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Type whose definition depends on a value
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_type
Form of diabetes mellitus
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
Type_2_diabetes
Form of diabetes mellitus
PMID 28373161. S2CID 11374615. Delli AJ, Lernmark A (2016). "Type 1 (insulin-dependent) diabetes mellitus: etiology, pathogenesis, prediction, and prevention"
Type_1_diabetes
Alternative foundation of mathematics
versions keep the core design of constructive logic using dependent types. Martin-Löf designed the type theory on the principles of mathematical constructivism
Intuitionistic_type_theory
Attribute of data
n>5\}} A dependent type is a type whose definition depends on a value. Two common examples of dependent types are dependent functions and dependent pairs
Data_type
Mathematical theory of data types
calculus of inductive constructions, while Lean is based on dependent type theory. Type theory was created to avoid paradoxes in naive set theory and
Type_theory
Computer science concept
variant of ML called Dependent ML has been created based on this type system, but because type checking for conventional dependent types is undecidable, not
Type_system
substitution operation necessitated by dependent types: if f {\displaystyle f} has the dependent function type ( x : A ) → B {\displaystyle (x:A)\to B}
Semantics_of_type_theory
Type theory in logic and mathematics
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
Homotopy_type_theory
Experimental programming language
Dependent ML extends ML by a restricted notion of dependent types: types may be dependent on static indices of type Nat (natural numbers). Dependent ML
Dependent_ML
Functional programming language
Agda is a dependently typed functional programming language originally developed by Ulf Norell at Chalmers University of Technology with implementation
Agda_(programming_language)
Concept in functional programming
types (or inductive datatypes) found in Rocq's Calculus of Inductive Constructions and other dependently typed languages, modulo the dependent types and
Generalized algebraic data type
Generalized_algebraic_data_type
Proof assistant and programming language
useful for functional programming and theorem proving, such as dependent types, type classes, multi-threading, an expressive tactic language, and a module
Lean_(proof_assistant)
Kind of proof calculus
versions. One branch, known as dependent type theory, is used in a number of computer-assisted proof systems. Dependent type theory allows quantifiers to
Natural_deduction
Functional programming language created in 2007
Idris is a purely-functional programming language with dependent types, quantity annotations, optional lazy evaluation, and features such as a totality
Idris_(programming_language)
Extent to which a programming language discourages type errors
as a pointer to another type. More sophisticated type systems, such as those supporting dependent types, can detect and reject out-of-bound accesses, preventing
Type_safety
Topics referred to by the same term
between database attributes allowing normalization. Dependent type, in computer science and logic, a type that depends on a value Hidden dependency, a relation
Dependency
Type of allergic reaction
usually take between 2 and 24 hours to develop. An example of complement dependent type II hypersensitivity is an acute hemolytic transfusion reaction following
Type_II_hypersensitivity
Interactive theorem prover software
based. Lean is both an interactive theorem prover and a functional, dependently-typed programming language. It is based on the calculus of inductive constructions
Proof_assistant
Type theory created by Thierry Coquand
extensionality and proof irrelevance. Pure type system Lambda cube System F Dependent type Intuitionistic type theory Homotopy type theory Coquand, Thierry; Gallier
Calculus_of_constructions
Data type in type theory
others. Quotient types have been studied in the context of Martin-Löf type theory, dependent type theory, higher-order logic, and homotopy type theory. To define
Quotient_type
Concept in programming language design
Shroff, Scott F. Smith. Type Inference for First-Class Messages with Match-Functions Bove, Ana; Dybjer, Peter (2009). "Dependent Types at Work" (PDF). Language
First-class_citizen
Group of voltage-gated ion channels permeable to Ca2+
Voltage-gated calcium channels (VGCCs), also known as voltage-dependent calcium channels (VDCCs), are a group of voltage-gated ion channels found in the
Voltage-gated_calcium_channel
Insulin-dependent (type I) diabetes mellitus
Insulin-dependent (type I) diabetes mellitus (IDDM) is a genetic heterogenous autoimmune disorder, which is triggered by genetic predisposition and environmental
