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.M3

Description

Synopsis

data M3
- = M3o
- | M3a
- | M3b
- | M3c
- | M3i

Documentation

data M3 Source #

\(M_3\) , is smallest non-distributive, yet modular lattice.

Constructors

M3o
M3a
M3b
M3c
M3i

Instances

Instances details

Bounded M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods minBound :: M3 Source # maxBound :: M3 Source #
Enum M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods succ :: M3 -> M3 Source # pred :: M3 -> M3 Source # toEnum :: Int -> M3 Source # fromEnum :: M3 -> Int Source # enumFrom :: M3 -> [ M3 ] Source # enumFromThen :: M3 -> M3 -> [ M3 ] Source # enumFromTo :: M3 -> M3 -> [ M3 ] Source # enumFromThenTo :: M3 -> M3 -> M3 -> [ M3 ] Source #
Eq M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods (==) :: M3 -> M3 -> Bool Source # (/=) :: M3 -> M3 -> Bool Source #
Data M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> M3 -> c M3 Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c M3 Source # toConstr :: M3 -> Constr Source # dataTypeOf :: M3 -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c M3 ) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c M3 ) Source # gmapT :: ( forall b. Data b => b -> b) -> M3 -> M3 Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> M3 -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> M3 -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> M3 -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> M3 -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> M3 -> m M3 Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> M3 -> m M3 Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> M3 -> m M3 Source #
Ord M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods compare :: M3 -> M3 -> Ordering Source # (<) :: M3 -> M3 -> Bool Source # (<=) :: M3 -> M3 -> Bool Source # (>) :: M3 -> M3 -> Bool Source # (>=) :: M3 -> M3 -> Bool Source # max :: M3 -> M3 -> M3 Source # min :: M3 -> M3 -> M3 Source #
Read M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods readsPrec :: Int -> ReadS M3 Source # readList :: ReadS [ M3 ] Source # readPrec :: ReadPrec M3 Source # readListPrec :: ReadPrec [ M3 ] Source #
Show M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods showsPrec :: Int -> M3 -> ShowS Source # show :: M3 -> String Source # showList :: [ M3 ] -> ShowS Source #
Generic M3 Source #
Instance details Defined in Algebra.Lattice.M3 Associated Types type Rep M3 :: Type -> Type Source # Methods from :: M3 -> Rep M3 x Source # to :: Rep M3 x -> M3 Source #
Function M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods function :: ( M3 -> b) -> M3 :-> b Source #
Arbitrary M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods arbitrary :: Gen M3 Source # shrink :: M3 -> [ M3 ] Source #
CoArbitrary M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods coarbitrary :: M3 -> Gen b -> Gen b Source #
NFData M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods rnf :: M3 -> () Source #
Hashable M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods hashWithSalt :: Int -> M3 -> Int Source # hash :: M3 -> Int Source #
Universe M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods universe :: [ M3 ] Source #
Finite M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods universeF :: [ M3 ] Source # cardinality :: Tagged M3 Natural Source #
PartialOrd M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods leq :: M3 -> M3 -> Bool Source # comparable :: M3 -> M3 -> Bool Source #
BoundedMeetSemiLattice M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods top :: M3 Source #
BoundedJoinSemiLattice M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods bottom :: M3 Source #
Lattice M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods (\/) :: M3 -> M3 -> M3 Source # (/\) :: M3 -> M3 -> M3 Source #
type Rep M3 Source #
Instance details Defined in Algebra.Lattice.M3 type Rep M3 = D1 (' MetaData "M3" "Algebra.Lattice.M3" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' False ) (( C1 (' MetaCons "M3o" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: C1 (' MetaCons "M3a" ' PrefixI ' False ) ( U1 :: Type -> Type )) :+: ( C1 (' MetaCons "M3b" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: ( C1 (' MetaCons "M3c" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: C1 (' MetaCons "M3i" ' PrefixI ' False ) ( U1 :: Type -> Type ))))