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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
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
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
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
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
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 has a low driving
Honda_Civic_Type_R
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
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
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)
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)
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
language Haskell which allows specifying correctness properties by using refinement types. Properties are verified using a satisfiability modulo theories (SMT)
Liquid_Haskell
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
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
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
In type theory, session types are used to ensure correctness in concurrent programs. They guarantee that messages sent and received between concurrent
Session_type
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
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
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
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
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)
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
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
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
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
Special performance editions of Honda car model families
rear spoiler and hood vent, featured a roof scoop, along with various refinements to reduce weight to 1,270 kg (2,800 lb). Under the body, panels and air
Honda_Type_R
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
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
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
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
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
Abstract data type for storing distinct values
{\displaystyle {\mathcal {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)
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
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
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
FDR (Failures-Divergences Refinement) and subsequently FDR2, FDR3 and FDR4 are refinement checking software tools, designed to check formal models expressed
FDR_(software)
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
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
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
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
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
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
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
Black and tan dog breed from Germany
The Dobermann is a German breed of medium-large working dog of pinscher type. In Canada and the United States it is known as the Doberman Pinscher. It
Dobermann
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
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
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
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
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
Machine for applying ink under pressure
individual letters) did not have the refinement and efficiency needed to become widely accepted. In China, movable type saw limited use, in part because a
Printing_press
Imperial 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
1825 novel
society. It is also known by the alternative title Tremaine; or, the Man of Refinement. It was a major influence on Benjamin Disraeli's debut novel Vivian Grey
Tremaine_(novel)
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
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
equilibrium refinement in signaling games. It aims to reduce possible outcome scenarios by restricting the possible sender types to types who could obtain
Intuitive_criterion
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
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
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
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
Pendulous Integrating Gyroscopic Accelerometer, an inertial guidance instrument
name of PIGA was suggested by Dr. Draper due to the addition of various refinements such as electromagnetic or optical sensing of pendulum position. Such
PIGA_accelerometer
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
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
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
could be produced by simplifying both the number of colors used, and the refinement of the detail in the image. Cheaper images, like the advertisement illustrated
History_of_printing
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
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
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)
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
Attempt to introduce indicative planning, profits and sales to Soviet firms
directive norms, and to pass over to a simpler, cheaper and more efficient type of control of the activities of enterprises. This control must be patterned
1965_Soviet_economic_reform
Oxide mineral
Retrieved 18 July 2026. Newnham, R. E.; de Haan, Y. M. (August 1962). "Refinement of the α Al2O3, Ti2O3, V2O3 and Cr2O3 structures*". Zeitschrift für Kristallographie
Corundum
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
Breed of herding dog
of the head, reminiscent of the Bentley mark, a feature linked to the refinement of this strain during the late nineteenth century. Their square build
Australian_Cattle_Dog
Subgenre of action game
some restrict the definition to games featuring spacecraft and certain types of character movement, while others allow a broader definition including
Shoot_'em_up
Country in South Asia
and comparative abundance that marked the Mewari landscape fostered refinements unattainable in other lands. Ameri, Marta (2018). "Letting the Pictures
India
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
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)
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
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
0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Alphabetically By type External links List of DC Comics characters: 0–9 List of DC Comics characters:
Lists_of_DC_Comics_characters
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
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
Sweet baked item
biscuit-making through the craft guilds. As the supply of sugar began, and the refinement and supply of flour increased, so did the ability to sample more leisurely
Biscuit
Utility aircraft under development
Indonesian turboprop airliner being developed by Indonesian Aerospace. A refinement of the CASA/IPTN CN-235, the N245 is designed for greater passenger capacity
Indonesian_Aerospace_N245
Ships deliberately set on fire during battle
on an ad hoc basis. The career of the modern fire ship, as a naval vessel type designed for this particular function and made a permanent addition to a
Fire_ship
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
Country in East Asia
Elite culture of the imperial period saw skill in art as a marker of refinement and high social status. Renowned art pieces often bear inscriptions and
China
Griffon-powered variants of the Supermarine Spitfire
Supermarine Spitfire Mark XVIII at Wikimedia Commons The Mk 18 was a refinement of the Mk XIV. It was identical in most respects including engine (the
Supermarine Spitfire (Griffon-powered variants)
Supermarine_Spitfire_(Griffon-powered_variants)
Strategy video game sub-genre
"real-time strategy" emerged from an extended period of evolution and refinement. Games sometimes perceived as ancestors of the real-time strategy genre
Real-time_strategy_game
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
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
Fictional character of the Drakengard series
YoRHa No. 2 Type B, commonly known as 2B, is a fictional android from the 2017 video game Nier: Automata, a spin-off of the Drakengard series developed
2B_(Nier:_Automata)
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
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
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