IDDM11
Programming language
Haskell. The type system is based on a Hindley–Milner type system with a variety of extensions, such as uniqueness types and size-dependent types. Futhark
Futhark (programming language)
Futhark_(programming_language)
Relationship between programs and proofs
Curry-Howard isomorphism, with a stronger type-language it becomes an isomorphism too, though still missing dependent types. Prawitz was presumably unaware of
Curry–Howard_correspondence
Computer scientist
Philosophy (Ph.D.) in Dependently Typed Functional Programs and their Proofs at the University of Edinburgh for their work in type theory. They formerly
Conor_McBride
Programming language
[citation needed], which is present because of the language's use of dependent type-checking and template instance resolution. These features usually require
ATS_(programming_language)
Functional programming language
programming language with dependent types, and the integrated development environment (IDE) usually packaged with the language. Epigram's type system is strong
Epigram (programming language)
Epigram_(programming_language)
Formal system in mathematical logic
introduce polymorphic types (like System F) or dependent types (like the Logical Framework) are not considered simply typed. The simple types, except for full
Simply_typed_lambda_calculus
American video game developer (born 1970)
A Multivalued Language with a Dependent Type System. Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming. Neal Glew, Tim Sweeney
Tim_Sweeney
Proof assistant
Rocq implements a dependently typed functional programming model; when viewed as a logical system, it implements a higher-order type theory. The development
Rocq
Type system used in computer programming and mathematics
which extend kinds to emulate features of a dependent type system. Attempts to combine subtyping and type inference have caused quite some frustration
Hindley–Milner_type_system
Determination of whether a given program halts for each input
to termination checking in dependently typed programming languages are sized types. The main idea is to annotate the types over which we can recurse with
Termination_analysis
in the same type system. A logical framework is based on a general treatment of syntax, rules and proofs by means of a dependently typed lambda calculus
Logical_framework
is defined by a type of shapes S and a type family of positions P, indexed by S. The extension of a container is a family of dependent pairs consisting
Container_(type_theory)
Personality disorder involving excess dependence on others
Dependent personality disorder (DPD) is a personality disorder characterized by a pervasive dependence on other people and subsequent submissiveness and
Dependent personality disorder
Dependent_personality_disorder
Proof assistant program
theory of types with dependent types, and is fundamentally a classical typed higher-order logic. The base types include uninterpreted types that may be
Prototype_Verification_System
Functional programming language inspired by ML and aimed at program verification
Science and Automation (Inria). Its type system includes dependent types, monadic effects, and refinement types. This allows expressing precise specifications
F*_(programming_language)
Medical condition
shortening. The researchers wanted to determine if protein kinase cGMP-dependent type II gene (PRKG2) had any effect on longitudinal growth in bones. The
Acromesomelic_dysplasia
Variable representing a data type in programming and type theory
In type theory and programming languages, a type variable is a mathematical variable ranging over types. Even in programming languages that allow mutable
Type_variable
Framework in lambda calculus
depend on terms, corresponding to dependent types. y-axis ( ↑ {\displaystyle \uparrow } ): terms that can depend on types, corresponding to polymorphism
Lambda_cube
Logic programming language
operator. nat : type. z : nat. s : nat -> nat. Here nat is a type, and z and s are constant terms. As a dependently typed system, types can be indexed
Twelf
Aircraft surveillance technology
Automatic Dependent Surveillance–Broadcast (ADS-B) is an aviation surveillance technology and form of electronic conspicuity in which an aircraft determines
Automatic Dependent Surveillance–Broadcast
Automatic_Dependent_Surveillance–Broadcast
Grammatical clause adding information to a primary clause
A dependent clause, also known as a subordinate clause, subclause or embedded clause, is a certain type of clause that juxtaposes an independent clause
Dependent_clause
Dialect of the Lisp programming language on the Java platform
simple and fast. While its type system is entirely dynamic, recent efforts have also sought the implementation of a dependent type system. The language was
Clojure
