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

Bounded M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods minBound :: M3 # maxBound :: M3 #
Enum M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods succ :: M3 -> M3 # pred :: M3 -> M3 # toEnum :: Int -> M3 # fromEnum :: M3 -> Int # enumFrom :: M3 -> [M3] # enumFromThen :: M3 -> M3 -> [M3] # enumFromTo :: M3 -> M3 -> [M3] # enumFromThenTo :: M3 -> M3 -> M3 -> [M3] #
Eq M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods (==) :: M3 -> M3 -> Bool # (/=) :: M3 -> M3 -> Bool #
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 # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c M3 # toConstr :: M3 -> Constr # dataTypeOf :: M3 -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c M3) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c M3) # gmapT :: (forall b. Data b => b -> b) -> M3 -> M3 # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> M3 -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> M3 -> r # gmapQ :: (forall d. Data d => d -> u) -> M3 -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> M3 -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> M3 -> m M3 # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> M3 -> m M3 # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> M3 -> m M3 #
Ord M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods compare :: M3 -> M3 -> Ordering # (<) :: M3 -> M3 -> Bool # (<=) :: M3 -> M3 -> Bool # (>) :: M3 -> M3 -> Bool # (>=) :: M3 -> M3 -> Bool # max :: M3 -> M3 -> M3 # min :: M3 -> M3 -> M3 #
Read M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods readsPrec :: Int -> ReadS M3 # readList :: ReadS [M3] # readPrec :: ReadPrec M3 # readListPrec :: ReadPrec [M3] #
Show M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods showsPrec :: Int -> M3 -> ShowS # show :: M3 -> String # showList :: [M3] -> ShowS #
Generic M3 Source #
Instance details Defined in Algebra.Lattice.M3 Associated Types type Rep M3 :: Type -> Type # Methods from :: M3 -> Rep M3 x # to :: Rep M3 x -> M3 #
Function M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods function :: (M3 -> b) -> M3 :-> b #
Arbitrary M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods arbitrary :: Gen M3 # shrink :: M3 -> [M3] #
CoArbitrary M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods coarbitrary :: M3 -> Gen b -> Gen b #
NFData M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods rnf :: M3 -> () #
Hashable M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods hashWithSalt :: Int -> M3 -> Int # hash :: M3 -> Int #
Universe M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods universe :: [M3] #
Finite M3 Source #
Instance details Defined in Algebra.Lattice.M3 Methods universeF :: [M3] # cardinality :: Tagged M3 Natural #
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-GNwPiglY2qIELYMTNuLIEL" 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))))