Algebra.Boolean.Free

Documentation

newtype FreeBoolean a

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

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

Defined in Algebra.Boolean.Free

Methods

fmap :: (a -> b) -> FreeBoolean a -> FreeBoolean b

(<$) :: a -> FreeBoolean b -> FreeBoolean a

Applicative FreeBoolean

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

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)

Defined in Algebra.Boolean.Free

Methods

(\/) :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a

join :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a

MeetSemiLattice (FreeBoolean a)

Defined in Algebra.Boolean.Free

Methods

(/\) :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a

meet :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a

Lattice (FreeBoolean a)

Defined in Algebra.Boolean.Free

BoundedJoinSemiLattice (FreeBoolean a)

Defined in Algebra.Boolean.Free

Methods

bottom :: FreeBoolean a

BoundedMeetSemiLattice (FreeBoolean a)

Defined in Algebra.Boolean.Free

Methods

top :: FreeBoolean a

BoundedLattice (FreeBoolean a)

Defined in Algebra.Boolean.Free

HeytingAlgebra (FreeBoolean a)

Defined in Algebra.Boolean.Free

Methods

(==>) :: FreeBoolean a -> FreeBoolean a -> FreeBoolean a

not :: FreeBoolean a -> FreeBoolean a

BooleanAlgebra (FreeBoolean a)

Defined in Algebra.Boolean.Free

type AlgebraType FreeBoolean (a :: *)

Defined in Algebra.Boolean.Free

type AlgebraType FreeBoolean (a :: *) = BooleanAlgebra a

type AlgebraType0 FreeBoolean (a :: *)

Defined in Algebra.Boolean.Free

type AlgebraType0 FreeBoolean (a :: *) = ()