Data.Unfolder

Unfolders provide a way to unfold data structures. They are basically Alternative instances, but the choose method allows the unfolder to do something special for the recursive positions of the data structure.

Unfolder

class Alternative f => Unfolder f where

Unfolders provide a way to unfold data structures. The methods have default implementations in terms of Alternative, but you can implement chooseMap to act on recursive positions of the data structure, or simply to provide a faster implementation than 'foldr ((|) . f) empty'.

Methods

choose :: [f a] -> f a

Choose one of the values from the list.

chooseMap :: (a -> f b) -> [a] -> f b

Choose one of the values from the list and apply the given function.

chooseInt :: Int -> f Int

Given a number n, return a number between '0' and 'n - 1'.

Instances

Unfolder []

Don't choose but return all items.

Methods

choose :: [[a]] -> [a]

chooseMap :: (a -> [b]) -> [a] -> [b]

chooseInt :: Int -> [Int]

Unfolder Maybe

Always choose the first item.

Methods

choose :: [Maybe a] -> Maybe a

chooseMap :: (a -> Maybe b) -> [a] -> Maybe b

chooseInt :: Int -> Maybe Int

Unfolder Seq

Don't choose but return all items.

Methods

choose :: [Seq a] -> Seq a

chooseMap :: (a -> Seq b) -> [a] -> Seq b

chooseInt :: Int -> Seq Int

Unfolder Arb

Limit the depth of the generated data structure by dividing the given size by the number of recursive positions.

Methods

choose :: [Arb a] -> Arb a

chooseMap :: (a -> Arb b) -> [a] -> Arb b

chooseInt :: Int -> Arb Int

Unfolder Nth

Methods

choose :: [Nth a] -> Nth a

chooseMap :: (a -> Nth b) -> [a] -> Nth b

chooseInt :: Int -> Nth Int

MonadPlus m => Unfolder (WrappedMonad m)

Derived instance.

Methods

choose :: [WrappedMonad m a] -> WrappedMonad m a

chooseMap :: (a -> WrappedMonad m b) -> [a] -> WrappedMonad m b

chooseInt :: Int -> WrappedMonad m Int

Unfolder f => Unfolder (Lift f)

Derived instance.

Methods

choose :: [Lift f a] -> Lift f a

chooseMap :: (a -> Lift f b) -> [a] -> Lift f b

chooseInt :: Int -> Lift f Int

(Functor m, Monad m) => Unfolder (MaybeT m)

Derived instance.

Methods

choose :: [MaybeT m a] -> MaybeT m a

chooseMap :: (a -> MaybeT m b) -> [a] -> MaybeT m b

chooseInt :: Int -> MaybeT m Int

Applicative f => Unfolder (ListT f)

Derived instance.

Methods

choose :: [ListT f a] -> ListT f a

chooseMap :: (a -> ListT f b) -> [a] -> ListT f b

chooseInt :: Int -> ListT f Int

Num a => Unfolder (NumConst a)

Unfolds to a constant numeric value. Useful for counting shapes.

Methods

choose :: [NumConst a a] -> NumConst a a

chooseMap :: (a -> NumConst a b) -> [a] -> NumConst a b

chooseInt :: Int -> NumConst a Int

Applicative f => Unfolder (BFS f)

Choose between values of a given depth only.

Methods

choose :: [BFS f a] -> BFS f a

chooseMap :: (a -> BFS f b) -> [a] -> BFS f b

chooseInt :: Int -> BFS f Int

Unfolder f => Unfolder (WithRec f)

Applies a certain function depending on the depth at every recursive position.

Methods

choose :: [WithRec f a] -> WithRec f a

chooseMap :: (a -> WithRec f b) -> [a] -> WithRec f b

chooseInt :: Int -> WithRec f Int

Unfolder f => Unfolder (DualA f)

Reverse the list passed to choose.

