A tactic for dealing with elements present in one set but not the other in merge.

A tactic of type SimpleWhenMissing a is an abstract representation of a function of type a -> Bool.

Since: 0.8.1

A tactic for dealing with elements present in both sets in merge.

A tactic of type SimpleWhenMatched a is an abstract representation of a function of type a -> Bool.

Since: 0.8.1

Merge two sets.

merge takes two SimpleWhenMissing tactics, a SimpleWhenMatched tactic, and two sets. It uses the tactics to merge the sets.

Consider

merge (filterMissing g1) (filterMissing g2) (filterMatched f) s1 s2

g1 = (==2)
g2 = (==3)
f  = (==6)
s1 = [2, 4, 6, 8, 10, 12]
s2 = [3, 6, 9, 12]

merge will pass the elements to g1, g2, or f as appropriate, producing a Bool for each element.

m1:      [   2,            4,     6,     8,           10     12]
m2:      [          3,            6,            9,           12]
result:  [g1 2,  g2 3,  g1 4,   f 6,  g1 8,  g2 9, g1 10,  f 12]
       = [True,  True, False,  True, False, False, False, False]

The result set contains the element for which we have True.

>>> merge (filterMissing g1) (filterMissing g2) (filterMatched f) s1 s2
fromList [2,3,6]

The other tactics below are optimizations or simplifications of filterMissing for special cases. Most importantly,

• dropMissing drops all elements.
• preserveMissing leaves all elements alone.

When merge is given three arguments, it is inlined at the call site. To prevent excessive inlining, you should typically use merge to define your custom combining functions.

Since: 0.8.1

Drop all the elements that are missing from the other set.

dropMissing :: SimpleWhenMissing a

dropMissing = filterMissing (\_ -> False)

but dropMissing is more efficient.

Since: 0.8.1

Preserve the elements that are missing from the other set.

preserveMissing :: SimpleWhenMissing a

preserveMissing = filterMissing (\_ -> True)

but preserveMissing is more efficient.

Since: 0.8.1

Filter the elements that are missing from the other set.

filterMissing :: (a -> Bool) -> SimpleWhenMissing a

Since: 0.8.1

When an element is found in both sets, drop the element.

Since: 0.8.1

When an element is found in both sets, keep the element.

Since: 0.8.1

When an element is found in both sets, choose whether to keep the element in the merged set.

Since: 0.8.1

A tactic for dealing with elements present in one set but not the other in merge or mergeA.

A tactic of type WhenMissing f a is an abstract representation of a function of type a -> f Bool.

Since: 0.8.1

A tactic for dealing with elements present in both sets in merge or mergeA.

A tactic of type WhenMatched f a is an abstract representation of a function of type a -> f Bool.

Since: 0.8.1

An applicative version of merge.

mergeA takes two WhenMissing tactics, a WhenMatched tactic, and two sets. It uses the tactics to merge the sets.

Behaves just like merge while allowing Applicative effects. Effects are performed in increasing order of elements.

Consider,

mergeA (filterAMissing g1) (filterAMissing g2) (filterAMatched f) s1 s2

g1 x = (x == 2) <$ putStrLn ("g1 " ++ show x)
g2 x = (x == 3) <$ putStrLn ("g2 " ++ show x)
f x = (x == 6) <$ putStrLn ("f " ++ show x)
s1 = [2, 4, 6, 8, 10, 12]
s2 = [3, 6, 9, 12]

As with merge, the result set is [2,3,6]. Additionally, g1, g2, and f perform IO effects, printing the elements in increasing order.

>>> mergeA (filterAMissing g1) (filterAMissing g2) (filterAMatched f) s1 s2
g1 2
g2 3
g1 4
f 6
g1 8
g2 9
g1 10
f 12
fromList [2,3,6]

When mergeA is given three arguments, it is inlined at the call site. To prevent excessive inlining, you should generally only use mergeA to define custom combining functions.

Examples

data Pair a = Pair !a !a deriving Functor

instance Applicative Pair where
   pure x = Pair x x
   liftA2 f (Pair x1 y1) (Pair x2 y2) = Pair (f x1 x2) (f y1 y2)

-- | Calculate the union and intersection of two sets.
unionIntersection :: Ord a => Set a -> Set a -> (Set a, Set a)
unionIntersection m1 m2 =
  case mergeA preserveAndDropMissing preserveAndDropMissing preserveMatched m1 m2 of
    Pair mu mi -> (mu, mi)
  where
    -- use Pair to build the union and intersection together
    preserveAndDropMissing = whenMissing (\_x -> Pair True False) (\s -> Pair s empty)

import Data.Functor.Const (Const(..))
import Data.Monoid (All(..))

-- | Whether the first set is a subset of the second set.
isSubsetOf :: Ord a => Set a -> Set a -> Bool
isSubsetOf m1 m2 =
  getAll (getConst (mergeA isEmpty dropMissing dropMatched m1 m2))
  where
    isEmpty = whenMissing (\_x -> Const (All False)) (\s -> Const (All (null s)))

Since: 0.8.1

Filter the elements that are missing from the other set using some Applicative action.

Since: 0.8.1

Create a WhenMissing from two functions.

whenMissing must be called with two functions f and g such that g = filterA f. g may be a more efficient way of applying f to all elements in a Set.

Warning: It is the caller's responsibility to ensure the above property.

Examples

preserveMissing :: Applicative f => WhenMissing f a
preserveMissing = whenMissing f g
  where
    f _x = pure True
    g s = pure s
    -- Note that this satisfies g = filterA f

import Data.Functor.Const (Const(..))
import Data.Monoid (All(..))

-- For a usage of this, see examples on mergeA
isEmpty :: WhenMissing (Const All) a
isEmpty = whenMissing f g
  where
    f _x = Const (All False)
    g s = Const (All (null s))
    -- Note that this satisfies g = filterA f

Since: 0.8.1

When an element is found in both sets, choose whether to keep the element in the merged set.

Since: 0.8.1

Along with filterAMissing, witnesses the isomorphism between WhenMissing f a and a -> f Bool.

Since: 0.8.1

Along with filterAMatched, witnesses the isomorphism between WhenMatched f a and a -> f Bool.

Since: 0.8.1