Copyright	(c) Conal Elliott 2008
License	BSD3
Maintainer	conal@conal.net
Stability	experimental
Safe Haskell	None
Language	Haskell2010

Data.Lub

Contents

Least upper bounds
Some useful special applications of lub
Generic deriving

Description

Compute least upper bound (lub) of two values, with respect to information content. I.e., merge the information available in each. For flat types (in which all values are either bottom or fully defined), lub is equivalent to unamb.

Synopsis

class HasLub a where
- lub :: a -> a -> a
- lubs :: [a] -> a
newtype Lub a = Lub {
- getLub :: a
}
flatLub :: a -> a -> a
parCommute :: HasLub b => (a -> a -> b) -> a -> a -> b
ptimes :: (HasLub a, Eq a, Num a) => a -> a -> a
class GHasLub f
genericLub :: (Generic a, GHasLub (Rep a)) => a -> a -> a

Least upper bounds

class HasLub a where Source #

Types that support information merging (lub)

Minimal complete definition

Nothing

Methods

lub :: a -> a -> a Source #

Least upper information bound. Combines information available from each argument. The arguments must be consistent, i.e., must have a common upper bound.

default lub :: (Generic a, GHasLub (Rep a)) => a -> a -> a Source #

lubs :: [a] -> a Source #

n-ary lub. Defaults to foldr lub undefined

Instances

Instances details

HasLub Bool Source #
Instance details Defined in Data.Lub Methods lub :: Bool -> Bool -> Bool Source # lubs :: [Bool] -> Bool Source #
HasLub Char Source #
Instance details Defined in Data.Lub Methods lub :: Char -> Char -> Char Source # lubs :: [Char] -> Char Source #
HasLub Double Source #
Instance details Defined in Data.Lub Methods lub :: Double -> Double -> Double Source # lubs :: [Double] -> Double Source #
HasLub Float Source #
Instance details Defined in Data.Lub Methods lub :: Float -> Float -> Float Source # lubs :: [Float] -> Float Source #
HasLub Int Source #
Instance details Defined in Data.Lub Methods lub :: Int -> Int -> Int Source # lubs :: [Int] -> Int Source #
HasLub Integer Source #
Instance details Defined in Data.Lub Methods lub :: Integer -> Integer -> Integer Source # lubs :: [Integer] -> Integer Source #
HasLub Ordering Source #
Instance details Defined in Data.Lub Methods lub :: Ordering -> Ordering -> Ordering Source # lubs :: [Ordering] -> Ordering Source #
HasLub () Source #
Instance details Defined in Data.Lub Methods lub :: () -> () -> () Source # lubs :: [()] -> () Source #
HasLub Void Source #
Instance details Defined in Data.Lub Methods lub :: Void -> Void -> Void Source # lubs :: [Void] -> Void Source #
HasLub TypeRep Source #
Instance details Defined in Data.Lub Methods lub :: TypeRep -> TypeRep -> TypeRep Source # lubs :: [TypeRep] -> TypeRep Source #
HasLub a => HasLub [a] Source #
Instance details Defined in Data.Lub Methods lub :: [a] -> [a] -> [a] Source # lubs :: [[a]] -> [a] Source #
HasLub a => HasLub (Maybe a) Source #
Instance details Defined in Data.Lub Methods lub :: Maybe a -> Maybe a -> Maybe a Source # lubs :: [Maybe a] -> Maybe a Source #
HasLub a => HasLub (ZipList a) Source #
Instance details Defined in Data.Lub Methods lub :: ZipList a -> ZipList a -> ZipList a Source # lubs :: [ZipList a] -> ZipList a Source #
HasLub a => HasLub (Identity a) Source #
Instance details Defined in Data.Lub Methods lub :: Identity a -> Identity a -> Identity a Source # lubs :: [Identity a] -> Identity a Source #
