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calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution. This is in contrast to
Explicit_substitution
Mathematical-logic system
evaluation of expressions in programming languages Explicit substitution – The theory of substitution, as used in β-reduction Harrop formula – A kind of
Lambda_calculus
Mathematical formalism
during substitution, an operation called capture-avoiding substitution. In programming languages with static scope, capture-avoiding substitution can be
Lambda_calculus_definition
Mathematical relation consisting of a multi-variable function equal to zero
y is restricted to nonnegative values. Some equations do not admit an explicit solution. The implicit function theorem provides conditions under which
Implicit_function
Formal languages for expressing mathematical theories
adopted and/or reinvented in areas such as typed lambda calculus and explicit substitution. Dependent types is one outstanding example. Automath was also the
Automath
Postulation about the significance of Christ's death
Penal substitution, also called penal substitutionary atonement and especially in older writings forensic theory, is a theory of the atonement within Protestant
Penal_substitution
Algorithmic process of solving equations
V} . Then a substitution σ {\displaystyle \sigma } is subsumed by another substitution τ {\displaystyle \tau } if there is a substitution θ {\displaystyle
Unification (computer science)
Unification_(computer_science)
System of formal deduction in logic
system uses a substitution rule and uses modus ponens as an inference rule. The exact same system was given (with an explicit substitution rule) by Alonzo
Hilbert_system
Theoretical model of computation
is Xavier Leroy's ZINC abstract machine, which underlies OCaml.) Explicit substitution Operational semantics SECD machine Semantics of programming languages
Krivine_machine
Feature of some Unix shells
form of process substitution (=(cmd)) that uses a temporary file instead of a pipe. The fish shell added its own process substitution with yet another
Process_substitution
Applicative computing systems Anonymous recursion Evaluation strategy Explicit substitution SKI combinator calculus Unlambda Currying Caml Cousineau G., Curien
Categorical_abstract_machine
Replacing one player with another during a match
substitute or by a starter who is currently on the bench. Free substitution or rolling substitution is a rule in some sports that allows players to enter and
Substitution_(sport)
Logical formalism using combinators instead of variables
system Categorical abstract machine Combinatory categorial grammar Explicit substitution Fixed point combinator Graph reduction machine Lambda calculus and
Combinatory_logic
Variable that stores data about other variables or program structure
be substituted by different instances. Attempts to formalize the notion of metavariable result in some kind of type theory. Explicit substitution Hunter
Metavariable
Branch of logic
inference rule, as well as a rule of substitution, which permits replacing any well-formed formula with any substitution-instance of it. Alternatively, one
Propositional_logic
proper, specifically, within the framework of explicit substitution. Term rewrite system Explicit substitution Memoization Sinot, François-Régis; Fernández
Director_string
Alignment of more than two molecular sequences
much simpler substitution matrix, wherein only identical matches and mismatches are considered, is typical. The scores in the substitution matrix may be
Multiple_sequence_alignment
sequences. Model-based methods like Maximum Likelihood also incorporate explicit substitution model. Understanding how Minimum evolution relate to these alternatives
Minimum_evolution
Segment of the sketch comedy TV series
this reading, then, comes from making this assumed, implicitly white norm explicit and, in doing so, it asks Comedy Central's desired white audience to grapple
Substitute Teacher (Key & Peele)
Substitute_Teacher_(Key_&_Peele)
Matrix representing the frequency of evolution of a protein or nucleotide sequence
type of disruptive substitution is likely to be removed from populations by the action of purifying selection because the substitution has a higher likelihood
Substitution_matrix
Theoretical computer model