Type of data structure
the VLA is said to have a variably modified data type that depends on a value (see Dependent type). The main purpose of VLAs is to simplify programming
Variable-length_array
Functional programming language
developed, including: Agda, a functional language with dependent types. Cayenne, with dependent types. Elm, a functional language to create web front-end
Haskell
Structure editor for monomorphic Martin-Löf type theory
Martin-Löf type theory developed at Chalmers University. It is a predecessor of the Alfa, Agda, Cayenne and Rocq proof assistants and dependently typed programming
ALF_(proof_assistant)
Programming paradigm
natively or using the Lightweight Modular Staging Framework Terra Use of dependent types allows proving that generated code is never invalid. However, this
Metaprogramming
Data type for values having two types
using dependent record types. In comparison to dependent intersection types, dependent record types constitute a strictly more specialized type theoretic
Intersection_type
Programming paradigm based on applying and composing functions
intuitionistic type theory, which lets types depend on terms. Such types are called dependent types. These type systems do not have decidable type inference
Functional_programming
Type of cancer
hormone-dependent cancer, is a type of cancer that is dependent on a hormone for growth and/or survival. Examples include breast cancer, which is dependent on
Hormone-sensitive_cancer
Formalism in computer science
uninhabited types. There exist, however, typed lambda calculi that are not strongly normalizing. For example the dependently typed lambda calculus with a type of
Typed_lambda_calculus
Topics referred to by the same term
data types indexed by another type or value Recursive data type, a data type for values that may contain other values of the same type Inductive type Induction
Inductive_data_type
Proof assistant program
Generalized Calculus of Constructions (GCC) and the Unified Theory of Dependent Types (UTT). "Software Search - zbMATH Open". zbmath.org. Retrieved 2022-11-03
LEGO_(proof_assistant)
Types constrained by a predicate
real world usage in Scala. Liquid Haskell Dependent types Freeman, T.; Pfenning, F. (1991). "Refinement types for ML" (PDF). Proceedings of the ACM Conference
Refinement_type
Proof assistant
of dependent goals. Matita implements a bidirectional type inference algorithm exploiting both inferred and expected types. The power of the type inference
Matita
Concept in mathematical modeling, statistical modeling and experimental sciences
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are the outcome of
Dependent and independent variables
Dependent_and_independent_variables
Class of enzymes
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
Topoisomerase
Style of dynamic typing in object-oriented programming
Structural typing is a static typing system that determines type compatibility and equivalence by a type's structure, whereas duck typing is dynamic and
Duck_typing
Protein-coding gene in humans
Voltage-dependent L-type calcium channel subunit alpha-1C (also known as Cav1.2) is a protein that in humans is encoded by the CACNA1C gene. Cav1.2 is
CACNA1C
over time as type theory developed. Per Martin-Löf found a type theory that corresponded to predicate logic by introducing dependent types, which became
History_of_type_theory
Behavior in the C++ programming language
argument-dependent lookup (ADL), or argument-dependent name lookup, applies to the lookup of an unqualified function name depending on the types of the
Argument-dependent name lookup
Argument-dependent_name_lookup
Computer algebra system
fricas). Both languages share a similar syntax and a sophisticated (dependent) type system. FriCAS is comprehensively documented and available as source
FriCAS
Formal system of logic
Russell. Simple types is sometimes also meant to exclude polymorphic and dependent types. First-order logic quantifies only variables that range over individuals;
Higher-order_logic
cubical type theory (PDF) (Thesis). "Cubical". Agda documentation. Vezzosi, Andrea; Mörtberg, Anders; Abel, Andreas (2021). "Cubical Agda: a dependently typed
Cubical_type_theory
Pseudoscientific personality questionnaire
that are dependent on sample characteristics and testing conditions". A 1973 study of university students in the United States found the INFP type was the
Myers–Briggs_Type_Indicator
Class of enzymes
In molecular biology, the copper type II ascorbate-dependent monooxygenases are a class of enzymes that require copper as a cofactor and which use ascorbate
Copper type II ascorbate-dependent monooxygenase
Copper_type_II_ascorbate-dependent_monooxygenase
Type of protein
