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Types constrained by a predicate
In type theory, a refinement type is a type endowed with a predicate which is assumed to hold for any element of the refined type. Refinement types can
Refinement_type
extends refinement calculus with a component language: it has been used in industrial developments. In type theory, a refinement type is a type endowed
Refinement_(computing)
Attribute of data
similar type. A refinement type is a type endowed with a predicate which is assumed to hold for any element of the refined type. For instance, the type of
Data_type
Extent to which a programming language discourages type errors
In computer science, type safety is the extent to which a programming language discourages or prevents type errors.[vague] Type-safe languages are sometimes
Type_safety
Computer science concept
of intersection types. A restricted form is refinement types. Union types are types describing values that belong to either of two types. For example, in
Type_system
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
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
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
Type system used in computer programming and mathematics
rather a consequence of the type rules defined next. Free type variables in a typing serve as placeholders for possible refinement. The binding effect of the
Hindley–Milner_type_system
Data type for values having two types
types are refinement types. Intersection types are useful for describing overloaded functions. For example, if number => number is the type of function
Intersection_type
High performance variant of the Honda Civic
driving experience compared with the FK8's greater refinement and usability. The interior of the Type R is based on the base model Civic and features a
Honda_Civic_Type_R
Validates computer program operations
state of the object. Typestates are capable of representing behavioral type refinements such as "method A must be invoked before method B is invoked, and method
Typestate_analysis
Programming language concept
In computer programming, type variance is the relationship between subtypes of a composite type (e.g. List[Int]) and the subtypes of its components (e
Type_variance
Subsets whose union equals the whole set
omitting some of them; whereas a refinement is made from any sets that are subsets of the sets in the cover. The refinement relation on the set of covers
Cover_(topology)
Type whose definition depends on a value
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
language Haskell which allows specifying correctness properties by using refinement types. Properties are verified using a satisfiability modulo theories (SMT)
Liquid_Haskell
British single-seat WWII fighter aircraft
new, high-powered, liquid-cooled, in-line aero engines. They also had refinements such as retractable undercarriages, fully enclosed cockpits, and low-drag
Supermarine_Spitfire
Motor vehicle
Jaguar S-Type diesel and it's getting hugely good press. Everyone is saying that it's (sic) twin-turbo 2.7L engine is a paragon of refinement, and quietness
Jaguar_S-Type_(1999)
Type system
Gradual typing is a type system that allows for both static typing and dynamic typing but enforces types at runtime. Gradual typing allows software developers
Gradual_typing
Bugatti racing car, 1924 to 1930
refinements being made. The car used an evolution of the three-valve 1,991 cc (121.5 cu in) overhead cam straight-eight engine first seen on the Type
Bugatti_Type_35
Class of type systems
type system (or property-based type system) is a major class of type systems in which type compatibility and equivalence are determined by the type's
Structural_type_system
directly. Types of democracy can be found across time, space, and language. The foregoing examples are just a few of the thousands of refinements of, and
Types_of_democracy
Volkswagen panel van
The Volkswagen Transporter, initially the Type 2, is a range of light commercial vehicles, built as vans, pickups, and cab-and-chassis variants, introduced
Volkswagen_Type_2
expected order and of the expected type. Session type systems have been adapted for both channel and actor systems. Session types are used to ensure desirable
Session_type
Concept in computing
a unique type guarantees that an object is used in a single-threaded way, with at most a single reference to it. If a value has a unique type, a function
Uniqueness_type
Form of type polymorphism
print(type(type(a))) # prints: <type 'type'> print(type(type(type(a)))) # prints: <type 'type'> print(type(type(type(type(a))))) # prints: <type 'type'> In
Subtyping
Feature of a programming language
abstract type (also known as existential types) is a type in a nominative type system that cannot be instantiated directly; by contrast, a concrete type can
Abstract_type
In graph theory and theoretical computer science, the colour refinement algorithm also known as the naive vertex classification, or the 1-dimensional version
Colour_refinement_algorithm