{\displaystyle \lambda {\widehat {\rho }}} calculus — a calculus that uses explicit substitution — with a left-to-right applicative-order reduction strategy, and
CEK_Machine
Bruijn notation has also been shown to be useful in calculi for explicit substitution in pure type systems. Mathematical notation De Bruijn, Nicolaas
De_Bruijn_notation
Policy on permits required to enter the Kingdom of the Netherlands in the Caribbean
A common visa exists since the end of 2010 for the territories of Aruba, Curaçao, Sint Maarten (landen (English: countries) within the Kingdom) and the
Visa policy of the Kingdom of the Netherlands in the Caribbean
Visa_policy_of_the_Kingdom_of_the_Netherlands_in_the_Caribbean
Republic (Italian: presidente supplente della Repubblica) is an office not explicitly provided for in the Constitution but deriving from the provision contained
List_of_presidents_of_Italy
Measure of responsiveness of growth rate of consumption
In economics, elasticity of intertemporal substitution (or intertemporal elasticity of substitution, EIS, IES) is a measure of responsiveness of the growth
Elasticity of intertemporal substitution
Elasticity_of_intertemporal_substitution
Generalization of the concept from statistical mechanics
above defines the Fisher information metric can be readily seen by explicitly substituting for the expectation value: g i j ( β ) = ⟨ ( H i − ⟨ H i ⟩ ) (
Partition function (mathematics)
Partition_function_(mathematics)
Mild or indirect word or expression
A euphemism is the substitution of a potentially offensive or unpleasant word or expression with one that is more pleasant or inoffensive. Some euphemisms
Euphemism
Canadian broadcasting practice
Simultaneous substitution (also known as simsubbing or signal substitution) is a practice mandated by the Canadian Radio-television and Telecommunications
Simultaneous_substitution
Legendary war in Greek mythology
debate. Although certainly very close, Achilles and Patroclus are never explicitly cast as lovers by Homer, but they were depicted as such in the archaic
Trojan_War
Category of cloud computing
owner's consent. Certain open-source licenses such as GPL-2.0 do not explicitly grant rights permitting distribution as a SaaS product in Germany. In
Software_as_a_service
Marvel Comics fictional character
result, Shooter ordered that Claremont and Byrne rewrite issue #137 to explicitly place in the story both a consequence and an ending commensurate with
Jean_Grey
Episodes of the American sitcom
appear in this episode. Alice states that Martha "has gone back east for a while", presumably to stay with George, although that is never explicitly said.
List of Dennis the Menace (1959 TV series) episodes
List_of_Dennis_the_Menace_(1959_TV_series)_episodes
Depiction of human sexuality in Indian audiovisual media
against explicit content, leading filmmakers to develop a "grammar of visual metaphors" to bypass censorship. Physical intimacy was routinely substituted with
Sex_in_Indian_entertainment
psilocybin, mescaline, DOM, 2C-B, 25I-NBOMe, MDA, and LSD among others, are explicitly controlled substances. In addition, most other psychedelic phenethylamines
Legal status of psychedelic drugs in Canada
Legal_status_of_psychedelic_drugs_in_Canada
Formula in calculus
evaluated. In integration, the counterpart to the chain rule is the substitution rule. Intuitively, the chain rule states that knowing the instantaneous
Chain_rule
Prime Minister of the United Kingdom since 2026
economic development with social benefits, with policies designed to explicitly channel the proceeds of growth towards communities, rejecting trickle-down
Andy_Burnham
Approach to finding numerical solutions of ordinary differential equations
differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and
Euler_method
World War II Nazi special-ops mission
two Sherman tanks in poor condition, and Skorzeny had to use German substitutes, five tanks (Panzer V "Panther") and six armored cars. The brigade was
Operation_Greif
Electronic structure method
substitution, each one is based on a different formulation of quantum mechanics theory. Here we give a simple derivation of the Peierls substitution,
Peierls_substitution
Functional programming language
only mathematically simple control mechanisms of pattern matching and substitution. Refal also includes a feature called the freezer to support efficient