Methods

choose :: [DualA f a] -> DualA f a

chooseMap :: (a -> DualA f b) -> [a] -> DualA f b

chooseInt :: Int -> DualA f Int

(ArrowZero a, ArrowPlus a) => Unfolder (WrappedArrow a b)

Derived instance.

Methods

choose :: [WrappedArrow a b a] -> WrappedArrow a b a

chooseMap :: (a -> WrappedArrow a b b) -> [a] -> WrappedArrow a b b

chooseInt :: Int -> WrappedArrow a b Int

Unfolder f => Unfolder (Reverse * f)

Derived instance.

Methods

choose :: [Reverse * f a] -> Reverse * f a

chooseMap :: (a -> Reverse * f b) -> [a] -> Reverse * f b

chooseInt :: Int -> Reverse * f Int

Unfolder f => Unfolder (Backwards * f)

Derived instance.

Methods

choose :: [Backwards * f a] -> Backwards * f a

chooseMap :: (a -> Backwards * f b) -> [a] -> Backwards * f b

chooseInt :: Int -> Backwards * f Int

(Monoid w, Unfolder m) => Unfolder (WriterT w m)

Derived instance.

Methods

choose :: [WriterT w m a] -> WriterT w m a

chooseMap :: (a -> WriterT w m b) -> [a] -> WriterT w m b

chooseInt :: Int -> WriterT w m Int

(MonadPlus m, Unfolder m) => Unfolder (StateT s m)

Derived instance.

Methods

choose :: [StateT s m a] -> StateT s m a

chooseMap :: (a -> StateT s m b) -> [a] -> StateT s m b

chooseInt :: Int -> StateT s m Int

(Functor m, Monad m, Monoid e) => Unfolder (ExceptT e m)

Derived instance.

Methods

choose :: [ExceptT e m a] -> ExceptT e m a

chooseMap :: (a -> ExceptT e m b) -> [a] -> ExceptT e m b

chooseInt :: Int -> ExceptT e m Int

(Functor m, Monad m, RandomGen g) => Unfolder (Random g m)

Choose randomly.

Methods

choose :: [Random g m a] -> Random g m a

chooseMap :: (a -> Random g m b) -> [a] -> Random g m b

chooseInt :: Int -> Random g m Int

(Unfolder p, Unfolder q) => Unfolder (Product * p q)

Derived instance.

Methods

choose :: [Product * p q a] -> Product * p q a

chooseMap :: (a -> Product * p q b) -> [a] -> Product * p q b

chooseInt :: Int -> Product * p q Int

Unfolder m => Unfolder (ReaderT * r m)

Derived instance.

Methods

choose :: [ReaderT * r m a] -> ReaderT * r m a

chooseMap :: (a -> ReaderT * r m b) -> [a] -> ReaderT * r m b

chooseInt :: Int -> ReaderT * r m Int

(Unfolder p, Applicative q) => Unfolder (Compose * * p q)

Derived instance.

Methods

choose :: [Compose * * p q a] -> Compose * * p q a

chooseMap :: (a -> Compose * * p q b) -> [a] -> Compose * * p q b

chooseInt :: Int -> Compose * * p q Int

(Monoid w, MonadPlus m, Unfolder m) => Unfolder (RWST r w s m)

Derived instance.

Methods

choose :: [RWST r w s m a] -> RWST r w s m a

chooseMap :: (a -> RWST r w s m b) -> [a] -> RWST r w s m b

chooseInt :: Int -> RWST r w s m Int

chooseMonadDefault :: (Monad m, Unfolder m) => [m a] -> m a

If an unfolder is monadic, choose can be implemented in terms of chooseInt.

chooseMapMonadDefault :: (Monad m, Unfolder m) => (a -> m b) -> [a] -> m b

If an unfolder is monadic, chooseMap can be implemented in terms of chooseInt.

between :: (Unfolder f, Enum a) => a -> a -> f a

If a datatype is enumerable, we can use chooseInt to generate a value. This is the function to use if you want to unfold a datatype that has no type arguments (has kind *).