Type system where types are associated with values and not variables
programming, latent typing refers to a type system where types are associated with values and not variables. An example latently typed language is Scheme
Latent_typing
Special performance editions of Honda car model families
Honda Type R models are special performance editions of their respective model families. The design of Type R models was originally focused on race conditions
Honda_Type_R
Curved curface derived from a coarse polygon mesh
recursive in nature. The process starts with a base level polygonal mesh. A refinement scheme is then applied to this mesh. This process takes that mesh and
Subdivision_surface
Major class of type system in computer science
of the types. Nominal systems are used to determine whether types are equivalent, as well as whether a type is a subtype of another. Nominal type systems
Nominal_type_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)
Explicit identification of variable type
In computer science, manifest typing is explicit identification by the software programmer of the type of each variable being declared. For example: if
Manifest_typing
Abstract data type for storing distinct values
be denoted by 2A or 𝒫(A). (Subtypes and subsets may be modeled by refinement types, and quotient sets may be replaced by setoids.) The characteristic
Set_(abstract_data_type)
Algorithms for mesh generation
In mesh generation, Delaunay refinements are algorithms for mesh generation based on the principle of adding Steiner points to the geometry of an input
Delaunay_refinement
Logical problem studied in computer science
usually have the extension ".smt2"). The LiquidHaskell tool implements a refinement type based verifier for Haskell that can use any SMTLIB2 compliant solver
Satisfiability modulo theories
Satisfiability_modulo_theories
Universal type in logic and computer science
actually top types in the type-system, but rather type-erased containers, from which the data is obtained through downcasting (or type refinement). std.variant
Any_type
Public university in El Paso, Texas, US
Motto Scientia et Humanitas (Latin) Motto in English "Knowledge and Refinement" Type Public research university Established April 16, 1913; 113 years ago (1913-04-16)
University of Texas at El Paso
University_of_Texas_at_El_Paso
Concept in abstract algebra
In mathematics, a refinement monoid is a commutative monoid M such that for any elements a0, a1, b0, b1 of M such that a0+a1=b0+b1, there are elements
Refinement_monoid
Formalism in computer science
considered (see kinds below). From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus, but from another point
Typed_lambda_calculus
is a refinement of Perfect Bayesian equilibrium in a signaling game proposed by Banks and Sobel (1987). One of the most widely-applied refinements is the
Divine_equilibrium
American Type Founders was the largest producer of foundry type in the world, not only of in-house designs, but also from designs that came from merged
List of American Type Founders typefaces
List_of_American_Type_Founders_typefaces
Formal rule for predicting how a game will be played
puts any one of the solutions in doubt, so a game theorist may apply a refinement to narrow down the solutions. Each successive solution concept presented
Solution_concept
Overreaction of the immune system to an antigen
Gell and Coombs classification with some slight refinements in that it subdivides type IV into type IVa, IVb, IVc, and IVd, adds non-allergic hypersensitivity
Hypersensitivity
2026 Indian film by Nitesh Tiwari
trilogy by producers; following several years of development and script refinement, it was restructured as a two-part film series under Tiwari's sole direction
Ramayana:_Part_1
Black and tan dog breed from Germany
The Dobermann is a German breed of working dog of pinscher type. In Canada and the United States it is known as the Doberman Pinscher. It was originally
Dobermann
Type of adjustable wrench
A monkey wrench is a type of smooth-jawed adjustable wrench, a 19th century American refinement of 18th-century English coach wrenches. It was widely used
Monkey_wrench
Graphic mark representing an entity
research, conceptualization, investigation of alternative candidates, refinement of a chosen design, testing across products, and finally adoption and
Logo
Electronic method of transmitting information with a carrier wave
modulation (SSB-SC) is a type of signal modulation used to transmit information, such as an audio signal, by radio waves. A refinement of amplitude modulation
Single-sideband_modulation
Strategies for composition and decomposition
leadership. A top-down approach (also known as stepwise design and stepwise refinement and in some cases used as a synonym of decomposition) is essentially the
Bottom-up and top-down approaches
Bottom-up_and_top-down_approaches
Of a function, an additional effect besides returning a value
but it is customary for programmers to avoid them. Effect systems extend types to keep track of effects, permitting concise notation for functions with