Refal
Process of mathematical modelling, performed on a computer
Carlo algorithm. Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simple closed form analytic solutions
Computer_simulation
Physical interaction of charged particles
the variable and limits of integration from t to φ makes this connection explicit: Δ P = ∫ − π − θ 2 π − θ 2 k q a q g r 2 ⋅ cos φ ⋅ d t d φ ⋅ d φ {\displaystyle
Coulomb_scattering
Replacement, insertion, or deletion of a single DNA or RNA nucleotide
to a high standard. There can also be replication errors that lead to substitution, insertion, or deletion mutations. In 1959 Ernst Freese coined the terms
Point_mutation
One of four stable isomers of butanediol
gamma-butyrolactone) as a Class C controlled substance. In Germany, the drug is not explicitly illegal, but might also be treated as illegal if used as a drug. It is
1,4-Butanediol
Shorthand to convey tone or intent
joke (which is commonly represented as /j). Tone indicators are used to explicitly state the author's intent, instead of leaving the message up to interpretation
Tone_indicator
entity must either be predefined (built into the markup language) or explicitly declared in a Document Type Definition (DTD). The format is the same as
List_of_Unicode_characters
Statement supporting a conclusion
their mode of expression, their role in arguments, and their content. Explicit premises are overtly stated, whereas implicit premises are tacitly assumed
Premise
Controlled language for technical documentation
misapplied within aerospace and military organizations, typically as a substitute for a grammar-based style guide. The result has led untrained writers
Simplified_Technical_English
Type system used in computer programming and mathematics
substitution. mgu {\displaystyle {\textsf {mgu}}} is a side-effect free version of union {\displaystyle {\textit {union}}} producing a substitution which
Hindley–Milner_type_system
Long-range anti-ship cruise missile
The P-700 Granit (Russian: П-700 "Гранит"; English: granite) is a Soviet and Russian naval anti-ship cruise missile. Its GRAU designation is 3M45 and its
P-700_Granit
Optimization replacing a function call with that function's source code
the last expression invoked inside it. Since C macros use mere textual substitution, this may result in unintended side-effects and inefficiency due to re-evaluation
Inline_expansion
Basic notion of sameness in mathematics
Z),} therefore X = Z . {\displaystyle X=Z.} Substitution: See Substitution (logic) § Proof of substitution in ZFC. Function application: Given a = b {\displaystyle
Equality_(mathematics)
Non-singular cubic surface in mathematics
2024-11-24. Clebsch, A. (1871), "Ueber die Anwendung der quadratischen Substitution auf die Gleichungen 5ten Grades und die geometrische Theorie des ebenen
Clebsch_surface
FC Barcelona's youth academy
have come up through La Masia in a La Liga match. After Dani Alves was substituted by Martín Montoya due to an injury in the 13th minute, Barça played the
La_Masia
1991 studio album by Naughty by Nature
soundtrack for Tony Hawk's Pro Skater 2. "Yoke the Joker" "Synthetic Substitution" by Melvin Bliss "Wickedest Man Alive" "Big Beat" by Billy Squier "O
Naughty_by_Nature_(album)
Italian computer scientist
required) Abadi, M.; Cardelli, L.; Curien, P. L.; Levy, J. J. (1990). "Explicit substitutions". Proceedings of the 17th ACM SIGPLAN-SIGACT Symposium on Principles
Luca_Cardelli
Name for a coin or unit of currency
Often it was expressed by a solidus symbol (/) (which may have begun as a substitute for ſ ('long s')) thus '1/9' means "one shilling and ninepence". A price
Shilling
In general, exponentiation fails to be commutative
given by x = y . {\displaystyle x=y.} Nontrivial solutions can be written explicitly using the Lambert W function. The idea is to write the equation as a e
Equation_xy_=_yx
Rule for substituting a set input with a set output
expansion, but in languages such as C where they use simple textual substitution, they have a number of severe disadvantages over other mechanisms for
Macro_(computer_science)
Modification of the Euler method for solving Hamilton's equations
mathematics, the semi-implicit Euler method, also called symplectic Euler, semi-explicit Euler, Euler–Cromer, and Newton–Størmer–Verlet (NSV), is a modification
