Safe Haskell	Safe
Language	Haskell2010

Math.Graph.Action

Description

actions as contravariant functor

Synopsis

newtype x :<-: a = Action {
- runAction :: a -> x
}
(!==!) :: (Universe a, Eq x) => (x :<-: a) -> (x :<-: a) -> Bool :<-: ()

Documentation

newtype x :<-: a Source #

See Lawvere,Rosebrugh: Sets for mathematics

Constructors

Action
Fields runAction :: a -> x

Instances

Instances details

Category (:<-:) Source #
Instance details Defined in Math.Graph.Action Methods id :: forall (a :: k). a :<-: a # (.) :: forall (b :: k) (c :: k) (a :: k). (b :<-: c) -> (a :<-: b) -> a :<-: c #
Contravariant ((:<-:) x) Source #
Instance details Defined in Math.Graph.Action Methods contramap :: (a' -> a) -> (x :<-: a) -> x :<-: a' # (>$) :: b -> (x :<-: b) -> x :<-: a #
BooleanLogic ((:<-:) Bool) Source #
Instance details Defined in Math.Graph.Action Methods true :: Bool :<-: a Source #
ImplicativeLogic ((:<-:) Bool) Source #
Instance details Defined in Math.Graph.Action Methods (-=>-) :: (Bool :<-: a) -> (Bool :<-: a) -> Bool :<-: a Source #
Propositional ((:<-:) soc) Source #
Instance details Defined in Math.Graph.Action Methods runProposition :: (soc :<-: a) -> a -> soc :<-: () Source #
PropositionalLogic ((:<-:) Bool) Source #
Instance details Defined in Math.Graph.Action Methods (-&-) :: (Bool :<-: a) -> (Bool :<-: a) -> Bool :<-: a Source # (-\|-) :: (Bool :<-: a) -> (Bool :<-: a) -> Bool :<-: a Source # invert :: (Bool :<-: a) -> Bool :<-: a Source #
Relational ((:<-:) Bool) Source #
Instance details Defined in Math.Graph.Action Methods relation :: (a -> Bool :<-: b) -> Bool :<-: (a, b) Source # unrelation :: (Bool :<-: (a, b)) -> a -> Bool :<-: b Source #
HasEqualizers ((:<-:) Bool) (Bool :<-: Bool) Source #
Instance details Defined in Math.Graph.Action Methods equalizer :: (a -> Bool :<-: Bool) -> (a -> Bool :<-: Bool) -> Bool :<-: a Source # pullback :: (a -> Bool :<-: Bool) -> (b -> Bool :<-: Bool) -> Bool :<-: (a, b) Source #
(Universe a, Eq x) => Eq (x :<-: a) Source #	separator f g
Instance details Defined in Math.Graph.Action Methods (==) :: (x :<-: a) -> (x :<-: a) -> Bool # (/=) :: (x :<-: a) -> (x :<-: a) -> Bool #

(!==!) :: (Universe a, Eq x) => (x :<-: a) -> (x :<-: a) -> Bool :<-: () infix 4 Source #

performance problem if a in x :<-: a is large!