Hoogle Search

Within LTS Haskell 22.23 (ghc-9.6.5)

Note that Stackage only displays results for the latest LTS and Nightly snapshot. Learn more.

Exact lookup

1. module Data.Eliminator.Monoid

   Eliminator functions for data types in Data.Monoid. All of these are re-exported from Data.Eliminator with the following exceptions:

   • First and Last are not re-exported from Data.Eliminator, as they clash with eliminators of the same names in Data.Eliminator.Functor and Data.Eliminator.Semigroup.
   • Sum and Product are not re-exported from Data.Eliminator, as they clash with eliminators of the same names in Data.Eliminator.Functor.

2. module Data.Invertible.Monoid

   Bidirectional transforms for Data.Monoid.

3. class Semigroup a => Monoid a

   loc	Data.Loc.Internal.Prelude

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

4. module Parameterized.Data.Monoid

   No documentation available.

5. class Monoid m => MonoidNull m

   monoid-subclasses	Data.Monoid.Null

   Extension of Monoid that allows testing a value for equality with mempty. The following law must hold:

   null x == (x == mempty)
   

   Furthermore, the performance of this method should be constant, i.e., independent of the length of its argument.

6. type Monoid' = Monoid

   monoid-extras	Data.Monoid.WithSemigroup

   For base < 4.11, the Monoid' constraint is a synonym for things which are instances of both Semigroup and Monoid. For base version 4.11 and onwards, Monoid has Semigroup as a superclass already, so for backwards compatibility Monoid' is provided as a synonym for Monoid.

7. class (SymmetricMonoidal m u, Profunctor arr) => Monoidal m u arr

   linear-base	Data.Profunctor.Linear

   A (Monoidal m u arr) is a profunctor arr that can be sequenced with the bifunctor m. In rough terms, you can combine two function-like things to one function-like thing that holds both input and output types with the bifunctor m.

8. module Data.Bifunctor.Monoidal

   No documentation available.

9. class (Tensor cat t1 i1, Tensor cat t2 i2, Tensor cat to io, Semigroupal cat t1 t2 to f, Unital cat i1 i2 io f) => Monoidal cat t1 i1 t2 i2 to io f

   monoidal-functors	Data.Bifunctor.Monoidal

   Given monoidal categories <math> and <math>. A bifunctor <math> is Monoidal if it maps between <math> and <math> while preserving their monoidal structure. Eg., a homomorphism of monoidal categories. See NCatlab for more details.

   Laws

   Right Unitality: <math>

   combine . grmap introduce ≡ bwd unitr . fwd unitr
   

   Left Unitality: <math>

   combine . glmap introduce ≡ fmap (bwd unitl) . fwd unitl
   

10. module Data.Functor.Monoidal

    No documentation available.

Page 2 of many | Previous | Next