| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Fcf.Class.Foldable
Description
Foldable types.
A minimal implementation of this interface is given by either FoldMap or
Foldr, but a default still needs to be given explicitly for the other.
data MyType a = ... {- Some custom Foldable type -}
-- Method 1: Implement Foldr, default FoldMap.
type instance Eval (Foldr f y xs) = ... {- Explicit implementation -}
type instance Eval (FoldMap f xs) = FoldMapDefault_ f xs {- Default -}
-- Method 2: Implement FoldMap, default Foldr.
type instance Eval (FoldMap f xs) = ... {- Explicit implementation -}
type instance Eval (Foldr f y xs) = FoldrDefault_ f y xs {- Default -}
Synopsis
- data Foldr :: (a -> b -> Exp b) -> b -> t a -> Exp b
- data FoldMap :: (a -> Exp m) -> t a -> Exp m
- type FoldMapDefault_ f xs = Eval (Foldr (Bicomap f Pure (.<>)) MEmpty xs)
- type FoldrDefault_ f y xs = Eval (UnEndo (Eval (FoldMap (Pure1 'Endo <=< Pure1 f) xs)) y)
- data And :: t Bool -> Exp Bool
- data Or :: t Bool -> Exp Bool
- data All :: (a -> Exp Bool) -> t a -> Exp Bool
- data Any :: (a -> Exp Bool) -> t a -> Exp Bool
- data Sum :: t Nat -> Exp Nat
- data Concat :: t m -> Exp m
- data ConcatMap :: (a -> Exp [b]) -> t a -> Exp [b]
Core interface
data Foldr :: (a -> b -> Exp b) -> b -> t a -> Exp b Source #
Right fold.
Example
>>>:kind! Eval (Foldr (+) 0 [1, 2, 3, 4])Eval (Foldr (+) 0 [1, 2, 3, 4]) :: Natural = 10
Instances
| type Eval (Foldr f y ('Left _a :: Either a3 a1) :: a2 -> Type) Source # | |
| type Eval (Foldr f y ('Right x :: Either a3 a1) :: a2 -> Type) Source # | |
| type Eval (Foldr f y ('Just x) :: a2 -> Type) Source # | |
| type Eval (Foldr f y ('Nothing :: Maybe a1) :: a2 -> Type) Source # | |
| type Eval (Foldr f y (x ': xs) :: a2 -> Type) Source # | |
| type Eval (Foldr f y ('[] :: [a1]) :: a2 -> Type) Source # | |
Defined in Fcf.Class.Foldable | |
data FoldMap :: (a -> Exp m) -> t a -> Exp m Source #
Type-level foldMap.
Instances
| type Eval (FoldMap f ('Left _a :: Either a3 a1) :: a2 -> Type) Source # | |
| type Eval (FoldMap f ('Right x :: Either a3 a1) :: a2 -> Type) Source # | |
| type Eval (FoldMap f ('Just x) :: a2 -> Type) Source # | |
| type Eval (FoldMap f ('Nothing :: Maybe a1) :: a2 -> Type) Source # | |
| type Eval (FoldMap f (x ': xs) :: a2 -> Type) Source # | |
| type Eval (FoldMap f ('[] :: [a1]) :: a2 -> Type) Source # | |
Defined in Fcf.Class.Foldable | |
Default implementations
type FoldMapDefault_ f xs = Eval (Foldr (Bicomap f Pure (.<>)) MEmpty xs) Source #
Default implementation of FoldMap.
Usage
To define an instance of FoldMap for a custom MyType for which you already have
an instance of Foldr:
type instanceEval(FoldMapf (xs :: MyType a)) =FoldMapDefault_f xs
Example
>>>:kind! FoldMapDefault_ Pure [EQ, LT, GT]FoldMapDefault_ Pure [EQ, LT, GT] :: Ordering = LT
type FoldrDefault_ f y xs = Eval (UnEndo (Eval (FoldMap (Pure1 'Endo <=< Pure1 f) xs)) y) Source #
Default implementation of Foldr.
Usage
To define an instance of Foldr for a custom MyType for which you already
have an instance of FoldMap:
type instanceEval(Foldrf y (xs :: MyType a)) =FoldrDefault_f y xs
Example
>>>:kind! FoldrDefault_ (.<>) EQ [EQ, LT, GT]FoldrDefault_ (.<>) EQ [EQ, LT, GT] :: Ordering = LT
Derived operations
Predicates
data And :: t Bool -> Exp Bool Source #
Give True if all of the booleans in the list are True.
Example
>>>:kind! Eval (And [True, True])Eval (And [True, True]) :: Bool = True
>>>:kind! Eval (And [True, True, False])Eval (And [True, True, False]) :: Bool = False
data Or :: t Bool -> Exp Bool Source #
Give True if any of the booleans in the list are True.
Example
>>>:kind! Eval (Or [True, True])Eval (Or [True, True]) :: Bool = True
>>>:kind! Eval (Or [False, False])Eval (Or [False, False]) :: Bool = False
data All :: (a -> Exp Bool) -> t a -> Exp Bool Source #
Whether all elements of the list satisfy a predicate.
Note: this identifier conflicts with All (from Data.Monoid).
Example
>>>:kind! Eval (All (Flip (<) 6) [0,1,2,3,4,5])Eval (All (Flip (<) 6) [0,1,2,3,4,5]) :: Bool = True
>>>:kind! Eval (All (Flip (<) 5) [0,1,2,3,4,5])Eval (All (Flip (<) 5) [0,1,2,3,4,5]) :: Bool = False
data Any :: (a -> Exp Bool) -> t a -> Exp Bool Source #
Whether any element of the list satisfies a predicate.
Note: this identifier conflicts with Any (from Fcf.Utils),
Any (from Data.Monoid), and Any (from GHC.Exts).
Example
>>>:kind! Eval (Any (Flip (<) 5) [0,1,2,3,4,5])Eval (Any (Flip (<) 5) [0,1,2,3,4,5]) :: Bool = True
>>>:kind! Eval (Any (Flip (<) 0) [0,1,2,3,4,5])Eval (Any (Flip (<) 0) [0,1,2,3,4,5]) :: Bool = False
Numbers
data Sum :: t Nat -> Exp Nat Source #
Sum a Nat-list.
Example
>>>:kind! Eval (Sum '[1,2,3])Eval (Sum '[1,2,3]) :: Natural = 6
Lists
data Concat :: t m -> Exp m Source #
Concatenate a collection of elements from a monoid.
Example
For example, fold a list of lists.
Concat :: [[a]] -> Exp [a]
>>>:kind! Eval (Concat ([[1,2], [3,4], [5,6]]))Eval (Concat ([[1,2], [3,4], [5,6]])) :: [Natural] = [1, 2, 3, 4, 5, 6]>>>:kind! Eval (Concat ([[Int, Maybe Int], [Maybe String, Either Double Int]]))Eval (Concat ([[Int, Maybe Int], [Maybe String, Either Double Int]])) :: [*] = [Int, Maybe Int, Maybe [Char], Either Double Int]