lattices-2.2.1: Fine-grained library for constructing and manipulating lattices

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.M2

Description

Synopsis

data M2
- = M2o
- | M2a
- | M2b
- | M2i
toSetBool :: M2 -> Set Bool
fromSetBool :: Set Bool -> M2

Documentation

data M2 Source #

\(M_2\) is isomorphic to \(\mathcal{P}\{\mathbb{B}\}\), i.e. powerset of Bool.

Constructors

M2o
M2a
M2b
M2i

Instances

Instances details

Arbitrary M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

arbitrary :: Gen M2 Source #

shrink :: M2 -> [M2] Source #

CoArbitrary M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

coarbitrary :: M2 -> Gen b -> Gen b Source #

Function M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

function :: (M2 -> b) -> M2 :-> b Source #

NFData M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

rnf :: M2 -> () #

Data M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> M2 -> c M2 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c M2 #

toConstr :: M2 -> Constr #

dataTypeOf :: M2 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c M2) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c M2) #

gmapT :: (forall b. Data b => b -> b) -> M2 -> M2 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> M2 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> M2 -> r #

gmapQ :: (forall d. Data d => d -> u) -> M2 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> M2 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> M2 -> m M2 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> M2 -> m M2 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> M2 -> m M2 #

Bounded M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

minBound :: M2 #

maxBound :: M2 #

Enum M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

succ :: M2 -> M2 #

pred :: M2 -> M2 #

toEnum :: Int -> M2 #

fromEnum :: M2 -> Int #

enumFrom :: M2 -> [M2] #

enumFromThen :: M2 -> M2 -> [M2] #

enumFromTo :: M2 -> M2 -> [M2] #

enumFromThenTo :: M2 -> M2 -> M2 -> [M2] #

Generic M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Associated Types

type Rep M2
Instance details Defined in Algebra.Lattice.M2 type Rep M2 = D1 ('MetaData "M2" "Algebra.Lattice.M2" "lattices-2.2.1-JY28lmhbcmEBv2dv2owR24" 'False) ((C1 ('MetaCons "M2o" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "M2a" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "M2b" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "M2i" 'PrefixI 'False) (U1 :: Type -> Type)))

Methods

from :: M2 -> Rep M2 x #

to :: Rep M2 x -> M2 #

Read M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

readsPrec :: Int -> ReadS M2 #

readList :: ReadS [M2] #

readPrec :: ReadPrec M2 #

readListPrec :: ReadPrec [M2] #

Show M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

showsPrec :: Int -> M2 -> ShowS #

show :: M2 -> String #

showList :: [M2] -> ShowS #

Instance details

Defined in Algebra.Lattice.M2

Methods

(==) :: M2 -> M2 -> Bool #

(/=) :: M2 -> M2 -> Bool #

Ord M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

compare :: M2 -> M2 -> Ordering #

(<) :: M2 -> M2 -> Bool #

(<=) :: M2 -> M2 -> Bool #

(>) :: M2 -> M2 -> Bool #

(>=) :: M2 -> M2 -> Bool #

max :: M2 -> M2 -> M2 #

min :: M2 -> M2 -> M2 #

Hashable M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

hashWithSalt :: Int -> M2 -> Int Source #

hash :: M2 -> Int Source #

Heyting M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

(==>) :: M2 -> M2 -> M2 Source #

neg :: M2 -> M2 Source #

(<=>) :: M2 -> M2 -> M2 Source #

BoundedJoinSemiLattice M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

bottom :: M2 Source #

BoundedMeetSemiLattice M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

top :: M2 Source #

Lattice M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

(\/) :: M2 -> M2 -> M2 Source #

(/\) :: M2 -> M2 -> M2 Source #

PartialOrd M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

leq :: M2 -> M2 -> Bool Source #

comparable :: M2 -> M2 -> Bool Source #

Finite M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

universeF :: [M2] Source #

cardinality :: Tagged M2 Natural Source #

Universe M2 Source #

Instance details

Defined in Algebra.Lattice.M2

Methods

universe :: [M2] Source #

type Rep M2 Source #

Instance details

Defined in Algebra.Lattice.M2

type Rep M2 = D1 ('MetaData "M2" "Algebra.Lattice.M2" "lattices-2.2.1-JY28lmhbcmEBv2dv2owR24" 'False) ((C1 ('MetaCons "M2o" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "M2a" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "M2b" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "M2i" 'PrefixI 'False) (U1 :: Type -> Type)))

toSetBool :: M2 -> Set Bool Source #

fromSetBool :: Set Bool -> M2 Source #