Data.Order.Extended

Lattice extensions

type Lifted = Either ()

type Lowered a = Either a ()

data Extended a

Add a bottom and top to a lattice.

The top is the absorbing element for the join, and the bottom is the absorbing element for the meet.

Constructors

Bottom

Extended a

Top

Instances

Functor Extended

Defined in Data.Order.Extended

Methods

fmap :: (a -> b) -> Extended a -> Extended b

(<$) :: a -> Extended b -> Extended a

Preorder a => Connection k () (Extended a)

Defined in Data.Connection.Class

Methods

conn :: Conn k () (Extended a)

Connection k Double (Extended Int32)

All Int32 values are exactly representable in a Double.

Defined in Data.Connection.Class

Methods

conn :: Conn k Double (Extended Int32)

Connection k Double (Extended Int16)

All Int16 values are exactly representable in a Double.

Defined in Data.Connection.Class

Methods

conn :: Conn k Double (Extended Int16)

Connection k Double (Extended Int8)

All Int08 values are exactly representable in a Double.

Defined in Data.Connection.Class

Methods

conn :: Conn k Double (Extended Int8)

Connection k Float (Extended Int16)

All Int16 values are exactly representable in a Float.

Defined in Data.Connection.Class

Methods

conn :: Conn k Float (Extended Int16)

Connection k Float (Extended Int8)

All Int08 values are exactly representable in a Float.

Defined in Data.Connection.Class

Methods

conn :: Conn k Float (Extended Int8)

Connection k Rational (Extended Integer)

Defined in Data.Connection.Class

Methods

conn :: Conn k Rational (Extended Integer)

Connection k Rational (Extended Int)

Defined in Data.Connection.Class

Methods

conn :: Conn k Rational (Extended Int)

Connection k Rational (Extended Int64)

Defined in Data.Connection.Class

Methods

conn :: Conn k Rational (Extended Int64)

Connection k Rational (Extended Int32)

Defined in Data.Connection.Class

Methods

conn :: Conn k Rational (Extended Int32)

Connection k Rational (Extended Int16)

Defined in Data.Connection.Class

Methods

conn :: Conn k Rational (Extended Int16)

Connection k Rational (Extended Int8)

Defined in Data.Connection.Class

Methods

conn :: Conn k Rational (Extended Int8)

Heyting a => Algebra 'R (Extended a)

Defined in Data.Lattice

Methods

algebra :: Extended a -> Conn 'R (Extended a) (Extended a)

Join a => Semilattice 'L (Extended a)

Defined in Data.Lattice

Methods

bounded :: Conn 'L () (Extended a)

semilattice :: Conn 'L (Extended a, Extended a) (Extended a)

Meet a => Semilattice 'R (Extended a)

Defined in Data.Lattice

Methods

bounded :: Conn 'R () (Extended a)

semilattice :: Conn 'R (Extended a, Extended a) (Extended a)

Eq a => Eq (Extended a)

Defined in Data.Order.Extended

Methods

(==) :: Extended a -> Extended a -> Bool

(/=) :: Extended a -> Extended a -> Bool

Ord a => Ord (Extended a)

Defined in Data.Order.Extended

Methods

compare :: Extended a -> Extended a -> Ordering

(<) :: Extended a -> Extended a -> Bool

(<=) :: Extended a -> Extended a -> Bool

(>) :: Extended a -> Extended a -> Bool

(>=) :: Extended a -> Extended a -> Bool

max :: Extended a -> Extended a -> Extended a

min :: Extended a -> Extended a -> Extended a

Show a => Show (Extended a)

Defined in Data.Order.Extended

Methods

showsPrec :: Int -> Extended a -> ShowS

show :: Extended a -> String

showList :: [Extended a] -> ShowS

Generic (Extended a)

Defined in Data.Order.Extended

Associated Types

type Rep (Extended a) :: Type -> Type

Methods

from :: Extended a -> Rep (Extended a) x

to :: Rep (Extended a) x -> Extended a

Preorder a => Preorder (Extended a)

Defined in Data.Order.Extended

Methods

(<~) :: Extended a -> Extended a -> Bool

(>~) :: Extended a -> Extended a -> Bool

(?~) :: Extended a -> Extended a -> Bool

(~~) :: Extended a -> Extended a -> Bool

(/~) :: Extended a -> Extended a -> Bool

plt :: Extended a -> Extended a -> Bool

pgt :: Extended a -> Extended a -> Bool

similar :: Extended a -> Extended a -> Bool

pmax :: Extended a -> Extended a -> Maybe (Extended a)

pmin :: Extended a -> Extended a -> Maybe (Extended a)

pcompare :: Extended a -> Extended a -> Maybe Ordering

Generic1 Extended

Defined in Data.Order.Extended

Associated Types

type Rep1 Extended :: k -> Type

Methods

from1 :: forall (a :: k). Extended a -> Rep1 Extended a

to1 :: forall (a :: k). Rep1 Extended a -> Extended a

type Rep (Extended a)

Defined in Data.Order.Extended

type Rep (Extended a) = D1 ('MetaData "Extended" "Data.Order.Extended" "connections-0.2.0-DeRRGdWJkv66Qly2VHCKTZ" 'False) (C1 ('MetaCons "Bottom" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "Extended" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type)))

type Rep1 Extended

Defined in Data.Order.Extended

type Rep1 Extended = D1 ('MetaData "Extended" "Data.Order.Extended" "connections-0.2.0-DeRRGdWJkv66Qly2VHCKTZ" 'False) (C1 ('MetaCons "Bottom" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "Extended" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type)))

extended :: b -> b -> (a -> b) -> Extended a -> b

Eliminate an Extended.

Lattice Extensions

liftMaybe :: (a -> Bool) -> (a -> b) -> a -> Maybe b

liftEitherL :: (a -> Bool) -> (a -> b) -> a -> Lifted b

liftEitherR :: (a -> Bool) -> (a -> b) -> a -> Lowered b

liftExtended :: (a -> Bool) -> (a -> Bool) -> (a -> b) -> a -> Extended b