Data.Can

This module contains the definition for the Can datatype. In practice, this type is isomorphic to Maybe These - the type with two possibly non-exclusive values and an empty case.

Datatypes

Categorically, the Can datatype represents the pointed product in the category Hask* of pointed Hask types. The category Hask* consists of Hask types affixed with a dedicated base point of an object along with the object - i.e. Maybe a in Hask. Hence, the product is (1 + a) * (1 + b) ~ 1 + a + b + a*b, or Maybe (These a b) in Hask. Pictorially, you can visualize this as:

Can:
        a
        |
Non +---+---+ (a,b)
        |
        b

The fact that we can think about Can as your average product gives us some reasoning power about how this thing will be able to interact with the coproduct in Hask*, called Wedge. Namely, facts about currying Can a b -> c ~ a -> b -> c and distributivity over Wedge along with other facts about its associativity, commutativity, and any other analogy with (',') that you can think of.

data Can a b

The Can data type represents values with two non-exclusive possibilities, as well as an empty case. This is a product of pointed types - i.e. of Maybe values. The result is a type, Can a b, which is isomorphic to Maybe (These a b).

Constructors

Non

One a

Eno b

Two a b

Instances

Bitraversable Can

Defined in Data.Can

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Can a b -> f (Can c d)

Bifoldable Can

Defined in Data.Can

Methods

bifold :: Monoid m => Can m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Can a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Can a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Can a b -> c

Bifunctor Can

Defined in Data.Can

Methods

bimap :: (a -> b) -> (c -> d) -> Can a c -> Can b d

first :: (a -> b) -> Can a c -> Can b c

second :: (b -> c) -> Can a b -> Can a c

Eq2 Can

Defined in Data.Can

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Can a c -> Can b d -> Bool

Ord2 Can

Defined in Data.Can

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Can a c -> Can b d -> Ordering

Read2 Can

Defined in Data.Can

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Can a b)

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Can a b]

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Can a b)

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Can a b]

Show2 Can

Defined in Data.Can

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Can a b -> ShowS

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Can a b] -> ShowS

Biapplicative Can

Defined in Data.Can

Methods

bipure :: a -> b -> Can a b

(<<*>>) :: Can (a -> b) (c -> d) -> Can a c -> Can b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Can a d -> Can b e -> Can c f

(*>>) :: Can a b -> Can c d -> Can c d

(<<*) :: Can a b -> Can c d -> Can a b

NFData2 Can

Defined in Data.Can

Methods

liftRnf2 :: (a -> ()) -> (b -> ()) -> Can a b -> ()

Hashable2 Can

Defined in Data.Can

Methods

liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Can a b -> Int

(Lift a, Lift b) => Lift (Can a b :: Type)

Defined in Data.Can

Methods

lift :: Can a b -> Q Exp

liftTyped :: Can a b -> Q (TExp (Can a b))

Semigroup a => Monad (Can a)

Defined in Data.Can

Methods

(>>=) :: Can a a0 -> (a0 -> Can a b) -> Can a b

(>>) :: Can a a0 -> Can a b -> Can a b

return :: a0 -> Can a a0

Functor (Can a)

Defined in Data.Can

Methods

fmap :: (a0 -> b) -> Can a a0 -> Can a b

(<$) :: a0 -> Can a b -> Can a a0

Semigroup a => Applicative (Can a)

Defined in Data.Can

Methods

pure :: a0 -> Can a a0

(<*>) :: Can a (a0 -> b) -> Can a a0 -> Can a b

liftA2 :: (a0 -> b -> c) -> Can a a0 -> Can a b -> Can a c

(*>) :: Can a a0 -> Can a b -> Can a b

(<*) :: Can a a0 -> Can a b -> Can a a0

Foldable (Can a)

Defined in Data.Can

Methods

fold :: Monoid m => Can a m -> m

foldMap :: Monoid m => (a0 -> m) -> Can a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Can a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Can a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Can a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Can a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Can a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Can a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Can a a0 -> a0

toList :: Can a a0 -> [a0]

null :: Can a a0 -> Bool

length :: Can a a0 -> Int

elem :: Eq a0 => a0 -> Can a a0 -> Bool

maximum :: Ord a0 => Can a a0 -> a0

minimum :: Ord a0 => Can a a0 -> a0

sum :: Num a0 => Can a a0 -> a0

product :: Num a0 => Can a a0 -> a0

Traversable (Can a)

