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monadic
monadic, a. (mɒˈnædɪk) [ad. Gr. µοναδικός composed of units, f. µοναδ-, µονάς monad.] 1. a. Composed of monads or units; pertaining to or of the nature of a monad; existing singly. Also quasi-n., that which is composed of units.1788 T. Taylor Proclus I. Diss. 14 The monadic, or that which is compose... Oxford English Dictionary
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Monadic
Monadic may refer to: Monadic, a relation or function having an arity of one in logic, mathematics, and computer science Monadic, an adjunction if and , a feature, type, or function related to a monad (functional programming) Monadic or univalent, a chemical valence Monadic, in theology, a religion wikipedia.org
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Merely monadic - HaskellWiki
Introduction. In Haskell, monadic types - types having an instance for the Monad class - can be thought of as abstract descriptors of computations which are inherently composable - smaller monadic expressions (actions) can be used to build larger ones. This monadic interface (as specified by Monad) provides actions additional flexibility in separating: . the time of composition: when it is ...
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What does the phrase Monadic Bind mean? - Medium
Reposting it here: Monadic bind is the name given to the (>>=) function or bind function, also known as chain, flatMap, or joinMap. I personally like to call it the "then" function borrowing ...
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Monadic predicate calculus
In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbols. wikipedia.org
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Dualizing the statement "A functor is monadic". This is another example of my struggle with the dualizing principle in Category theory. There are two notions, monadicity and comonadicity. I want to see how exactly the...
"$G$ is monadic" means $G$ has a left adjoint $F$ such that the comparison functor $c:\mathcal{C}\to (GF)-\mathbf{Alg}$ is an equivalence. Thus the dual of "$G$ is monadic" is "$G^{\mathrm{op}}$ is comonadic."
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Monadic Boolean algebra
Monadic Boolean algebras form a variety. Likewise, monadic Boolean algebras supply the algebraic semantics for S5. Hence S5-algebra is a synonym for monadic Boolean algebra. wikipedia.org
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Monadic signature with constant > Consider a signature $\Sigma = \\{ P^1, R^1, c\\}$. Where $P^1, R^1$ are unary predicates, and $c$ is a constant. > > Let A be a formula in FOL over $\Sigma$. Prove/Disprove: > > If...
$A'$ is a sentence over the purely monadic signature $(P^1, R^1)$ and hence is satisfiable iff it is satisfiable in a model with at most 4 elements.
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Monadic second-order logic
class NP, the class of problems that may be expressed in existential monadic second-order logic has been called monadic NP. The restriction to monadic logic makes it possible to prove separations in this logic that remain unproven for non-monadic second-order logic. wikipedia.org
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Is there a non-trivial monad, which is an equivalence of categories I assume a category $C$ and a monad $M : C → C$. Then I assume that $M$ is a (possibly adjoint) equivalence of categories. Does this mean that there ...
Yes, $M$ must be naturally isomorphic to the identity. The trick is to use the other unit identity together with naturality of $\mu$. Rather than explicitly constructing an inverse to the unit as you have done, let me give a slightly less direct argument that I think is clearer. Let $u:id_C\to M$ de...
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Proof of Decidability of Monadic First Order Logic I'm looking for the proof of decidability of Monadic FOL (i.e. FOL limited to predicate symbols of arity at most one and no function symbols). In the Wikipedia page ...
I have no reference, but it seems to me fairly straightforward that monadic FOL would be decidable: If you only have monadic predicates, and given that any sentence in monadic FOL would have only a finite number of monadic predicates (say $n$), then you can distinguish at most $2^n$ different 'kinds'
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monadic predicate logic This is my first post, so if I am doing anything wrong, please notify me. In predicate logic, can one produce a truth-functional extension of a sentence containing 3 constants for a set conta...
First realize that the $a,b,c$ in the sentence are constant symbols, while the $a $ and $b$ in the domain are objects, and these are different. That is, an interpretation needs to map each of the constants $a,b,c$ to either one of the objects $a$ and $b$ ...which is a little confusing... But can of ...
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Verilog按位或（"|"）monadic - VoidCC
在所提供的实例中，与|代码是功能上等同于相同的省略了|编码。三个可能的理由，并保持|对所提供的代码是：. 它给出指导合成：第一或address位，然后比较，而不是每个address位比较为0，则取与的结果为0， 。这是不同的门配置相同的功能结果。 cn.voidcc.com
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15. 모나드 역전 프로그램-유한생명(有限生命) (Monadic Reversal Program-Finite Life)
Apr 23, 2023너희들이 '마하라타 에너지(Maharata energy)'를 받기 위해서는 현재 처하고 있는 십자가형(十字架刑:crucifixion)에서 내려와야만 하는데, 이것을 위해서는 못 박힌 모나드 역전(Monadic reversed)을 풀어야만 가능하다는 것이란다.
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Non-monadic adjunction Could someone give some examples of a non-monadic adjunctions please? Possibly explaining why they are not monadic and how they contradict the monadicity theorem? Thanks!
A classical example : the forgetful functor from topological spaces to sets. The left adjoint is the "discrete space" functor (sending a set $X$ to the discrete space with underlying space $X$), and the composition just gives the identity on Sets, so clearly Top is not the Eilenberg-Moore category o...
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