Semi-implicit_Euler_method
Consonantal sound often represented by ⟨ʒ⟩ in IPA
fricative. In English, the phoneme [ʒ] is often found as a hyperforeign substitute for [dʒ] in certain borrowings, Beijing (Mandarin Chinese [tɕ], a voiceless
Voiced_postalveolar_fricative
Mathematical models of changing DNA
probability matrix are described in the mathematics of substitution models section of the substitution model page. By expressing models in terms of the instantaneous
Models_of_DNA_evolution
Pharmaceutical compound
is not a controlled substance in Canada as of 2025. Ergine is not an explicitly controlled substance in the United States. However, it could be considered
Isoergine
Conspiracy theory about race and culture
genocide conspiracy theory except in the substitution of antisemitic tropes with Islamophobia. This substitution, along with a use of simple catch-all slogans
Great Replacement conspiracy theory
Great_Replacement_conspiracy_theory
Twenty-third letter of the Latin alphabet
distinct ligature ⟨W⟩ was gradual and was only apparent in abecedaria, explicit listings of all individual letters. It was probably considered a separate
W
Variety of English spoken in Scotland
(standard in American English), interdict for '"injunction", and sheriff-substitute for "acting sheriff". In Scottish education a short leet is a list of
Scottish_English
American sports comedy-drama television series
tactical brilliance, being dubbed the "Wonder Kid" after an inspired substitution which results in a Richmond victory over Tottenham in the FA Cup, Nate
Ted_Lasso
Pharmaceutical compound
good tolerability. 4-PrO-MET is not an explicitly controlled substance in the United States or in Canada. Substituted tryptamine 4-PrO-DMT and 4-PrO-DiPT
4-PrO-MET
Performing order of mathematical operations
this convention is not universally understood, and some authors prefer explicit parentheses. Some calculators and programming languages require parentheses
Order_of_operations
Software design pattern
using std::ostream; class Printer { private: ostream& stream; public: explicit Printer(ostream& out): stream{out} {} template <typename T> Printer& print(T&&
Curiously recurring template pattern
Curiously_recurring_template_pattern
her; a male police officer visits her house to interview her, views the explicit content, and gives her his Instagram details, and they meet up socially;
List_of_Dispatches_episodes
Game theory concept
more in market 2. If the Cournot equilibrium of this model is calculated explicitly, we find x 1 ∗ = max { 0 , 8 p 1 − 2 5 } , x 2 ∗ = max { 0 , 2 − 3 p 1
Strategic_complements
Partial differential equation
{\displaystyle \varphi } that satisfies different boundary conditions. Explicit expressions for the viscous Burgers' equation are available. Some of the
Burgers'_equation
Hormone therapy used to treat symptoms of menopause
(1999). "Theoretical basis for the benefit of postmenopausal estrogen substitution". Experimental Gerontology. 34 (5): 587–604. doi:10.1016/S0531-5565(99)00032-7
Hormone_replacement_therapy
Monetary symbol used in many national currencies
world, including most currencies denominated "dollar" or "peso". The explicitly double-barred sign is called cifrão in the Portuguese language. The sign
Dollar_sign
Characterizes spherical triangles with fixed base and area
{\tfrac {1}{2}}|PA^{*}|\,\tan {\tfrac {1}{2}}|PB^{*}|,} from which we can explicitly construct the point C {\displaystyle C} on g {\displaystyle g} such that
Lexell's_theorem
broadly be defined as recreational purposes but also receives frequent, explicit mention as an essential component of his writing toolkit, such as in his
History and culture of substituted amphetamines
History_and_culture_of_substituted_amphetamines
Phenolic compound found in Norway spruces
McDonough, G.N. Mott, "Process for the preparation of arylalkylamines and substituted arylalkylamines", published 1992-12-29, assigned to Hoechst Celanese
Piceol
Football match between Inter Milan and AC Milan
respective clubs would often not play together, with one usually being substituted by the other at half-time. Rivera ended up losing the starting line-up
Derby_della_Madonnina
the face of it". A legal term typically used to state that a document's explicit terms are defective absent further investigation. Also, "contempt ex facie"
