Copyright	(C) 2019 Oleg Grenrus
License	BSD-3-Clause (see the file LICENSE)
Maintainer	Oleg Grenrus <oleg.grenrus@iki.fi>
Safe Haskell	Safe
Language	Haskell2010

Algebra.Lattice.M2

Description

Synopsis

data M2
- = M2o
- | M2a
- | M2b
- | M2i
toSetBool :: M2 -> Set Bool
fromSetBool :: Set Bool -> M2

Documentation

data M2 Source #

\(M_2\) is isomorphic to \(\mathcal{P}\{\mathbb{B}\}\) , i.e. powerset of Bool .

Constructors

M2o
M2a
M2b
M2i

Instances

Instances details

Bounded M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods minBound :: M2 Source # maxBound :: M2 Source #
Enum M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods succ :: M2 -> M2 Source # pred :: M2 -> M2 Source # toEnum :: Int -> M2 Source # fromEnum :: M2 -> Int Source # enumFrom :: M2 -> [ M2 ] Source # enumFromThen :: M2 -> M2 -> [ M2 ] Source # enumFromTo :: M2 -> M2 -> [ M2 ] Source # enumFromThenTo :: M2 -> M2 -> M2 -> [ M2 ] Source #
Eq M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods (==) :: M2 -> M2 -> Bool Source # (/=) :: M2 -> M2 -> Bool Source #
Data M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> M2 -> c M2 Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c M2 Source # toConstr :: M2 -> Constr Source # dataTypeOf :: M2 -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c M2 ) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c M2 ) Source # gmapT :: ( forall b. Data b => b -> b) -> M2 -> M2 Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> M2 -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> M2 -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> M2 -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> M2 -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> M2 -> m M2 Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> M2 -> m M2 Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> M2 -> m M2 Source #
Ord M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods compare :: M2 -> M2 -> Ordering Source # (<) :: M2 -> M2 -> Bool Source # (<=) :: M2 -> M2 -> Bool Source # (>) :: M2 -> M2 -> Bool Source # (>=) :: M2 -> M2 -> Bool Source # max :: M2 -> M2 -> M2 Source # min :: M2 -> M2 -> M2 Source #
Read M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods readsPrec :: Int -> ReadS M2 Source # readList :: ReadS [ M2 ] Source # readPrec :: ReadPrec M2 Source # readListPrec :: ReadPrec [ M2 ] Source #
Show M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods showsPrec :: Int -> M2 -> ShowS Source # show :: M2 -> String Source # showList :: [ M2 ] -> ShowS Source #
Generic M2 Source #
Instance details Defined in Algebra.Lattice.M2 Associated Types type Rep M2 :: Type -> Type Source # Methods from :: M2 -> Rep M2 x Source # to :: Rep M2 x -> M2 Source #
Function M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods function :: ( M2 -> b) -> M2 :-> b Source #
Arbitrary M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods arbitrary :: Gen M2 Source # shrink :: M2 -> [ M2 ] Source #
CoArbitrary M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods coarbitrary :: M2 -> Gen b -> Gen b Source #
NFData M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods rnf :: M2 -> () Source #
Hashable M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods hashWithSalt :: Int -> M2 -> Int Source # hash :: M2 -> Int Source #
Universe M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods universe :: [ M2 ] Source #
Finite M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods universeF :: [ M2 ] Source # cardinality :: Tagged M2 Natural Source #
PartialOrd M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods leq :: M2 -> M2 -> Bool Source # comparable :: M2 -> M2 -> Bool Source #
BoundedMeetSemiLattice M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods top :: M2 Source #
BoundedJoinSemiLattice M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods bottom :: M2 Source #
Lattice M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods (\/) :: M2 -> M2 -> M2 Source # (/\) :: M2 -> M2 -> M2 Source #
Heyting M2 Source #
Instance details Defined in Algebra.Lattice.M2 Methods (==>) :: M2 -> M2 -> M2 Source # neg :: M2 -> M2 Source # (<=>) :: M2 -> M2 -> M2 Source #
type Rep M2 Source #
Instance details Defined in Algebra.Lattice.M2 type Rep M2 = D1 (' MetaData "M2" "Algebra.Lattice.M2" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' False ) (( C1 (' MetaCons "M2o" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: C1 (' MetaCons "M2a" ' PrefixI ' False ) ( U1 :: Type -> Type )) :+: ( C1 (' MetaCons "M2b" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: C1 (' MetaCons "M2i" ' PrefixI ' False ) ( U1 :: Type -> Type )))

toSetBool :: M2 -> Set Bool Source #

fromSetBool :: Set Bool -> M2 Source #