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Data type that refers to itself in its definition
programming, a recursive data type is a data type whose definition contains values of the same type. It is also known as a recursively defined, inductively
Recursive_data_type
Concept in functional programming
a generalized algebraic data type (GADT, also first-class phantom type, guarded recursive datatype, or equality-qualified type) is a generalization of
Generalized algebraic data type
Generalized_algebraic_data_type
Data type defined by combining other types
programming and type theory, an algebraic data type (ADT) is a composite data type, i.e. a type formed by combining other types. An algebraic data type is defined
Algebraic_data_type
Attribute of data
indicating its current type for enhanced type safety. An algebraic data type (ADT) is a possibly recursive sum type of product types. A value of an ADT consists
Data_type
Use of functions that call themselves
solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems
Recursion_(computer_science)
Relational database programming language
many types of statements, which may be informally classed as sublanguages, commonly: data query language (DQL), data definition language (DDL), data control
SQL
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
Inductive_data_type
Way to represent data types in the lambda calculus
represent algebraic data types in the lambda calculus, following their syntactic definition without regard whether they are recursive or not. This is unlike
Mogensen–Scott_encoding
hierarchical query is a type of SQL query that handles hierarchical model data. These are useful for working with databases of graph-structured data, such as river
Hierarchical and recursive queries in SQL
Hierarchical_and_recursive_queries_in_SQL
Finite, ordered collection of items
allow list types to be indexed or sliced like array types, in which case the data type is more accurately described as an array. In type theory and functional
List_(abstract_data_type)
Process where AI repeatedly improves itself
Recursive self-improvement (RSI) is a process in which an artificial intelligence (AI) system iteratively designs a more capable successor. This may trigger
Recursive_self-improvement
Acronym whose expansion includes a copy of itself
A recursive acronym is an acronym that refers to itself, and appears most frequently in computer programming. The term was first used in print in 1979
Recursive_acronym
Family of higher-order functions
function that analyzes a recursive data structure and, through use of a given combining operation, recombines the results of recursively processing its constituent
Fold_(higher-order_function)
Top-down parser utilizing recursion
computer science, a recursive descent parser is a kind of top-down parser built from a set of mutually recursive procedures (or a non-recursive equivalent) where
Recursive_descent_parser
Process of repeating items in a self-similar way
references can occur. A process that exhibits recursion is recursive. Video feedback displays recursive images, as does an infinity mirror. In mathematics and
Recursion
Defining elements of a set in terms of other elements in the set
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements
Recursive_definition
Twelfth letter of the Greek alphabet
notation) In type theory: Used to introduce a recursive data type. For example, list(τ)=μα.1+τα is the type of lists with elements of type τ (a type variable):
Mu_(letter)
Feature of a typed formal language that builds new types from old ones
types. Kind (type theory) Algebraic data type Recursive data type Marlow, Simon (April 2010), "4.1.2 Syntax of Types", Haskell 2010 Language Report, retrieved
Type_constructor
Higher-order function which returns some fixed point of the input function
means to allow for recursive definitions. Applied to a non-constant function of one variable that treats its argument as a piece of data (such as e.g. the
Fixed-point_combinator
Linked node hierarchical data structure
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node
Tree_(abstract_data_type)
Computer science concept
representing various types of data, expressions that provide structuring rules for data, expressions representing various operations on data, and constructs
Type_system
Abstract data type
In computer science, a stack is an abstract data type that serves as a collection of elements with two main operations: Push, which adds an element to
Stack_(abstract_data_type)
arrays containing primitive types, but was extended to handle higher-order and recursive data types in the work on Data Parallel Haskell. Flattening
Flattening_transformation
Computers accessing information referentially
sized types, indirection is often used to define recursive data types. For example, Rust requires recursive enum variants to contain a pointer-like type such
Indirection
Study of programming languages via mathematical objects
then solve the recursive definition there. Polymorphic data types are data types that are defined with a parameter. For example, the type of α lists is
Denotational_semantics
Functional programming construct
