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.N5

Description

Synopsis

data N5
- = N5o
- | N5a
- | N5b
- | N5c
- | N5i

Documentation

data N5 Source #

\(N_5\), is smallest non-modular (and non-distributive) lattice.

Constructors

N5o
N5a
N5b
N5c
N5i

Instances

Instances details

Arbitrary N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

arbitrary :: Gen N5

shrink :: N5 -> [N5]

CoArbitrary N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

coarbitrary :: N5 -> Gen b -> Gen b

Function N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

function :: (N5 -> b) -> N5 :-> b

Data N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> N5 -> c N5

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c N5

toConstr :: N5 -> Constr

dataTypeOf :: N5 -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c N5)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c N5)

gmapT :: (forall b. Data b => b -> b) -> N5 -> N5

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> N5 -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> N5 -> r

gmapQ :: (forall d. Data d => d -> u) -> N5 -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> N5 -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> N5 -> m N5

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> N5 -> m N5

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> N5 -> m N5

Bounded N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

minBound :: N5

maxBound :: N5

Enum N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

succ :: N5 -> N5

pred :: N5 -> N5

toEnum :: Int -> N5

fromEnum :: N5 -> Int

enumFrom :: N5 -> [N5]

enumFromThen :: N5 -> N5 -> [N5]

enumFromTo :: N5 -> N5 -> [N5]

enumFromThenTo :: N5 -> N5 -> N5 -> [N5]

Generic N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Associated Types

type Rep N5

Instance details

Defined in Algebra.Lattice.N5

type Rep N5 = D1 ('MetaData "N5" "Algebra.Lattice.N5" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) ((C1 ('MetaCons "N5o" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "N5a" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "N5b" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "N5c" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "N5i" 'PrefixI 'False) (U1 :: Type -> Type))))

Methods

from :: N5 -> Rep N5 x

to :: Rep N5 x -> N5

Read N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

readsPrec :: Int -> ReadS N5

readList :: ReadS [N5]

readPrec :: ReadPrec N5

readListPrec :: ReadPrec [N5]

Show N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

showsPrec :: Int -> N5 -> ShowS

show :: N5 -> String

showList :: [N5] -> ShowS

NFData N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

rnf :: N5 -> ()

Eq N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

(==) :: N5 -> N5 -> Bool

(/=) :: N5 -> N5 -> Bool

Ord N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

compare :: N5 -> N5 -> Ordering

(<) :: N5 -> N5 -> Bool

(<=) :: N5 -> N5 -> Bool

(>) :: N5 -> N5 -> Bool

(>=) :: N5 -> N5 -> Bool

max :: N5 -> N5 -> N5

min :: N5 -> N5 -> N5

Hashable N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

hashWithSalt :: Int -> N5 -> Int

hash :: N5 -> Int

BoundedJoinSemiLattice N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

bottom :: N5 Source #

BoundedMeetSemiLattice N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

top :: N5 Source #

Lattice N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

(\/) :: N5 -> N5 -> N5 Source #

(/\) :: N5 -> N5 -> N5 Source #

PartialOrd N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

leq :: N5 -> N5 -> Bool Source #

comparable :: N5 -> N5 -> Bool Source #

Finite N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

universeF :: [N5]

cardinality :: Tagged N5 Natural

Universe N5 Source #

Instance details

Defined in Algebra.Lattice.N5

Methods

universe :: [N5]

type Rep N5 Source #

Instance details

Defined in Algebra.Lattice.N5

type Rep N5 = D1 ('MetaData "N5" "Algebra.Lattice.N5" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) ((C1 ('MetaCons "N5o" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "N5a" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "N5b" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "N5c" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "N5i" 'PrefixI 'False) (U1 :: Type -> Type))))