betweenD :: (Unfolder f, Enum a) => a -> a -> f a

betweenD uses choose to generate a value. It chooses between the lower bound and one of the higher values. This means that f.e. breadth-first unfolding and arbitrary will prefer lower values.

boundedEnum :: (Unfolder f, Bounded a, Enum a) => f a

If a datatype is also bounded, we choose between all possible values.

boundedEnum = between minBound maxBound

boundedEnumD :: (Unfolder f, Bounded a, Enum a) => f a

boundedEnumD = betweenD minBound maxBound

Unfolder instances

newtype Random g m a

Constructors

Random

Fields

• getRandom :: StateT g m a

Instances

Monad m => Monad (Random g m)

Methods

(>>=) :: Random g m a -> (a -> Random g m b) -> Random g m b

(>>) :: Random g m a -> Random g m b -> Random g m b

return :: a -> Random g m a

fail :: String -> Random g m a

Functor m => Functor (Random g m)

Methods

fmap :: (a -> b) -> Random g m a -> Random g m b

(<$) :: a -> Random g m b -> Random g m a

Monad m => Applicative (Random g m)

Methods

pure :: a -> Random g m a

(<*>) :: Random g m (a -> b) -> Random g m a -> Random g m b

(*>) :: Random g m a -> Random g m b -> Random g m b

(<*) :: Random g m a -> Random g m b -> Random g m a

(Functor m, Monad m, RandomGen g) => Alternative (Random g m)

Methods

empty :: Random g m a

(<|>) :: Random g m a -> Random g m a -> Random g m a

some :: Random g m a -> Random g m [a]

many :: Random g m a -> Random g m [a]

(Functor m, Monad m, RandomGen g) => MonadPlus (Random g m)

Methods

mzero :: Random g m a

mplus :: Random g m a -> Random g m a -> Random g m a

(Functor m, Monad m, RandomGen g) => Unfolder (Random g m)

Choose randomly.

Methods

choose :: [Random g m a] -> Random g m a

chooseMap :: (a -> Random g m b) -> [a] -> Random g m b

chooseInt :: Int -> Random g m Int

data Arb a

A variant of Test.QuickCheck.Gen, with failure and a count of the number of recursive positions.

Constructors

Arb Int (Gen (Maybe a))

Instances

Functor Arb

Methods

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

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

Applicative Arb

Methods

pure :: a -> Arb a

(<*>) :: Arb (a -> b) -> Arb a -> Arb b

(*>) :: Arb a -> Arb b -> Arb b

(<*) :: Arb a -> Arb b -> Arb a

Alternative Arb

Methods

empty :: Arb a

(<|>) :: Arb a -> Arb a -> Arb a

some :: Arb a -> Arb [a]

many :: Arb a -> Arb [a]

Unfolder Arb

Limit the depth of the generated data structure by dividing the given size by the number of recursive positions.

Methods

choose :: [Arb a] -> Arb a

chooseMap :: (a -> Arb b) -> [a] -> Arb b

chooseInt :: Int -> Arb Int

arbUnit :: Arbitrary a => Arb a

newtype NumConst a x

Variant of Constant that does multiplication of the constants for <*> and addition for <|>.

Constructors

NumConst

Fields

• getNumConst :: a

Instances

Functor (NumConst a)

Methods

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

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

Num a => Applicative (NumConst a)

Methods

pure :: a -> NumConst a a

(<*>) :: NumConst a (a -> b) -> NumConst a a -> NumConst a b

(*>) :: NumConst a a -> NumConst a b -> NumConst a b

(<*) :: NumConst a a -> NumConst a b -> NumConst a a

Num a => Alternative (NumConst a)

Methods

empty :: NumConst a a

(<|>) :: NumConst a a -> NumConst a a -> NumConst a a

some :: NumConst a a -> NumConst a [a]

many :: NumConst a a -> NumConst a [a]

Num a => Unfolder (NumConst a)

Unfolds to a constant numeric value. Useful for counting shapes.