Side effect (computer science)
Side_effect_(computer_science)
Russian five-shot, bolt-action military rifle
Manufacture Nationale d'Armes de Châtellerault. There have been several refinements and variations of the original rifle, the most common being the M1891/30
Mosin–Nagant
Scientific software research institute
Michael H.; Vazou, Niki; Jhala, Ranjit (2024-01-05). "Mechanizing Refinement Types". Proceedings of the ACM on Programming Languages. 8: 2099–2128. doi:10
IMDEA_Software_Institute
always open to subsequent refinement from a confrontation with the empirical evidence. The contrast with Weber's ‘ideal type’ came from the latter's ‘accentuation’
Normal_type
Quality of zero being an even number
ISBN 978-1-56750-037-0 Lovas, William; Pfenning, Frank (2008-01-22), "A Bidirectional Refinement Type System for LF", Electronic Notes in Theoretical Computer Science, 196:
Parity_of_zero
Facility that processes crude oil
oil refineries use many different technologies and can be thought of as types of chemical plants. Since December 2008, the world's largest oil refinery
Oil_refinery
Normative ethical theories
short descriptions of redirect targets Phronesis – Ancient Greek word for a type of wisdom or intelligence Rule according to higher law – Belief that universal
Virtue_ethics
Term in narrative theory
being perceived, and with what degree of subjective colouring. Bal's refinement has been influential but also debated. Genette himself responded critically
Focalisation
Moveable bridge type
bascule name derives from the location where it is widely used, and is a refinement by Joseph Strauss of the fixed-trunnion. There are 44 movable bridges
Bascule_bridge
Motor vehicle
rear suspension. Having released the Mark X with its many technical refinements, Jaguar boss Sir William Lyons expected the Mark 2 would need updating
Jaguar_S-Type_(1963)
Numerical method for solving physical or engineering problems
the basis function, one has a p-method. If one combines these two refinement types, one obtains an hp-method (hp-FEM). In the hp-FEM, the polynomial degrees
Finite_element_method
Compact composite lens
FRAY-nel, -nəl; /ˈfrɛnɛl, -əl/ FREN-el, -əl; or /freɪˈnɛl/ fray-NEL) is a type of composite compact lens which reduces the amount of material required compared
Fresnel_lens
Counterintuitive result in probability
a typewriter keyboard for an infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare. More
Infinite_monkey_theorem
Potentially hazardous near-Earth asteroid
sun temple's persea tree. Apophis will evolve from an Aten- into an Apollo-type asteroid as a result of the 2029 encounter. Apollo asteroids are usually
99942_Apophis
Oil used in food and cooking, of vegetable or animal origin
oil extraction and refinement are separate processes. Extraction first removes the oil, typically from a seed, nut or fruit. Refinement then alters the appearance
Cooking_oil
British four-engined narrow-body jet airliner
rudder segment for greater control effectiveness; these aerodynamic refinements considerably elongated the testing process. The certification programme
Vickers_VC10
pedophilic activities in their comment sections, and fluctuating policies on the types of content that is eligible to be monetized with advertising. YouTube was
History_of_YouTube
Word derived from sophistry
Wiktionary, the free dictionary. Sophistication refers to the qualities of refinement, good taste, and wisdom. By contrast, its original use was as a pejorative
Sophistication
Soviet military intermediate rifle cartridge
01 mm from its tip, and it was lacking a boat tail. After some further refinements, a pilot production series of this cartridge began in March 1944. After
7.62×39mm
Computer program for the Boolean satisfiability problem
constraint programming competitions in editions 2018 up until 2025. Certain types of large random satisfiable instances of SAT can be solved by survey propagation
SAT_solver
Idea that everyone faces consequence as they deserve
v t e Bullying Types Abusive supervision Cyberbullying Disability bullying Displaced aggression Doxing LGBTQ bullying Hazing Military bullying Mobbing
Just-world_fallacy
Method of strengthening materials by changing grain size
angular pressing (ECAP) or high-pressure torsion (HPT), can lead to grain refinement and the creation of new grain boundaries with tailored characteristics
Grain_boundary_strengthening
FDR (Failures-Divergences Refinement) and subsequently FDR2, FDR3 and FDR4 are refinement checking software tools, designed to check formal models expressed
FDR_(software)
Island country in Southeast Asia
Archived from the original on 8 April 2008. Retrieved 27 February 2011. "Refinements to Mother Tongue Language Policy" (Press release). Ministry of Education
Singapore
British heavy fighter aircraft of WWII
The Bristol Type 156 Beaufighter (often called the Beau) is a British multi-role aircraft developed during the Second World War by the Bristol Aeroplane
Bristol_Beaufighter
Type of polygon mesh in computer graphics
