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  1. class (Reflexive g, Transitive g) => Preorder g

    algebraic-graphs Algebra.Graph.Class

    The class of preorder graphs that are both reflexive and transitive.

  2. class (Reflexive g, Transitive g) => Preorder (g :: Type -> Type)

    algebraic-graphs Algebra.Graph.HigherKinded.Class

    The class of preorder graphs that are both reflexive and transitive.

  3. type Path a = [(a, a)]

    algebraic-graphs Algebra.Graph.Label

    A path is a list of edges.

  4. newtype PowerSet a

    algebraic-graphs Algebra.Graph.Label

    The power set over the underlying set of elements a. If a is a monoid, then the power set forms a Dioid as follows: 

    zero    = PowerSet Set.empty
one     = PowerSet $ Set.singleton mempty
x <+> y = PowerSet $ Set.union (getPowerSet x) (getPowerSet y)
x <.> y = PowerSet $ cartesianProductWith mappend (getPowerSet x) (getPowerSet y)

  5. PowerSet :: Set a -> PowerSet a

    algebraic-graphs Algebra.Graph.Label

    No documentation available.

  6. Pay :: Alphabet

    algebraic-graphs Algebra.Graph.Labelled.Example.Automaton

    Pay for the order

  7. Payment :: State

    algebraic-graphs Algebra.Graph.Labelled.Example.Automaton

    Making the payment

  8. module Algebra.Graph.Relation.Preorder

    An abstract implementation of preorder relations. Use Algebra.Graph.Class for polymorphic construction and manipulation.

  9. data PreorderRelation a

    algebraic-graphs Algebra.Graph.Relation.Preorder

    The PreorderRelation data type represents a binary relation that is both reflexive and transitive. Preorders satisfy all laws of the Preorder type class and, in particular, the self-loop axiom: 

    vertex x == vertex x * vertex x
    and the closure axiom: 
    y /= empty ==> x * y + x * z + y * z == x * y + y * z
    For example, the following holds: 
    path xs == (clique xs :: PreorderRelation Int)
    The Show instance produces reflexively and transitively closed expressions: 
    show (1             :: PreorderRelation Int) == "edge 1 1"
show (1 * 2         :: PreorderRelation Int) == "edges [(1,1),(1,2),(2,2)]"
show (1 * 2 + 2 * 3 :: PreorderRelation Int) == "edges [(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)]"

  10. module Sound.ALSA.PCM

    No documentation available.

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