HasLub a => HasLub (Lub a) Source #
Instance details Defined in Data.Lub Methods lub :: Lub a -> Lub a -> Lub a Source # lubs :: [Lub a] -> Lub a Source #
HasLub b => HasLub (a -> b) Source #
Instance details Defined in Data.Lub Methods lub :: (a -> b) -> (a -> b) -> a -> b Source # lubs :: [a -> b] -> a -> b Source #
(HasLub a, HasLub b) => HasLub (Either a b) Source #
Instance details Defined in Data.Lub Methods lub :: Either a b -> Either a b -> Either a b Source # lubs :: [Either a b] -> Either a b Source #
HasLub (TypeRep a) Source #
Instance details Defined in Data.Lub Methods lub :: TypeRep a -> TypeRep a -> TypeRep a Source # lubs :: [TypeRep a] -> TypeRep a Source #
(HasLub a, HasLub b) => HasLub (a, b) Source #
Instance details Defined in Data.Lub Methods lub :: (a, b) -> (a, b) -> (a, b) Source # lubs :: [(a, b)] -> (a, b) Source #
HasLub (Proxy t) Source #
Instance details Defined in Data.Lub Methods lub :: Proxy t -> Proxy t -> Proxy t Source # lubs :: [Proxy t] -> Proxy t Source #
(HasLub a, HasLub b, HasLub c) => HasLub (a, b, c) Source #
Instance details Defined in Data.Lub Methods lub :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # lubs :: [(a, b, c)] -> (a, b, c) Source #
HasLub a => HasLub (Const a b) Source #
Instance details Defined in Data.Lub Methods lub :: Const a b -> Const a b -> Const a b Source # lubs :: [Const a b] -> Const a b Source #
HasLub (a :~: b) Source #
Instance details Defined in Data.Lub Methods lub :: (a :~: b) -> (a :~: b) -> a :~: b Source # lubs :: [a :~: b] -> a :~: b Source #
(HasLub (f a), HasLub (g a)) => HasLub ((f :+: g) a) Source #
Instance details Defined in Data.Lub Methods lub :: (f :+: g) a -> (f :+: g) a -> (f :+: g) a Source # lubs :: [(f :+: g) a] -> (f :+: g) a Source #
(HasLub (f a), HasLub (g a)) => HasLub ((f :*: g) a) Source #
Instance details Defined in Data.Lub Methods lub :: (f :: g) a -> (f :: g) a -> (f :: g) a Source # lubs :: [(f :: g) a] -> (f :*: g) a Source #
(HasLub a, HasLub b, HasLub c, HasLub d) => HasLub (a, b, c, d) Source #
Instance details Defined in Data.Lub Methods lub :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # lubs :: [(a, b, c, d)] -> (a, b, c, d) Source #
(HasLub (f a), HasLub (g a)) => HasLub (Product f g a) Source #
Instance details Defined in Data.Lub Methods lub :: Product f g a -> Product f g a -> Product f g a Source # lubs :: [Product f g a] -> Product f g a Source #
(HasLub (f a), HasLub (g a)) => HasLub (Sum f g a) Source #
Instance details Defined in Data.Lub Methods lub :: Sum f g a -> Sum f g a -> Sum f g a Source # lubs :: [Sum f g a] -> Sum f g a Source #
HasLub (a :~~: b) Source #
Instance details Defined in Data.Lub Methods lub :: (a :~~: b) -> (a :~~: b) -> a :~~: b Source # lubs :: [a :~~: b] -> a :~~: b Source #
(HasLub a, HasLub b, HasLub c, HasLub d, HasLub e) => HasLub (a, b, c, d, e) Source #
Instance details Defined in Data.Lub Methods lub :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # lubs :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #
HasLub (f (g a)) => HasLub (Compose f g a) Source #
Instance details Defined in Data.Lub Methods lub :: Compose f g a -> Compose f g a -> Compose f g a Source # lubs :: [Compose f g a] -> Compose f g a Source #

newtype Lub a Source #

The Semigroup operation takes the least upper bound.