known sodium-dependent phosphate transporters found in humans include (but are not limited to): Sodium-Phosphate Cotransporter Proteins, Type I (TC# 2.A
Sodium/phosphate cotransporter
Sodium/phosphate_cotransporter
Type I site-specific deoxyribonuclease (EC 3.1.21.3, type I restriction enzyme, deoxyribonuclease (ATP- and S-adenosyl-L-methionine-dependent), restriction-modification
Type I site-specific deoxyribonuclease
Type_I_site-specific_deoxyribonuclease
Category where every morphism is invertible; generalization of a group
presence of dependent typing, a category in general can be viewed as a typed monoid, and similarly, a groupoid can be viewed as simply a typed group. The
Groupoid
Protein kinase
cGMP-dependent protein kinase or protein kinase G (PKG) is a serine/threonine-specific protein kinase that is activated by cGMP. It phosphorylates a number
CGMP-dependent_protein_kinase
C++ keyword
templates. It is used for specifying that a dependent name in a template definition or declaration is a type. In the original C++ compilers before the first
Typename
Protein-coding gene in the species Homo sapiens
cAMP-dependent protein kinase type II-alpha regulatory subunit is an enzyme that in humans is encoded by the PRKAR2A gene. cAMP is a signaling molecule
PRKAR2A
Typed lambda calculus
expressive typed lambda calculi, including those with dependent types. According to Girard, the "F" in System F was picked by chance. The typing rules of
System_F
Medical simulation computer program
completely lacking endogenous insulin secretion — i.e. insulin-dependent patients with type 1 diabetes mellitus. The AIDA model contains a single extra-cellular
AIDA interactive educational freeware diabetes simulator
AIDA_interactive_educational_freeware_diabetes_simulator
Protein-coding gene in the species Homo sapiens
cAMP-dependent protein kinase type I-alpha regulatory subunit is an enzyme that in humans is encoded by the PRKAR1A gene. cAMP is a signaling molecule
PRKAR1A
Proving or disproving the correctness of certain intended algorithms
proving, type systems, and lightweight formal methods. A promising type-based verification approach is dependently typed programming, in which the types of
Formal_verification
Class of enzymes
dehydrogenase. There are three main types of MDHs: NAD+-dependent MDH, pyrrolo-quinoline quinone dependent MDH, and oxygen-dependent alcohol oxidase. This enzyme
Methanol_dehydrogenase
Property of certain fluids to change viscosity over time
continuum mechanics, time-dependent viscosity is a property of fluids whose viscosity changes as a function of time. The most common type of this is thixotropy
Time-dependent_viscosity
Group of endocrine diseases characterized by high blood sugar levels
The term "type 1 diabetes" has replaced several former terms, including childhood-onset diabetes, juvenile diabetes, and insulin-dependent diabetes mellitus
Diabetes
Branch of logic using category theory to study mathematical structures
polymorphic and dependent types was developed largely after this book was published. Jacobs, Bart (1999). Categorical Logic and Type Theory. Studies in
Categorical_logic
Abuse case in California
The Turpin case involved the abuse of children and dependent adults by their biological parents, David and Louise Turpin of Perris, California, US. The
Turpin_case
Family of type systems based on substructural logic
Substructural type systems are a family of type systems analogous to substructural logics where one or more of the structural rules are absent or only
Substructural_type_system
Type of types in a type system
science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator (type constructor). A
Kind_(type_theory)
Protein-coding gene in the species Homo sapiens
cAMP-dependent protein kinase type I-beta regulatory subunit is an enzyme that in humans is encoded by the PRKAR1B gene. Mutations in PRKAR1B cause neurodegenerative
PRKAR1B
comparison of the features of the type systems and type checking of multiple programming languages. Brief definitions A nominal type system means that the language
Comparison of programming languages by type system
Comparison_of_programming_languages_by_type_system
Fundamental Buddhist teaching
प्रतीत्यसमुत्पाद, Pāli: paṭiccasamuppāda), commonly translated as dependent origination, or dependent arising, is a key doctrine in Buddhism shared by all schools
Pratītyasamutpāda
Concept in category theory
play an important role in categorical semantics of type theory, and in particular that of dependent type theories. Fibred categories were introduced by Alexander
Fibred_category
for every pair of objects, a set of morphisms. A partial (equiv. dependently typed) binary operation called composition is provided on morphisms, every
List_of_types_of_functions
Class of enzymes that divide DNA