Methods

choose :: [NumConst a a] -> NumConst a a

chooseMap :: (a -> NumConst a b) -> [a] -> NumConst a b

chooseInt :: Int -> NumConst a Int

Eq a => Eq (NumConst a x)

Methods

(==) :: NumConst a x -> NumConst a x -> Bool

(/=) :: NumConst a x -> NumConst a x -> Bool

Show a => Show (NumConst a x)

Methods

showsPrec :: Int -> NumConst a x -> ShowS

show :: NumConst a x -> String

showList :: [NumConst a x] -> ShowS

data Nth a

Constructors

Nth

Fields

• size :: Integer
• getNth :: Integer -> a

Instances

Functor Nth

Methods

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

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

Applicative Nth

Methods

pure :: a -> Nth a

(<*>) :: Nth (a -> b) -> Nth a -> Nth b

(*>) :: Nth a -> Nth b -> Nth b

(<*) :: Nth a -> Nth b -> Nth a

Alternative Nth

Methods

empty :: Nth a

(<|>) :: Nth a -> Nth a -> Nth a

some :: Nth a -> Nth [a]

many :: Nth a -> Nth [a]

Unfolder Nth

Methods

choose :: [Nth a] -> Nth a

chooseMap :: (a -> Nth b) -> [a] -> Nth b

chooseInt :: Int -> Nth Int

UnfolderTransformer

class UnfolderTransformer t where

An UnfolderTransformer changes the way an Unfolder unfolds.

Minimal complete definition

lift

Methods

lift :: Unfolder f => f a -> t f a

Lift a computation from the argument unfolder to the constructed unfolder.

Instances

UnfolderTransformer BFS

Methods

lift :: Unfolder f => f a -> BFS f a

UnfolderTransformer WithRec

Methods

lift :: Unfolder f => f a -> WithRec f a

UnfolderTransformer DualA

Methods

lift :: Unfolder f => f a -> DualA f a

ala :: (UnfolderTransformer t, Unfolder f) => (t f b -> f b) -> (t f a -> t f b) -> f a -> f b

Run an unfolding function with one argument using an UnfolderTransformer, given a way to run the transformer.

ala2 :: (UnfolderTransformer t, Unfolder f) => (t f c -> f c) -> (t f a -> t f b -> t f c) -> f a -> f b -> f c

Run an unfolding function with two arguments using an UnfolderTransformer, given a way to run the transformer.

ala3 :: (UnfolderTransformer t, Unfolder f) => (t f d -> f d) -> (t f a -> t f b -> t f c -> t f d) -> f a -> f b -> f c -> f d

Run an unfolding function with three arguments using an UnfolderTransformer, given a way to run the transformer.

UnfolderTransformer instances

newtype DualA f a

DualA flips the <|> operator from Alternative.

Constructors

DualA

Fields

• getDualA :: f a

Instances

UnfolderTransformer DualA

Methods

lift :: Unfolder f => f a -> DualA f a

Functor f => Functor (DualA f)

Methods

fmap :: (a -> b) -> DualA f a -> DualA f b

(<$) :: a -> DualA f b -> DualA f a

Applicative f => Applicative (DualA f)

Methods

pure :: a -> DualA f a

(<*>) :: DualA f (a -> b) -> DualA f a -> DualA f b

(*>) :: DualA f a -> DualA f b -> DualA f b

(<*) :: DualA f a -> DualA f b -> DualA f a

Alternative f => Alternative (DualA f)

Methods

empty :: DualA f a

(<|>) :: DualA f a -> DualA f a -> DualA f a

some :: DualA f a -> DualA f [a]

many :: DualA f a -> DualA f [a]

Unfolder f => Unfolder (DualA f)

Reverse the list passed to choose.