Defined in Data.Can

Methods

traverse :: Applicative f => (a0 -> f b) -> Can a a0 -> f (Can a b)

sequenceA :: Applicative f => Can a (f a0) -> f (Can a a0)

mapM :: Monad m => (a0 -> m b) -> Can a a0 -> m (Can a b)

sequence :: Monad m => Can a (m a0) -> m (Can a a0)

Eq a => Eq1 (Can a)

Defined in Data.Can

Methods

liftEq :: (a0 -> b -> Bool) -> Can a a0 -> Can a b -> Bool

Ord a => Ord1 (Can a)

Defined in Data.Can

Methods

liftCompare :: (a0 -> b -> Ordering) -> Can a a0 -> Can a b -> Ordering

Read a => Read1 (Can a)

Defined in Data.Can

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Can a a0)

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Can a a0]

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Can a a0)

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Can a a0]

Show a => Show1 (Can a)

Defined in Data.Can

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Can a a0 -> ShowS

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Can a a0] -> ShowS

Semigroup a => MonadZip (Can a)

Defined in Data.Can

Methods

mzip :: Can a a0 -> Can a b -> Can a (a0, b)

mzipWith :: (a0 -> b -> c) -> Can a a0 -> Can a b -> Can a c

munzip :: Can a (a0, b) -> (Can a a0, Can a b)

Semigroup a => Alternative (Can a)

Defined in Data.Can

Methods

empty :: Can a a0

(<|>) :: Can a a0 -> Can a a0 -> Can a a0

some :: Can a a0 -> Can a [a0]

many :: Can a a0 -> Can a [a0]

Semigroup a => MonadPlus (Can a)

Defined in Data.Can

Methods

mzero :: Can a a0

mplus :: Can a a0 -> Can a a0 -> Can a a0

NFData a => NFData1 (Can a)

Defined in Data.Can

Methods

liftRnf :: (a0 -> ()) -> Can a a0 -> ()

Hashable a => Hashable1 (Can a)

Defined in Data.Can

Methods

liftHashWithSalt :: (Int -> a0 -> Int) -> Int -> Can a a0 -> Int

Generic1 (Can a :: Type -> Type)

Defined in Data.Can

Associated Types

type Rep1 (Can a) :: k -> Type

Methods

from1 :: forall (a0 :: k). Can a a0 -> Rep1 (Can a) a0

to1 :: forall (a0 :: k). Rep1 (Can a) a0 -> Can a a0

(Eq a, Eq b) => Eq (Can a b)

Defined in Data.Can

Methods

(==) :: Can a b -> Can a b -> Bool

(/=) :: Can a b -> Can a b -> Bool

(Data a, Data b) => Data (Can a b)

Defined in Data.Can

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Can a b -> c (Can a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Can a b)

toConstr :: Can a b -> Constr

dataTypeOf :: Can a b -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Can a b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Can a b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Can a b -> Can a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Can a b -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Can a b -> r

gmapQ :: (forall d. Data d => d -> u) -> Can a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Can a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Can a b -> m (Can a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Can a b -> m (Can a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Can a b -> m (Can a b)

(Ord a, Ord b) => Ord (Can a b)

Defined in Data.Can

Methods

compare :: Can a b -> Can a b -> Ordering

(<) :: Can a b -> Can a b -> Bool

(<=) :: Can a b -> Can a b -> Bool

(>) :: Can a b -> Can a b -> Bool

(>=) :: Can a b -> Can a b -> Bool

max :: Can a b -> Can a b -> Can a b

min :: Can a b -> Can a b -> Can a b

(Read a, Read b) => Read (Can a b)

Defined in Data.Can

Methods

readsPrec :: Int -> ReadS (Can a b)

readList :: ReadS [Can a b]

readPrec :: ReadPrec (Can a b)

readListPrec :: ReadPrec [Can a b]

(Show a, Show b) => Show (Can a b)

Defined in Data.Can

Methods

showsPrec :: Int -> Can a b -> ShowS

show :: Can a b -> String

showList :: [Can a b] -> ShowS

Generic (Can a b)