"Crystal structure and mechanism of action of the N6-methyladenine-dependent type IIM restriction endonuclease R.DpnI". Nucleic Acids Research. 40 (15):
Restriction_enzyme
Topics referred to by the same term
Idris (programming language), a functional programming language with dependent types Idris (operating system), a multi-tasking, Unix-like, multi-user, real-time
Idris
Automatic detection of the type of an expression in a formal language
In type theory, type inference (sometimes called type reconstruction) is the automatic detection of the type of an expression. These include programming
Type_inference
American computer scientist
WYRE-ik) is an American computer scientist specializing in type theory, type inference, dependent types, and functional programming. She is a professor of computer
Stephanie_Weirich
Mathematical-logic system
calculi from a practical type system perspective; some topics like dependent types are only mentioned, but subtyping is an important topic. Documents
Lambda_calculus
Type of category in category theory
because, when interpreting P as a dependent type y : Y ⊢ P ( y ) : T y p e {\displaystyle y:Y\vdash P(y):\mathrm {Type} } , the functors Σ p {\displaystyle
Cartesian_closed_category
Protein-coding gene in the species Homo sapiens
Matrix metalloproteinase-14 (MMP14), also known as MT1-MMP, is a zinc-dependent type I transmembrane metalloproteinase characterized by a modular structure
MMP14
Programming paradigm restricted to provably terminating programs
possible to do I/O in a total functional programming language (with dependent types) also without codata. Both Epigram and Charity could be considered
Total_functional_programming
especially flexible and expressive type systems (notably dependently typed programming languages) allow types to be manipulated in the same ways as regular terms
Phase_distinction
DEPENDENT TYPE
DEPENDENT TYPE
Girl/Female
Tamil
Ashritha | ஆஷà¯à®°à®¿à®¤à®¾
Dependant
Ashritha | ஆஷà¯à®°à®¿à®¤à®¾
Girl/Female
Hindu
Independent, Submissive, Willing, Dependent
Girl/Female
Tamil
Swayambhi | ஸà¯à®µà®¯à®¾à®®à¯à®ªà¯€
Independent
Swayambhi | ஸà¯à®µà®¯à®¾à®®à¯à®ªà¯€
Girl/Female
Hindu
Independent, Submissive, Willing, Dependent
Boy/Male
Indian
Independent
Girl/Female
Tamil
Ashrita | ஆஷà¯à®°à®¿à®¤à®¾
Dependant
Ashrita | ஆஷà¯à®°à®¿à®¤à®¾
Girl/Female
Tamil
Independent
Girl/Female
Tamil
Asritha | அஸà¯à®°à¯€à®¤à®¾
Dependent
Asritha | அஸà¯à®°à¯€à®¤à®¾
Girl/Female
Indian
Dependant
Girl/Female
Tamil
Independent, Submissive, Willing, Dependent
Boy/Male
Tamil
Visravas | விஸராவாஸ
Dependence
Visravas | விஸராவாஸ
Girl/Female
Indian
Dependant
Girl/Female
Gujarati, Hindu, Indian, Malayalam, Marathi, Tamil, Telugu
Helpfully; Dependant
Boy/Male
Hebrew
Descendent.
Girl/Female
Tamil
Independent, Submissive, Willing, Dependent
Girl/Female
Indian
Dependent
Girl/Female
Indian
Self Dependent
Girl/Female
Gujarati, Hindu, Indian, Sanskrit
Self Dependant
Boy/Male
Muslim
Independent
Boy/Male
Hindu, Indian, Parsi, Tamil
Self Dependent; Royal Face
DEPENDENT TYPE
DEPENDENT TYPE
DEPENDENT TYPE
DEPENDENT TYPE
DEPENDENT TYPE
DEPENDENT TYPE
DEPENDENT TYPE
n.
One who depends; one who is sustained by another, or who relies on another for support of favor; a hanger-on; a retainer; as, a numerous train of dependents.
a.
Supported from above; suspended; depending; pendulous; hanging; as, a pendent leaf.
n.
A thing hanging down; a dependence.
a.
Not dependent upon another quantity in respect to value or rate of variation; -- said of quantities or functions.
a.
Depending; pendent loosely; hanging; swinging.
a.
Relying on, or subject to, something else for support; not able to exist, or sustain itself, or to perform anything, without the will, power, or aid of something else; not self-sustaining; contingent or conditioned; subordinate; -- often with on or upon; as, dependent on God; dependent upon friends.
n.
That which depends; anything dependent or suspended; anything attached a subordinate to, or contingent on, something else.
a.
Affording a comfortable livelihood; as, an independent property.
n.
A dependency; a dependent territory.
a.
Not dependent; free; not subject to control by others; not relying on others; not subordinate; as, few men are wholly independent.
n.
One who depends; a dependent.
v. t.
A deponent verb.
n.
The act or state of depending; state of being dependent; a hanging down or from; suspension from a support.
adv.
In a dependent manner.
n.
State of being dependent; dependence; state of being subordinate; subordination; concatenation; connection; reliance; trust.
a.
Dependent on one's self; self-depending; self-reliant.
a.
Marked by despondence; given to despondence; low-spirited; as, a despondent manner; a despondent prisoner.
n.
See Dependent, Dependence, Dependency.
a.
Hanging down; as, a dependent bough or leaf.
a.
Depending on itself; independent.