List_of_Latin_phrases_(full)
In logic, a statement which is always true
predicate logic that can be reduced to propositional tautologies by substitution. Propositional logic begins with propositional variables, atomic units
Tautology_(logic)
Type of rice wine used in Japanese cuisine
mirin), or mirin-fu chomiryo (literally: mirin-like seasoning), which are substitutes not actually mirin. They are blends of sweetener syrups, flavorings such
Mirin
like Trudy, who previously believed she was dark-skinned until Oscar explicitly points it out to her. Penny then gets the idea to protest the sorority's
List of The Proud Family: Louder and Prouder episodes
List_of_The_Proud_Family:_Louder_and_Prouder_episodes
Mathematical functions
}}={\frac {1}{2}}\cdot {\frac {1\cdot 3\cdots (2k-1)}{2\cdot 4\cdots (2k)}}} . Explicit formulas are g n ( x ) = ∑ k = 1 n 2 k − 1 ( n − 1 n − k ) ( x k ) = ∑
Mittag-Leffler_polynomials
American football league
case, Repole acknowledged instability (annual stadium changes and the substitution of the successful XFL Roughnecks with the Gamblers) as the key reason
United Football League (2024–present)
United_Football_League_(2024–present)
Base pairs in molecular genetics
different approaches towards approximating the environmental effects, without explicit considerations of any specific environmental interactions. This has further
Non-canonical_base_pairing
Philosophical theory
functions and of our own capability are, to a large extent, beyond our explicit understanding. The theory was articulated by Michael Polanyi in his book
Polanyi's_paradox
Shell command for scheduling periodic jobs
inaccuracies of computer time-of-day tracking, Unix alarm scheduling, explicit time-of-day changes, and process management, all of which account for the
Cron
Telephone conversation describing sex activities
between two or more people by means of the telephone that is sexually explicit and is intended to provoke sexual arousal in one or more participants.
Phone_sex
Computer text file character representing blank space
display the character as a fixed-width blank, however the Unicode standard explicitly states that it does not act as a space. Unicode's coverage of the Korean
Whitespace_character
Period of the history of Spain corresponding to the Contemporary Age
1910). The social orientation of the governmental measures included the substitution of consumption by a progressive tax on urban incomes and a boost to primary
Contemporary_history_of_Spain
White brined cheese from Czechia and Slovakia
It is usually not matured (Czech: nezrající). It is mainly used as a substitute of sirene in the Bulgarian shopska salad or instead of feta in greek salad
Balkánský_sýr
2023 film by Emerald Fennell
2023. Retrieved 18 January 2024. Mahale, Jenna. "Jacob Elordi to star in explicit The Talented Mr Ripley-esque new movie". i-D. Archived from the original
Saltburn_(film)
Mathematical symbol of equality
readily available equals sign on most keyboards is commonly used as a substitute for a double hyphen. In linguistic interlinear glosses, an equals sign
Equals_sign
Chemical compound
in Canada as of 2025. Quipazine is not an explicitly controlled substance in the United States. Substituted piperazine 2C-B-PP CPQ FPPQ ORG-37684 Winter
Quipazine
Ion or molecule bound to a metal atom
mechanisms are recognized: associative substitution or by dissociative substitution. Associative substitution closely resembles the SN2 mechanism in organic
Ligand
and 1990, the bridge was being renovated, therefore, soldiers built a substitute bridge ca. 700 metres (2,300 ft) to the north of the Poniatowski Bridge
Transport_in_Warsaw
Polynesian language
glottal stops, although to avoid the complications caused by automatic substitution of basic punctuation characters for letters in digital documents, and
Tahitian_language
System used in industry to eliminate or minimize exposure to hazards
of the hazard and protecting themselves. Substitution has less priority than elimination because the substitute can possibly also come with a hazard. Engineering
Hierarchy_of_hazard_controls
Type of permutation
MathWorld. Ross Tang, "An Explicit Formula for the Euler zigzag numbers (Up/down numbers) from power series" A simple explicit formula for An. "A Survey
Alternating_permutation
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