Constructors

Lub
Fields getLub :: a

Instances

Instances details

Monad Lub Source #
Instance details Defined in Data.Lub Methods (>>=) :: Lub a -> (a -> Lub b) -> Lub b # (>>) :: Lub a -> Lub b -> Lub b # return :: a -> Lub a #
Functor Lub Source #
Instance details Defined in Data.Lub Methods fmap :: (a -> b) -> Lub a -> Lub b # (<$) :: a -> Lub b -> Lub a #
Applicative Lub Source #
Instance details Defined in Data.Lub Methods pure :: a -> Lub a # (<>) :: Lub (a -> b) -> Lub a -> Lub b # liftA2 :: (a -> b -> c) -> Lub a -> Lub b -> Lub c # (>) :: Lub a -> Lub b -> Lub b # (<*) :: Lub a -> Lub b -> Lub a #
Eq a => Eq (Lub a) Source #
Instance details Defined in Data.Lub Methods (==) :: Lub a -> Lub a -> Bool # (/=) :: Lub a -> Lub a -> Bool #
Ord a => Ord (Lub a) Source #
Instance details Defined in Data.Lub Methods compare :: Lub a -> Lub a -> Ordering # (<) :: Lub a -> Lub a -> Bool # (<=) :: Lub a -> Lub a -> Bool # (>) :: Lub a -> Lub a -> Bool # (>=) :: Lub a -> Lub a -> Bool # max :: Lub a -> Lub a -> Lub a # min :: Lub a -> Lub a -> Lub a #
Read a => Read (Lub a) Source #
Instance details Defined in Data.Lub Methods readsPrec :: Int -> ReadS (Lub a) # readList :: ReadS [Lub a] # readPrec :: ReadPrec (Lub a) # readListPrec :: ReadPrec [Lub a] #
Show a => Show (Lub a) Source #
Instance details Defined in Data.Lub Methods showsPrec :: Int -> Lub a -> ShowS # show :: Lub a -> String # showList :: [Lub a] -> ShowS #
Generic (Lub a) Source #
Instance details Defined in Data.Lub Associated Types type Rep (Lub a) :: Type -> Type # Methods from :: Lub a -> Rep (Lub a) x # to :: Rep (Lub a) x -> Lub a #
HasLub a => Semigroup (Lub a) Source #
Instance details Defined in Data.Lub Methods (<>) :: Lub a -> Lub a -> Lub a # sconcat :: NonEmpty (Lub a) -> Lub a # stimes :: Integral b => b -> Lub a -> Lub a #
HasLub a => Monoid (Lub a) Source #
Instance details Defined in Data.Lub Methods mempty :: Lub a # mappend :: Lub a -> Lub a -> Lub a # mconcat :: [Lub a] -> Lub a #
HasLub a => HasLub (Lub a) Source #
Instance details Defined in Data.Lub Methods lub :: Lub a -> Lub a -> Lub a Source # lubs :: [Lub a] -> Lub a Source #
type Rep (Lub a) Source #
Instance details Defined in Data.Lub type Rep (Lub a) = D1 ('MetaData "Lub" "Data.Lub" "lub-0.1.8-EVcRzQDgXRgLOxIQy65ZCB" 'True) (C1 ('MetaCons "Lub" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLub") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

flatLub :: a -> a -> a Source #

A lub for flat domains. Equivalent to unamb. Handy for defining HasLub instances, e.g.,

  instance HasLub Integer where lub = flatLub

Some useful special applications of `lub`

parCommute :: HasLub b => (a -> a -> b) -> a -> a -> b Source #

Turn a binary commutative operation into that tries both orders in parallel, lub-merging the results. Useful when there are special cases that don't require evaluating both arguments.

Similar to parCommute from Unamb, but uses lub instead of unamb.

ptimes :: (HasLub a, Eq a, Num a) => a -> a -> a Source #

Multiplication optimized for either argument being zero or one, where the other might be expensive/delayed.

Generic deriving

class GHasLub f Source #

Used for generic deriving of HasLub

Minimal complete definition

glub

Instances

Instances details

GHasLub' f => GHasLub (D1 ('MetaData _q _r _s 'False) f) Source #
Instance details Defined in Data.Lub Methods glub :: (Generic a, Rep a ~ D1 ('MetaData _q _r _s 'False) f) => a -> a -> a
HasLub x => GHasLub (D1 ('MetaData _q _r _s 'True) (C1 _t (S1 _u (K1 _v x :: Type -> Type)))) Source #
Instance details Defined in Data.Lub Methods glub :: (Generic a, Rep a ~ D1 ('MetaData _q _r _s 'True) (C1 _t (S1 _u (K1 _v x)))) => a -> a -> a

genericLub :: (Generic a, GHasLub (Rep a)) => a -> a -> a Source #

A suitable definition of lub for instances of Generic.

Least upper bounds

Instances

Instances

Some useful special applications of lub

Generic deriving

Instances

Some useful special applications of `lub`