recursive data type. The compiler verifies at compile-time that the list of cases is exhaustive and none are redundant. type color = Red | Black type
Pattern_matching
Subroutine call performed as final action of a procedure
target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end
Tail_call
as Milner–Mycroft typability or the Milner–Mycroft calculus) refers to a recursive parametrically polymorphic function where the type parameter changes
Polymorphic_recursion
System to identify resources on a network
brokenness and DNS whitelisting List of DNS record types List of managed DNS providers Multicast DNS Public recursive name server resolv.conf Split-horizon DNS
Domain_Name_System
Abstract data type for storing distinct values
In computer science, a set is an abstract data type that can store distinct values, without any particular order. It is a computer implementation of the
Set_(abstract_data_type)
Type of error-correcting code using convolution
data is also used in the output symbols (Output 2). Codes with output symbols that do not include the input data are called non-systematic. Recursive
Convolutional_code
Mathematical theory of data types
respectively, and defines the set of types recursively as follows: if a {\displaystyle a} and b {\displaystyle b} are types, then so is ⟨ a , b ⟩ {\displaystyle
Type_theory
Adaptive filter algorithm for digital signal processing
Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost
Recursive least squares filter
Recursive_least_squares_filter
1999 edition of the SQL standard
allows only single inheritance. SQL:1999 added a WITH [RECURSIVE] construct allowing recursive queries, like transitive closure, to be specified in the
SQL:1999
Union data structure with enforced cases
when that type is manipulated. This is critical in defining recursive datatypes, in which some component of a value may have the same type as that value
Tagged_union
Artificial intelligence model developed by TypeSafe AI
the choices of that question. This is the only type of output by Jev. The official API returns further data, but these are computed by simple programs, not
Jev_(AI_model)
Text-string-oriented programming language
patterns as a first-class data type, a data type whose values can be manipulated in all ways permitted to any other data type in the programming language
SNOBOL
Scripting language created in 1994
originally an abbreviation of "Personal Home Page", but it now stands for the recursive backronym "PHP: Hypertext Preprocessor". PHP code is usually processed
PHP
Procedural programming language
recursive, non-numeric, machine-independent applications, such as system and language software. It was a typeless language, with the only data type being
B_(programming_language)
Suite of IETF specifications
request to a recursive name server, and use the Authenticated Data (AD) bit in the response as a "hint to find out whether the recursive name server was
Domain Name System Security Extensions
Domain_Name_System_Security_Extensions
Public recursive DNS resolver based in Switzerland
Quad9 is a global public recursive DNS resolver that blocks access to domains associated with malware and phishing. Quad9 is operated by the Quad9 Foundation
Quad9
Technique of representing an aggregate data structure
that it can be adapted to lists, trees, and other recursively defined data structures. Such modified data structures are usually referred to as "a tree with
Zipper_(data_structure)
Rooted binary tree data structure
pseudocode implements the BST search procedure through recursion. The recursive procedure continues until a nil {\displaystyle {\text{nil}}} or the key
Binary_search_tree
Object which stores memory addresses in a computer program
structuring data in such cons-lists, these languages facilitate recursive means for building and processing data—for example, by recursively accessing the
Pointer (computer programming)
Pointer_(computer_programming)
Fixed-point theorem
in the theory of computable functions. It is also used to define recursive data types, e.g. linked lists, in domain theory. Kleene fixed-point theorem
Bourbaki–Witt_theorem
Algorithms which recursively solve subproblems
divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough
Divide-and-conquer_algorithm
Method in computer programming of forming higher-level object types
and object aggregation are closely related ways to combine objects or data types into more complex ones. In conversation, the distinction between composition
Object_composition
Limited form of tree data structure
child and the right child. That is, it is a k-ary tree where k = 2. A recursive definition using set theory is that a binary tree is a triple (L, S, R)
Binary_tree
Data structure that always preserves the previous version of itself when it is modified
versions, the data structure is called confluently persistent. Structures that are not persistent are called ephemeral. These types of data structures are
Persistent_data_structure
Organization of information or objects into (usually self-similar) layers
with lexical scope nested data structures such as records, objects, classes, etc. nested virtualization, also called recursive virtualization: running a
Nesting_(computing)
Origins and events of data
