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 choose to act on recursive positions of the data structure, or simply to provide a faster implementation than asum.

Methods

choose :: [f x] -> f x

Choose one of the values from the list.

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.

Unfolder Maybe

Always choose the first item.

Unfolder Arb

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

MonadPlus m => Unfolder (WrappedMonad m)

Derived instance.

Unfolder f => Unfolder (Reverse f)

Derived instance.

Unfolder f => Unfolder (Backwards f)

Derived instance.

Unfolder f => Unfolder (Lift f)

Derived instance.

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

Derived instance.

Applicative f => Unfolder (ListT f)

Derived instance.

Num a => Unfolder (NumConst a)

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

Applicative f => Unfolder (BFS f)

Choose between values of a given depth only.

Unfolder f => Unfolder (WithRec f)

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

Unfolder f => Unfolder (DualA f)

Reverse the list passed to choose.

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

Derived instance.

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

Derived instance.

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

Derived instance.

Unfolder m => Unfolder (ReaderT r m)

Derived instance.

(Functor m, Monad m, Error e) => Unfolder (ErrorT e m)

Derived instance.

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

Derived instance.

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

Derived instance.

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

Choose randomly.

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

Derived instance.

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

If an unfolder is monadic, choose 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)

Functor m => Functor (Random g m)

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

(Monad m, Functor m) => Applicative (Random g m)

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

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

Choose randomly.

data Arb a

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

Constructors

Arb Int (StdGen -> Int -> Maybe a)

Instances

Functor Arb

Applicative Arb

Alternative Arb

Unfolder Arb

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

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)

Num a => Applicative (NumConst a)

Num a => Alternative (NumConst a)

Num a => Unfolder (NumConst a)

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

Eq a => Eq (NumConst a x)

Show a => Show (NumConst a x)

UnfolderTransformer

class UnfolderTransformer t where

An UnfolderTransformer changes the way an Unfolder unfolds.

Methods

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

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

Instances

UnfolderTransformer BFS

UnfolderTransformer WithRec

UnfolderTransformer DualA

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

Functor f => Functor (DualA f)

Applicative f => Applicative (DualA f)

Alternative f => Alternative (DualA f)

Unfolder f => Unfolder (DualA f)

Reverse the list passed to choose.

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

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

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

Functor f => Functor (WithRec f)

Applicative f => Applicative (WithRec f)

Alternative f => Alternative (WithRec f)

Unfolder f => Unfolder (WithRec f)

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

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

Functor f => Functor (BFS f)

Applicative f => Applicative (BFS f)

Applicative f => Alternative (BFS f)

Applicative f => Unfolder (BFS f)

Choose between values of a given depth only.

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.