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  1. class (Tensor cat t1 i1, Tensor cat t0 i0, Semigroupal cat t1 t0 f, Unital cat i1 i0 f) => Monoidal (cat :: Type -> Type -> Type) (t1 :: Type -> Type -> Type) i1 (t0 :: Type -> Type -> Type) i0 (f :: Type -> Type)

    monoidal-functors Data.Functor.Monoidal

    Given monoidal categories <math> and <math>. A functor <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

  2. module Data.Trifunctor.Monoidal

    No documentation available.

  3. class (Tensor cat t1 i1, Tensor cat t2 i2, Tensor cat t3 i3, Tensor cat to io, Semigroupal cat t1 t2 t3 to f, Unital cat i1 i2 i3 io f) => Monoidal (cat :: Type -> Type -> Type) (t1 :: Type -> Type -> Type) i1 (t2 :: Type -> Type -> Type) i2 (t3 :: Type -> Type -> Type) i3 (to :: Type -> Type -> Type) io (f :: Type -> Type -> Type -> Type)

    monoidal-functors Data.Trifunctor.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

  4. module Data.LCA.Online.Monoidal

    Provides online calculation of the the lowest common ancestor in O(log h) by compressing the spine of the paths using a skew-binary random access list. This library implements the technique described in my talk http://www.slideshare.net/ekmett/skewbinary-online-lowest-common-ancestor-search to improve the known asymptotic bounds on both online lowest common ancestor search http://en.wikipedia.org/wiki/Lowest_common_ancestor and the online level ancestor problem: http://en.wikipedia.org/wiki/Level_ancestor_problem Algorithms used here assume that the key values chosen for k are globally unique. This version provides access to a monoidal "summary" of the elided path for many operations.

  5. module Data.MonoidMap

    This module contains a newtype wrapper around Map that has a correct Group instance compared to the one for MonoidalMap, in that it has a unique neutral element. This comes with different constraints on the parameters (check the instances for Semigroup and Monoid of the corresponding data structures if you're interested).

  6. newtype MonoidMap k v

    monoid-map Data.MonoidMap

    Newtype wrapper around Data.Map.Monoidal.MonoidalMap

  7. MonoidMap :: MonoidalMap k v -> MonoidMap k v

    monoid-map Data.MonoidMap

    No documentation available.

  8. monoidConcatMap :: (Storable a, Monoid m) => (a -> m) -> Vector a -> m

    storablevector Data.StorableVector

    Deprecated: Use foldMap instead.

  9. monoidConcatMap :: (Storable a, Monoid m) => (a -> m) -> Vector a -> m

    storablevector Data.StorableVector.Lazy

    Deprecated: Use foldMap instead.

  10. monoidMap :: (Ord k, DecidablyEmpty v) => MonoidalMap k v -> MonoidMap k v

    monoid-map Data.MonoidMap

    Convert a MonoidalMap into a MonoidMap

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