recovery, auditing and compliance analysis: "Lineage is a simple type of why provenance." Data governance plays a critical role in managing metadata by establishing
Data_lineage
Standard data modeling language for product data
specify the type of entity attributes and aggregate members. Datatypes can be used in a recursive way to build up more and more complex data types. E.g. it
EXPRESS (data modeling language)
EXPRESS_(data_modeling_language)
Conversion process for computer data
features such as a data type tags, support for cyclic data structures, indentation-sensitive syntax, and multiple forms of scalar data quoting. YAML is
Serialization
3-volume treatise on mathematics, 1910–1913
theory specifies the rules of syntax (rules of grammar) usually as a recursive definition that starts with "0" and specifies how to build acceptable
Principia_Mathematica
Diagram that represents a workflow or process
Business process mapping Data and information visualization Interactive EasyFlow Process architecture Pseudocode Recursive transition network Unified
Flowchart
Compact encoding of digital data
coding PackBits PAQ Prediction by partial matching Range coding Re-Pair Recursive indexing Rice coding Run-length encoding Sequitur algorithm Shannon coding
Data_compression
In-band data value that must be handled specially by computer code
dummy data) is a special value in the context of an algorithm which uses its presence as a condition of termination, typically in a loop or recursive algorithm
Sentinel_value
Area of automatic programming
structured distances have been advocated for a better handling of recursive data types and structures; abstraction has also been explored as a more powerful
Inductive_programming
Malicious archive file designed to disrupt the program or system reading it
example of a recursive zip bomb is titled 42.zip, which is a zip file of unknown authorship consisting of 42 kilobytes of compressed data, containing five
Zip_bomb
Programming language
→ False More complex data structures can be obtained by recursive data types. For instance, a list of elements, where the type of elements is arbitrary
Curry_(programming_language)
Two functions defined from each other
Just as algorithms on recursive datatypes can naturally be given by recursive functions, algorithms on mutually recursive data structures can be naturally
Mutual_recursion
Tree data structure that partitions a 2D area
to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The data associated with a leaf cell varies by application
Quadtree
Programming function applied recursively to its previous result
recursive type, according to a generic pattern, generalizing the ana for lists given above. For example, the unfold for the tree data structure data Tree
Anamorphism
Open-source, strongly-typed database
function types), which can be defined recursively. This can have advantages for graph data workloads, as most graph algorithms are formulated recursively. TypeDB's
TypeDB
Mathematical-logic system
is M; this means a recursive function definition cannot be written with let. The letrec construction would allow writing recursive function definitions
Lambda_calculus
Sequence of program instructions invokable by other software
subroutine nesting and recursive subroutines. The Burroughs B5000 (1961) is one of the first computers to store subroutine return data on a stack. The DEC
Function (computer programming)
Function_(computer_programming)
Type of neural network which utilizes recursion
A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce
Recursive_neural_network
Programming paradigm based on applying and composing functions
passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable
Functional_programming
recursively bounded quantification, introduced in 1989, allows for more precise typing of functions that are applied on recursive types. A recursive type
Bounded_quantification
Type of data model
information on a given object requires a recursive traversal of the metadata, followed by a recursive traversal of the data that stops when every attribute retrieved
Entity–attribute–value_model
Programming paradigm restricted to provably terminating programs
lists (which would be rejected by a substructural recursive checker) is, using Haskell: import Data.List (partition) qsort [] = [] qsort [a] = [a] qsort
Total_functional_programming
Tree-like structure for data
Concepts. 4th ed., McGraw-Hill, 2004, p. 11, 21. Michael J. Kamfonas/Recursive Hierarchies: The Relational Taboo! Archived 2008-11-08 at the Wayback
Hierarchical_database_model
Programming language with English-like syntax
of this limitation is that PERFORM cannot be used to write recursive code. To write recursive routines, one must use a nested subprogram. Another simple
COBOL
Algorithm that estimates unknowns from a series of measurements over time
that processes data saved from the Kalman filter forward pass. The equations for the backward pass involve the recursive computation of data which are used
Kalman_filter
Computer network architecture proposal
The Recursive InterNetwork Architecture (RINA) is a new computer network architecture proposed as an alternative to the architecture of the currently
Recursive Internetwork Architecture
Recursive_Internetwork_Architecture
Class of algorithms
