Safe Haskell	None
Language	Haskell2010

Algebra.Boolean.Free

Synopsis

newtype FreeBoolean a = FreeBoolean {
- runFreeBoolean :: forall h. BooleanAlgebra h => (a -> h) -> h
}

Documentation

newtype FreeBoolean a Source #

Free Boolean algebra. FreeAlgebra instance provides all the usual combinators for a free algebra.

Constructors

FreeBoolean
Fields runFreeBoolean :: forall h. BooleanAlgebra h => (a -> h) -> h

Instances

Monad FreeBoolean Source #
Instance details Defined in Algebra.Boolean.Free Methods (>>=) :: FreeBoolean a -> (a -> FreeBoolean b) -> FreeBoolean b # (>>) :: FreeBoolean a -> FreeBoolean b -> FreeBoolean b # return :: a -> FreeBoolean a # fail :: String -> FreeBoolean a #
Functor FreeBoolean Source #
Instance details Defined in Algebra.Boolean.Free Methods fmap :: (a -> b) -> FreeBoolean a -> FreeBoolean b # (<$) :: a -> FreeBoolean b -> FreeBoolean a #
Applicative FreeBoolean Source #
Instance details Defined in Algebra.Boolean.Free Methods pure :: a -> FreeBoolean a # (<>) :: FreeBoolean (a -> b) -> FreeBoolean a -> FreeBoolean b # liftA2 :: (a -> b -> c) -> FreeBoolean a -> FreeBoolean b -> FreeBoolean c # (>) :: FreeBoolean a -> FreeBoolean b -> FreeBoolean b # (<*) :: FreeBoolean a -> FreeBoolean b -> FreeBoolean a #
FreeAlgebra FreeBoolean Source #
Instance details Defined in Algebra.Boolean.Free Methods returnFree :: a -> FreeBoolean a # foldMapFree :: (AlgebraType FreeBoolean d, AlgebraType0 FreeBoolean a) => (a -> d) -> FreeBoolean a -> d # codom :: AlgebraType0 FreeBoolean a => Proof (AlgebraType FreeBoolean (FreeBoolean a)) (FreeBoolean a) # forget :: AlgebraType FreeBoolean a => Proof (AlgebraType0 FreeBoolean a) (FreeBoolean a) #
JoinSemiLattice (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free Methods (\/) :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a # join :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a #
MeetSemiLattice (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free Methods (/\) :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a # meet :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a #
Lattice (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free
BoundedJoinSemiLattice (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free Methods bottom :: FreeBoolean a #
BoundedMeetSemiLattice (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free Methods top :: FreeBoolean a #
BoundedLattice (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free
BooleanAlgebra (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free
HeytingAlgebra (FreeBoolean a) Source #
Instance details Defined in Algebra.Boolean.Free Methods (==>) :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a Source # not :: FreeBoolean a -> FreeBoolean a Source #
type AlgebraType FreeBoolean (a :: Type) Source #
Instance details Defined in Algebra.Boolean.Free type AlgebraType FreeBoolean (a :: Type) = BooleanAlgebra a
type AlgebraType0 FreeBoolean (a :: Type) Source #
Instance details Defined in Algebra.Boolean.Free type AlgebraType0 FreeBoolean (a :: Type) = ()