(prosody) Containing only one kind of metrical foot.
Used in a Sentence
monoid
Definitions, parts of speech, synonyms, and sentence examples for monoid.
Editorial note
The Monoid operation mappend is guaranteed to be associative, so the order is irrelevant.
Examples18
Definitions2
Parts of speech2
Quick take
(prosody) Containing only one kind of metrical foot.
Meaning at a glance
The clearest senses and uses of monoid gathered in one view.
(algebra, functional programming) A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
Definitions
Core meanings and parts of speech for monoid.
adjective
(prosody) Containing only one kind of metrical foot.
noun
(algebra, functional programming) A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
Example sentences
The Monoid operation mappend is guaranteed to be associative, so the order is irrelevant.
The way FizzBuzz can be expressed as a Monoid is cool.
Integers are a clearly monoid under Sum and Product, and set intersection is clearly a semigroup but not a monoid (if our universe is open) because there is no identity.
So, the set of all distributions form a monoid under convolution if you allow the Dirac delta-function to act as `mempty` -- in a certain representation, this appears as the termwise-summing monoid.
It's more about the philosophy, some languages recognize this way of thinking, having tiny bits of ~monoid-ic logic that works for N.
It's the exact same reason why the empty sum is zero (zero being the neutral element of a monoid using additive notation).
Useful to see Monoid applied so naturally to a real world problem problem.
The question of whether something is a valid instance of Monoid or Functor or Monad is simple: does it abide by the laws?
Think of Monoid or the sad M in otherwise good Ubuntu Mono.
Yes, I know that a monoid and a monad are two different terms, there's no confusion.
For example, Spire's mathematical data structures (group, ring, field, boolean algebra) tend to be useful, as are Scalaz's monad/monoid/applicative.
Ubuntu mono and Monoid both stand out as looking good to me (M+ is a close third, but has larger line spacing than I'm used to).
Quote examples
In Haskell, it's entirely clear whether a new type "is really" a Monoid or Functor - does it obey the laws?
Nobody insists "monoid in the category of endofunctors" is universally preferable.
The equivalent for Monad would probably be "flatMappable", and Monoid would be "appendable".
If we called Monoid "Appendable", then we would have to consider whether a new and different thing jived with our notion of "append".
Proper noun examples
Monoids permit folding, folding implies the existence of some monoid.
'Monoid', 'Monad', 'State', 'Reader', 'Function', 'Lambda', 'Typeclass' are all examples of terminology in Haskell None of those words are inherently more difficult than the OO ones, you're just not familiar with them.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use monoid in a sentence?
The Monoid operation mappend is guaranteed to be associative, so the order is irrelevant.
What does monoid mean?
(prosody) Containing only one kind of metrical foot.
What part of speech is monoid?
monoid is commonly used as adjective, noun.