Defined in Data.Can

Associated Types

type Rep (Can a b) :: Type -> Type

Methods

from :: Can a b -> Rep (Can a b) x

to :: Rep (Can a b) x -> Can a b

(Semigroup a, Semigroup b) => Semigroup (Can a b)

Defined in Data.Can

Methods

(<>) :: Can a b -> Can a b -> Can a b

sconcat :: NonEmpty (Can a b) -> Can a b

stimes :: Integral b0 => b0 -> Can a b -> Can a b

(Semigroup a, Semigroup b) => Monoid (Can a b)

Defined in Data.Can

Methods

mempty :: Can a b

mappend :: Can a b -> Can a b -> Can a b

mconcat :: [Can a b] -> Can a b

(Binary a, Binary b) => Binary (Can a b)

Defined in Data.Can

Methods

put :: Can a b -> Put

get :: Get (Can a b)

putList :: [Can a b] -> Put

(NFData a, NFData b) => NFData (Can a b)

Defined in Data.Can

Methods

rnf :: Can a b -> ()

(Hashable a, Hashable b) => Hashable (Can a b)

Defined in Data.Can

Methods

hashWithSalt :: Int -> Can a b -> Int

hash :: Can a b -> Int

type Rep1 (Can a :: Type -> Type)

Defined in Data.Can

type Rep1 (Can a :: Type -> Type) = D1 ('MetaData "Can" "Data.Can" "smash-0.1.2-JyUt5QWxQKg2J1iRgHHlBe" 'False) ((C1 ('MetaCons "Non" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "One" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) :+: (C1 ('MetaCons "Eno" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "Two" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)))

type Rep (Can a b)

Defined in Data.Can

type Rep (Can a b) = D1 ('MetaData "Can" "Data.Can" "smash-0.1.2-JyUt5QWxQKg2J1iRgHHlBe" 'False) ((C1 ('MetaCons "Non" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "One" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) :+: (C1 ('MetaCons "Eno" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)) :+: C1 ('MetaCons "Two" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b))))

Type synonyms

type (⊗) a b = Can a b

A type operator synonym for Can

Combinators

canFst :: Can a b -> Maybe a

Project the left value of a Can datatype. This is analogous to fst for (',').

canSnd :: Can a b -> Maybe b

Project the right value of a Can datatype. This is analogous to snd for (',').

isOne :: Can a b -> Bool

Detect if a Can is a One case.

isEno :: Can a b -> Bool

Detect if a Can is a Eno case.

isTwo :: Can a b -> Bool

Detect if a Can is a Two case.

isNon :: Can a b -> Bool

Detect if a Can is a Non case.

Eliminators

can

Arguments

:: c

default value to supply for the Non case

-> (a -> c)

eliminator for the One case

-> (b -> c)

eliminator for the Eno case

-> (a -> b -> c)

eliminator for the Two case

-> Can a b

-> c

Case elimination for the Can datatype

canWithMerge

Arguments

:: c

default value to supply for the Non case

-> (a -> c)

eliminator for the One case

-> (b -> c)

eliminator for the Eno case

-> (c -> c -> c)

merger for the Two case

-> Can a b

-> c

Case elimination for the Can datatype, with uniform behaviour.

canEach

Arguments

:: Monoid c

=> (a -> c)

eliminator for the One case

-> (b -> c)

eliminator for the Eno case

-> Can a b

-> c

Case elimination for the Can datatype, with uniform behaviour over a Monoid result.

canEachA

Arguments

:: Applicative m

=> Monoid c

=> (a -> m c)

eliminator for the One case

-> (b -> m c)

eliminator for the Eno case

-> Can a b

-> m c

Case elimination for the Can datatype, with uniform behaviour over a Monoid result in the context of an Applicative.

