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monad    音标拼音: [m'onæd]
n. 单位,单一体,单细胞生物

单位,单一体,单细胞生物

monad
一元

monad
n 1: (chemistry) an atom having a valence of one
2: a singular metaphysical entity from which material properties
are said to derive [synonym: {monad}, {monas}]
3: (biology) a single-celled microorganism (especially a
flagellate protozoan)

Monad \Mon"ad\, n. [L. monas, -adis, a unit, Gr. ?, ?, fr.
mo`nos alone.]
1. An ultimate atom, or simple, unextended point; something
ultimate and indivisible.
[1913 Webster]

2. (Philos. of Leibnitz) The elementary and indestructible
units which were conceived of as endowed with the power to
produce all the changes they undergo, and thus determine
all physical and spiritual phenomena.
[1913 Webster]

3. (Zool.) One of the smallest flagellate Infusoria; esp.,
the species of the genus {Monas}, and allied genera.
[1913 Webster]

4. (Biol.) A simple, minute organism; a primary cell, germ,
or plastid.
[1913 Webster]

5. (Chem.) An atom or radical whose valence is one, or which
can combine with, be replaced by, or exchanged for, one
atom of hydrogen.
[1913 Webster]

{Monad deme} (Biol.), in tectology, a unit of the first order
of individuality.
[1913 Webster]

63 Moby Thesaurus words for "monad":
I, ace, air, an existence, atom, atomic particles, being, body,
brute matter, building block, chemical element, component,
constituent, creature, critter, earth, electron, element,
elementary particle, elementary unit, entelechy, entity, fire,
fundamental particle, hyle, hypostasis, individual, ion, life,
material, material world, materiality, matter, meson, molecule,
natural world, nature, no other, none else, nothing else,
nought beside, nuclear particle, object, one, one and only,
organism, person, persona, personality, physical world, plenum,
proton, quark, something, soul, stuff, substance, substratum,
the four elements, thing, unit, unit of being, water

/mo'nad/ A technique from
{category theory} which has been adopted as a way of dealing
with {state} in {functional programming languages} in such a
way that the details of the state are hidden or abstracted out
of code that merely passes it on unchanged.

A monad has three components: a means of augmenting an
existing type, a means of creating a default value of this new
type from a value of the original type, and a replacement for
the basic application operator for the old type that works
with the new type.

The alternative to passing state via a monad is to add an
extra argument and return value to many functions which have
no interest in that state. Monads can encapsulate state, side
effects, exception handling, global data, etc. in a purely
lazily functional way.

A monad can be expressed as the triple, (M, unitM, bindM)
where M is a function on types and (using {Haskell} notation):

unitM :: a -> M a
bindM :: M a -> (a -> M b) -> M b

I.e. unitM converts an ordinary value of type a in to monadic
form and bindM applies a function to a monadic value after
de-monadising it. E.g. a state transformer monad:

type S a = State -> (a, State)
unitS a = \ s0 -> (a, s0)
m `bindS` k = \ s0 -> let (a,s1) = m s0
in k a s1

Here unitS adds some initial state to an ordinary value and
bindS applies function k to a value m. (`fun` is Haskell
notation for using a function as an {infix} operator). Both m
and k take a state as input and return a new state as part of
their output. The construction

m `bindS` k

composes these two state transformers into one while also
passing the value of m to k.

Monads are a powerful tool in {functional programming}. If a
program is written using a monad to pass around a variable
(like the state in the example above) then it is easy to
change what is passed around simply by changing the monad.
Only the parts of the program which deal directly with the
quantity concerned need be altered, parts which merely pass it
on unchanged will stay the same.

In functional programming, unitM is often called initM or
returnM and bindM is called thenM. A third function, mapM is
frequently defined in terms of then and return. This applies
a given function to a list of monadic values, threading some
variable (e.g. state) through the applications:

mapM :: (a -> M b) -> [a] -> M [b]
mapM f [] = returnM []
mapM f (x:xs) = f x `thenM` ( \ x2 ->
mapM f xs `thenM` ( \ xs2 ->
returnM (x2 : xs2) ))

(2000-03-09)


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  • haskell - What is a monad? - Stack Overflow
    Here the monad-pattern is used to avoid repetitive code This is similar to how some other languages use macros to simplify syntax, although macros achieve the same goal in a very different way Note that it is the combination of the monad pattern and the monad-friendly syntax in Haskell which result in the cleaner code
  • What is it that Leibniz calls a “Monad”?
    Also, every monad has a dedicated corpus, a body which is itself assembled from parts, which themselves have their dedicated monads, lower in the hierarchy Only the monas monadum exists without one All in all, this is a very difficult topic I hope I was of any help, and did not add to your confusion
  • haskell - A monad is just a monoid in the category of endofunctors . . .
    In summary, any monad is by definition an endofunctor, hence an object in the category of endofunctors, where the monadic join and return operators satisfy the definition of a monoid in that particular (strict) monoidal category
  • functional programming - Monad interface in C++ - Stack Overflow
    Monad<DummyType2>>, std::is_same<constructor_return_t<Monad, DummyType>, Monad<DummyType>>> {}; Note that even though we generally expect the type constructor to take a single type T as an argument, I've used a variadic template template parameter to account for default allocators typically used in STL containers
  • haskell - Why do we need monads? - Stack Overflow
    In my humble opinion the answers to the famous question "What is a monad?", especially the most voted ones, try to explain what is a monad without clearly explaining why monads are really necessary
  • What are monadic bind and monadic return for C++23 optional?
    What about other libraries? Boost Hana defines concepts for Functor, Applicative, Monad, and many others, giving you a way to implement automatically all the abstractions that leverage those concepts at the cost of giving some minimal definition
  • Simple explanation of a monad - Mathematics Stack Exchange
    They are very much the same because a monad in Haskell is just an example of a category-theoretical monad in the category $\bf Hask$ (well, internal to Hask that is ) Its pretty much the same as $\bf Set$ though





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