stack (LIFO) or queue (FIFO). As a tree is a self-referential (recursively defined) data structure, traversal can be defined by recursion or, more subtly
Tree_traversal
Chatbot developed by Microsoft
Artificial general intelligence superintelligence AI agent Intelligent agent Recursive self-improvement Planning Computer vision General game playing Knowledge
Tay_(chatbot)
American artificial intelligence company
from ChatGPT's training data and outputs. However, these pieces of text usually contained detailed descriptions of various types of violence, including
OpenAI
Human-readable data serialization language
and April 2002 as YAML Ain't Markup Language, a recursive acronym, to distinguish its purpose as data-oriented rather than document markup. A cheat sheet
YAML
Divide and conquer sorting algorithm
sometimes called partition-exchange sort. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory
Quicksort
Free and open-source object relational database management system
fewest features needed to completely support data types. These features included the ability to define types and to fully describe relationships – something
PostgreSQL
Type of algorithm in computer science
computer science, corecursion is a type of operation that is dual to (structural) recursion. Whereas recursion consumes a data structure by first handling the
Corecursion
Data structure in computer science
Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional
Octree
Programming language
(no type, no name) qsort([]) -> []; % If the list [] is empty, return an empty list (nothing to sort) qsort([Pivot|Rest]) -> % Compose recursively a list
Erlang_(programming_language)
Data structure in tree form sorted for fast lookup
trees of other formats. search-recursive(key, node) if node is NULL return EMPTY_TREE if key < node.key return search-recursive(key, node.left) else if key
Search_tree
Tree data structure with a variable and unbounded number of branches per node
Well-founded rose trees can be defined by a recursive construction of entities of the following types: A base entity is an element of a predefined ground
Rose_tree
Study of computable functions and Turing degrees
mathematical constructions can be effectively performed is sometimes called recursive mathematics. Computability theory originated in the 1930s, with the work
Computability_theory
Data structure with nodes pointing to the next node
singly linked linear list is a recursive data structure, because it contains a pointer to a smaller object of the same type. For that reason, many operations
Linked_list
Type of software
research such as transcription analysis, coding and text interpretation, recursive abstraction, content analysis, discourse analysis, grounded theory methodology
Computer-assisted qualitative data analysis software
Computer-assisted_qualitative_data_analysis_software
Recursive function
value). Fusion of these two recursive computations into a single recursive pattern then avoids building the intermediate data structure. This is an example
Hylomorphism (computer science)
Hylomorphism_(computer_science)
Set of markup declarations for SGML-family markup language
entities in the declared content type of elements or in the declared type of attributes (here the ENTITY type for the data attribute), or the SGML parser
Document_type_definition
Ability of a computing system to simulate Turing machines
Leopold Kronecker formulated notions of computability, defining primitive recursive functions. These functions can be calculated by rote computation, but
Turing_completeness
Design technique for parallel algorithms
jumping is considered a software design pattern for operating on recursive data types in parallel. As a technique for following linked paths, graph algorithms
Pointer_jumping
Local variable in computer programming
itself is defined along that local data although they exist in a somewhat similar, but not identical, form also in recursive languages with dynamic scoping
Automatic_variable
Generalization of linear programming
combination of the two that calls the iterative algorithm from the recursive algorithm. The recursive algorithm repeatedly chooses random samples whose size is
LP-type_problem
Chinese text-to-video model
Artificial general intelligence superintelligence AI agent Intelligent agent Recursive self-improvement Planning Computer vision General game playing Knowledge
Kling_AI
Programming language
reduces the need for the manual type annotations that are required in most statically typed languages. For example, the data types of variables and the signatures
OCaml
General-purpose functional programming language
loc * loc (* corners *) Note that a type synonym cannot be recursive; datatypes are necessary to define recursive constructors. (This is not at issue
Standard_ML
Data serialization format
recursive case of the definition of S-expressions is traditionally implemented using cons cells. S-expressions were originally intended only for data
S-expression
Parsing technique
is a type of shift-reduce parser, and does bottom-up parsing. A formal grammar that contains left recursion cannot be parsed by a naive recursive descent
Top-down_parsing
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travel, tourism, insurance