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  1. dual :: Method

    coinor-clp Numeric.COINOR.CLP.Monad

    No documentation available.

  2. dual :: a <-> Dual a

    invertible Data.Invertible.Monoid

    (Un)wrap the Dual monoid.

  3. dual :: Shift r => r -> r

    diff-loc DiffLoc.Shift

    No documentation available.

  4. data DualSym0 (a1 :: TyFun a Dual a)

    singletons-base Data.Monoid.Singletons

    No documentation available.

  5. type family DualSym1 (a6989586621679696372 :: a) :: Dual a

    singletons-base Data.Monoid.Singletons

    No documentation available.

  6. data DualSym0 (a1 :: TyFun a Dual a)

    singletons-base Data.Semigroup.Singletons

    No documentation available.

  7. type family DualSym1 (a6989586621679696372 :: a) :: Dual a

    singletons-base Data.Semigroup.Singletons

    No documentation available.

  8. DualJoining :: JoiningType

    text-icu Data.Text.ICU.Char

    No documentation available.

  9. data DUALTree d u a l

    dual-tree Data.Tree.DUAL

    Rose (n-ary) trees with both upwards- (i.e. cached) and downwards-traveling (i.e. accumulating) monoidal annotations. Abstractly, a DUALTree is a rose (n-ary) tree with data (of type l) at leaves, data (of type a) at internal nodes, and two types of monoidal annotations, one (of type u) travelling "up" the tree and one (of type d) traveling "down". See the documentation at the top of this file for full details. DUALTree comes with some instances:

    • Functor, for modifying leaf data. Note that fmap of course cannot alter any u annotations.
    • Semigroup. DUALTreeNEs form a semigroup where (<>) corresponds to adjoining two trees under a common parent root, with sconcat specialized to put all the trees under a single parent. Note that this does not satisfy associativity up to structural equality, but only up to observational equivalence under flatten. Technically using foldDUAL directly enables one to observe the difference, but it is understood that foldDUAL should be used only in ways such that reassociation of subtrees "does not matter".
    • Monoid. The identity is the empty tree.

  10. newtype DUALTree d u a l

    dual-tree Data.Tree.DUAL.Internal

    Rose (n-ary) trees with both upwards- (i.e. cached) and downwards-traveling (i.e. accumulating) monoidal annotations. Abstractly, a DUALTree is a rose (n-ary) tree with data (of type l) at leaves, data (of type a) at internal nodes, and two types of monoidal annotations, one (of type u) travelling "up" the tree and one (of type d) traveling "down". See the documentation at the top of this file for full details. DUALTree comes with some instances:

    • Functor, for modifying leaf data. Note that fmap of course cannot alter any u annotations.
    • Semigroup. DUALTreeNEs form a semigroup where (<>) corresponds to adjoining two trees under a common parent root, with sconcat specialized to put all the trees under a single parent. Note that this does not satisfy associativity up to structural equality, but only up to observational equivalence under flatten. Technically using foldDUAL directly enables one to observe the difference, but it is understood that foldDUAL should be used only in ways such that reassociation of subtrees "does not matter".
    • Monoid. The identity is the empty tree.

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