equality of dependent types in a program may require computations. If arbitrary values are allowed in dependent types, then deciding type equality may involve deciding whether two arbitrary programs produce the same result; hence the decidability of type checking may depend on the given type theory's semantics of equality, that is, whether the type theory is intensional or extensional.[1]
^Hofmann, Martin (1995), Extensional concepts in intensional type theory(PDF)
a dependenttype is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory...
n>5\}} A dependenttype is a type whose definition depends on a value. Two common examples of dependenttypes are dependent functions and dependent pairs...
Type 2 diabetes (T2D), formerly known as adult-onset diabetes, is a form of diabetes mellitus that is characterized by high blood sugar, insulin resistance...
Homotopy type theory continues in this line using type theory. Researchers are exploring connections between dependenttypes (especially the identity type) and...
expressive type system that satisfies all programming practices in a type safe manner. A programming language compiler can also implement a dependenttype or...
versions keep the core design of constructive logic using dependenttypes. Martin-Löf designed the type theory on the principles of mathematical constructivism...
usually take between 2 and 24 hours to develop. An example of complement dependenttype II hypersensitivity is an acute hemolytic transfusion reaction following...
by a restricted notion of dependenttypes: types may be dependent on static indices of type Nat (natural numbers). Dependent ML employs a constraint theorem...
integral area. As such, a dependent territory includes a range of non-integrated not fully to non-independent territory types, from associated states to...
between database attributes allowing normalization. Dependenttype, in computer science and logic, a type that depends on a value Hidden dependency, a relation...
versions. One branch, known as dependenttype theory, is used in a number of computer-assisted proof systems. Dependenttype theory allows quantifiers to...
using dependent record types. In comparison to dependent intersection types, dependent record types constitute a strictly more specialized type theoretic...
"Crystal structure and mechanism of action of the N6-methyladenine-dependenttype IIM restriction endonuclease R.DpnI". Nucleic Acids Research. 40 (15):...
A Multivalued Language with a DependentType System. Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming. Neal Glew, Tim Sweeney...
only type II enzyme to do this, all the others catalyze DNA relaxation. Type II enzymes are mechanistically distinct from type I in being ATP-dependent and...
A dependent clause, also known as a subordinate clause, subclause or embedded clause, is a certain type of clause that juxtaposes an independent clause...
posted to the Types mailing list "A very short note on homotopy lambda calculus", which sketched the outlines of a type theory with dependent products, sums...
extensionality and proof irrelevance. Pure type system Lambda cube System F Dependenttype Intuitionistic type theory Homotopy type theory Calculus of Inductive Constructions...
Calculus of Inductive Constructions and other dependentlytyped languages, modulo the dependenttypes and except that the latter have an additional positivity...
intuitionistic type theory, which lets types depend on terms. Such types are called dependenttypes. These type systems do not have decidable type inference...
Dependent personality disorder (DPD) is a personality disorder characterized by a pervasive psychological dependence on other people. This personality...
Global Information