Copyright	(C) 2019 Oleg Grenrus
License	BSD-3-Clause (see the file LICENSE)
Maintainer	Oleg Grenrus <[email protected]>
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

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 #

Function M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

function :: (M3 -> b) -> M3 :-> b #

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 :: forall r r'. (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 #

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] #

Generic M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Associated Types

type Rep M3

Instance details

Defined in Algebra.Lattice.M3

type Rep M3 = D1 ('MetaData "M3" "Algebra.Lattice.M3" "lattices-2.2.1-4ZqKgQGtAR39qggTebvCaP" '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))))

Methods

from :: M3 -> Rep M3 x #

to :: Rep M3 x -> 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 #

NFData M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

rnf :: M3 -> () #

Eq M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

(==) :: M3 -> M3 -> Bool #

(/=) :: M3 -> M3 -> Bool #

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 #

Hashable M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

hashWithSalt :: Int -> M3 -> Int #

hash :: M3 -> Int #

BoundedJoinSemiLattice M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

bottom :: M3 Source #

BoundedMeetSemiLattice M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

top :: M3 Source #

Lattice M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

(\/) :: M3 -> M3 -> M3 Source #

(/\) :: M3 -> M3 -> M3 Source #

PartialOrd M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

leq :: M3 -> M3 -> Bool Source #

comparable :: M3 -> M3 -> Bool Source #

Finite M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

universeF :: [M3] #

cardinality :: Tagged M3 Natural #

Universe M3 Source #

Instance details

Defined in Algebra.Lattice.M3

Methods

universe :: [M3] #

type Rep M3 Source #

Instance details

Defined in Algebra.Lattice.M3

type Rep M3 = D1 ('MetaData "M3" "Algebra.Lattice.M3" "lattices-2.2.1-4ZqKgQGtAR39qggTebvCaP" '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))))