Methods

choose :: [DualA f a] -> DualA f a

chooseMap :: (a -> DualA f b) -> [a] -> DualA f b

chooseInt :: Int -> DualA f Int

Eq (f a) => Eq (DualA f a)

Methods

(==) :: DualA f a -> DualA f a -> Bool

(/=) :: DualA f a -> DualA f a -> Bool

Show (f a) => Show (DualA f a)

Methods

showsPrec :: Int -> DualA f a -> ShowS

show :: DualA f a -> String

showList :: [DualA f a] -> ShowS

data NT f g

Natural transformations

Constructors

NT

Fields

• getNT :: forall a. f a -> g a

newtype WithRec f a

Constructors

WithRec

Fields

• getWithRec :: ReaderT (Int -> NT f f) f a

Instances

UnfolderTransformer WithRec

Methods

lift :: Unfolder f => f a -> WithRec f a

Functor f => Functor (WithRec f)

Methods

fmap :: (a -> b) -> WithRec f a -> WithRec f b

(<$) :: a -> WithRec f b -> WithRec f a

Applicative f => Applicative (WithRec f)

Methods

pure :: a -> WithRec f a

(<*>) :: WithRec f (a -> b) -> WithRec f a -> WithRec f b

(*>) :: WithRec f a -> WithRec f b -> WithRec f b

(<*) :: WithRec f a -> WithRec f b -> WithRec f a

Alternative f => Alternative (WithRec f)

Methods

empty :: WithRec f a

(<|>) :: WithRec f a -> WithRec f a -> WithRec f a

some :: WithRec f a -> WithRec f [a]

many :: WithRec f a -> WithRec f [a]

Unfolder f => Unfolder (WithRec f)

Applies a certain function depending on the depth at every recursive position.

Methods

choose :: [WithRec f a] -> WithRec f a

chooseMap :: (a -> WithRec f b) -> [a] -> WithRec f b

chooseInt :: Int -> WithRec f Int

withRec :: (Int -> NT f f) -> WithRec f a -> f a

Apply a certain function of type f a -> f a to the result of a choose. The depth is passed as Int, so you can apply a different function at each depth. Because of a forall, the function needs to be wrapped in a NT constructor. See limitDepth for an example how to use this function.

limitDepth :: Unfolder f => Int -> WithRec f a -> f a

Limit the depth of an unfolding.

newtype BFS f x

Return a generator of values of a given depth. Returns Nothing if there are no values of that depth or deeper. The depth is the number of choose calls.

Constructors

BFS

Fields

• getBFS :: (Int, Split) -> Maybe [f x]

Instances

UnfolderTransformer BFS

Methods

lift :: Unfolder f => f a -> BFS f a

Functor f => Functor (BFS f)

Methods

fmap :: (a -> b) -> BFS f a -> BFS f b

(<$) :: a -> BFS f b -> BFS f a

Applicative f => Applicative (BFS f)

Methods

pure :: a -> BFS f a

(<*>) :: BFS f (a -> b) -> BFS f a -> BFS f b

(*>) :: BFS f a -> BFS f b -> BFS f b

(<*) :: BFS f a -> BFS f b -> BFS f a

Applicative f => Alternative (BFS f)

Methods

empty :: BFS f a

(<|>) :: BFS f a -> BFS f a -> BFS f a

some :: BFS f a -> BFS f [a]

many :: BFS f a -> BFS f [a]

Applicative f => Unfolder (BFS f)

Choose between values of a given depth only.

Methods

choose :: [BFS f a] -> BFS f a

chooseMap :: (a -> BFS f b) -> [a] -> BFS f b

chooseInt :: Int -> BFS f Int

type Split = Int -> [(Int, Int)]

bfs :: Unfolder f => BFS f x -> f x

Change the order of unfolding to be breadth-first, by maximum depth of the components.

bfsBySum :: Unfolder f => BFS f x -> f x

Change the order of unfolding to be breadth-first, by the sum of depths of the components.