lattices-2: Fine-grained library for constructing and manipulating lattices

Copyright(C) 2019 Oleg Grenrus
LicenseBSD-3-Clause (see the file LICENSE)
MaintainerOleg Grenrus <oleg.grenrus@iki.fi>
Safe HaskellSafe
LanguageHaskell2010

Algebra.Lattice.M3

Description

 
Synopsis

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

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

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))))