Folding and Unfolding

foldOnes :: Foldable f => (a -> m -> m) -> m -> f (Can a b) -> m

Fold over the One cases of a Foldable of Cans by some accumulating function.

foldEnos :: Foldable f => (b -> m -> m) -> m -> f (Can a b) -> m

Fold over the Eno cases of a Foldable of Cans by some accumulating function.

foldTwos :: Foldable f => (a -> b -> m -> m) -> m -> f (Can a b) -> m

Fold over the Two cases of a Foldable of Cans by some accumulating function.

gatherCans :: Can [a] [b] -> [Can a b]

Gather a Can of two lists and produce a list of Can values, mapping the Non case to the empty list, One' case to a list of Ones, the Eno case to a list of Enos, or zipping Two along both lists.

unfoldr :: Alternative f => (b -> Can a b) -> b -> f a

Unfold from right to left into a pointed product. For a variant that accumulates in the seed instead of just updating with a new value, see accumUntil and accumUntilM.

unfoldrM :: (Monad m, Alternative f) => (b -> m (Can a b)) -> b -> m (f a)

Unfold from right to left into a monadic computation over a pointed product

iterateUntil :: Alternative f => (b -> Can a b) -> b -> f a

Iterate on a seed, accumulating a result. See iterateUntilM for more details.

iterateUntilM :: Monad m => Alternative f => (b -> m (Can a b)) -> b -> m (f a)

Iterate on a seed, which may result in one of four scenarios:

1. The function yields a Non value, which terminates the iteration.
2. The function yields a One value.
3. The function yields a Eno value, which changes the seed and iteration continues with the new seed.
4. The function yields the a value of a Two case.

accumUntil :: Alternative f => Monoid b => (b -> Can a b) -> f a

Iterate on a seed, accumulating values and monoidally updating the seed with each update.

accumUntilM :: Monad m => Alternative f => Monoid b => (b -> m (Can a b)) -> m (f a)

Iterate on a seed, accumulating values and monoidally updating a seed within a monad.

Filtering

ones :: Foldable f => f (Can a b) -> [a]

Given a Foldable of Cans, collect the values of the One cases, if any.

enos :: Foldable f => f (Can a b) -> [b]

Given a Foldable of Cans, collect the values of the Eno cases, if any.

twos :: Foldable f => f (Can a b) -> [(a, b)]

Given a Foldable of Cans, collect the values of the Two cases, if any.

filterOnes :: Foldable f => f (Can a b) -> [Can a b]

Filter the One cases of a Foldable of Can values.

filterEnos :: Foldable f => f (Can a b) -> [Can a b]

Filter the Eno cases of a Foldable of Can values.

filterTwos :: Foldable f => f (Can a b) -> [Can a b]

Filter the Two cases of a Foldable of Can values.

filterNons :: Foldable f => f (Can a b) -> [Can a b]

Filter the Non cases of a Foldable of Can values.

Curry & Uncurry

canCurry :: (Can a b -> Maybe c) -> Maybe a -> Maybe b -> Maybe c

Curry a function from a Can to a Maybe value, resulting in a function of curried Maybe values. This is analogous to currying for (->).

canUncurry :: (Maybe a -> Maybe b -> Maybe c) -> Can a b -> Maybe c

Uncurry a function from a Can to a Maybe value, resulting in a function of curried Maybe values. This is analogous to uncurrying for (->).

Partitioning

partitionCans :: Foldable t => Alternative f => t (Can a b) -> (f a, f b)

Given a Foldable of Cans, partition it into a tuple of alternatives their parts.

partitionAll :: Foldable f => f (Can a b) -> ([a], [b], [(a, b)])

Partition a list of Can values into a triple of lists of all of their constituent parts

partitionEithers :: Foldable f => f (Either a b) -> Can [a] [b]

Partition a list of Either values, separating them into a Can value of lists of left and right values, or Non in the case of an empty list.

mapCans :: Traversable t => Alternative f => (a -> Can b c) -> t a -> (f b, f c)

Partition a structure by mapping its contents into Cans, and folding over (<|>).

Distributivity

distributeCan :: Can (a, b) c -> (Can a c, Can b c)

Distribute a Can value over a product.

codistributeCan :: Either (Can a c) (Can b c) -> Can (Either a b) c

Codistribute a coproduct over a Can value.

Associativity

reassocLR :: Can (Can a b) c -> Can a (Can b c)

Re-associate a Can of cans from left to right.

reassocRL :: Can a (Can b c) -> Can (Can a b) c

Re-associate a Can of cans from right to left.

Symmetry

swapCan :: Can a b -> Can b a

Swap the positions of values in a Can.