was based on generalized bi-cubic uniform B-splines. The subdivision refinement algorithm was developed in 1978 by Daniel Doo and Malcolm Sabin. The Doo-Sabin
Doo–Sabin_subdivision_surface
Form of song
alphabetic and neumes notation over the text, but as a rule have less rhythmic refinement compared to the earlier group. However, the comparison between the two
Gregorian_chant
String used to identify a name of a web or internet resource
subdivision into URL and URN. URL is a useful but informal concept: a URL is a type of URI that identifies a resource via a representation of its primary access
Uniform_Resource_Identifier
Sports car
7M-GE engine was rated at 149 kW (200 hp; 203 PS) at 6,000 rpm. Further refinement on the turbo model increased power to 173 kW (232 hp; 235 PS) at 5,600
Toyota_Supra
Programming language syntax designed for ease of use
from the original (PDF) on March 31, 2017. Chugh, Ravi (2013). Nested Refinement Types for JavaScript (PhD). UC San Diego. "C Language LLVM Documentation"
Syntactic_sugar
Fine powder green tea
economic significance of matcha, which had long been a symbol of elite refinement and ceremonial practice. Tea producers in Uji, who had enjoyed exclusive
Matcha
Computer science field
used for verification when two descriptions are not equivalent. During refinement, the specification is complemented with details that are unnecessary in
Model_checking
language theory, flow-sensitive typing (also called flow typing or occurrence typing) is a type system where the type of an expression depends on its
Flow-sensitive_typing
English musician and songwriter (born 1942)
Beatles." Critics described Rubber Soul as a significant advance in the refinement and profundity of the band's music and lyrics. Considered a high point
Paul_McCartney
Japanese attack aircraft family
in which the aircraft was typically used as a level bomber. Further refinement of the design during the late 1930s led to the development of the faster
Nakajima_B5N
Prosthesis used to change the size, shape, and contour of a person's breast
Capsular Contracture? A 23-Year Single-Surgeon Experience and Proposed Refinement of Baker Grade III". Aesthetic Plastic Surgery. doi:10.1007/s00266-026-06276-2
Breast_implant
Programming paradigm restricted to provably terminating programs
result for those inputs; or excluding them by use of type system features such as refinement types. These restrictions mean that total functional programming
Total_functional_programming
Analysis of computer programs without executing them
companies. The OMG (Object Management Group) published a study regarding the types of software analysis required for software quality measurement and assessment
Static_program_analysis
Object-oriented programming principle
Circle–ellipse problem Composition over inheritance Program refinement Referential transparency Type signature SOLID – the "L" in "SOLID" stands for Liskov
Liskov_substitution_principle
Country in East Asia
nature as allegory. During the imperial era, skill in art was a marker of refinement and high social status. By the Song period, landscape paintings became
China
1940 plan for German invasion of Britain
On 12 November 1940, Hitler issued Directive No. 18 demanding further refinement to the invasion plan. On 1 May 1941, fresh invasion orders were issued
Operation_Sea_Lion
equilibrium, in game theory, a refinement of Nash Equilibrium for extensive form games Sequential equilibrium, in game theory, a refinement of Nash Equilibrium for
List_of_types_of_equilibrium
Office skyscraper in Manhattan, New York
Preceded by 40 Wall Street Surpassed by Empire State Building General information Type Office building Architectural style Art Deco Location 405 Lexington Avenue
Chrysler_Building
Biological process to convert light into chemical energy
during the Boring Billion. Archaea such as Halobacterium also perform a type of non-carbon-fixing anoxygenic photosynthesis, where the simpler photopigment
Photosynthesis
Checking software against expectations
services describes private beta testing in short rounds, with updates and refinement informed by feedback. An empirical study of continuous software engineering
Software_testing
Team sport
are rarely employed in high-level competitions. Sky ball serve: a specific type of underhand serve occasionally used in beach volleyball, where the ball
Volleyball
a type of equilibrium refinement in signaling games. It aims to reduce possible outcome scenarios by restricting the possible sender types to types who
Intuitive_criterion
Graphical symbol or pictogram used to point or indicate direction
century. The arrow can be seen in the work of Paul Klee. In a further refinement of the symbol, John Richard Green's A Short History of the English People
Arrow_(symbol)
Oxide mineral
Retrieved 2 November 2026. Newnham, R. E.; de Haan, Y. M. (August 1962). "Refinement of the α Al2O3, Ti2O3, V2O3 and Cr2O3 structures*". Zeitschrift für Kristallographie
Corundum
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