Data.Functor.Free

A free functor is left adjoint to a forgetful functor. In this package the forgetful functor forgets class constraints.

Documentation

newtype Free c a

The free functor for class c.

Free c a is basically an expression tree with operations from class c and variables/placeholders of type a, created with unit. Monadic bind allows you to replace each of these variables with another sub-expression.

Constructors

Free

Fields

• runFree :: forall b. c b => (a -> b) -> b

Instances

Monad (Free c)

Defined in Data.Functor.Free

Methods

(>>=) :: Free c a -> (a -> Free c b) -> Free c b

(>>) :: Free c a -> Free c b -> Free c b

return :: a -> Free c a

Functor (Free c)

Defined in Data.Functor.Free

Methods

fmap :: (a -> b) -> Free c a -> Free c b

(<$) :: a -> Free c b -> Free c a

Applicative (Free c)

Defined in Data.Functor.Free

Methods

pure :: a -> Free c a

(<*>) :: Free c (a -> b) -> Free c a -> Free c b

liftA2 :: (a -> b -> c0) -> Free c a -> Free c b -> Free c c0

(*>) :: Free c a -> Free c b -> Free c b

(<*) :: Free c a -> Free c b -> Free c a

(forall (f :: Type -> Type) x. Applicative f => c (Ap f (Free c x))) => Foldable (Free c)

Defined in Data.Functor.Free

Methods

fold :: Monoid m => Free c m -> m

foldMap :: Monoid m => (a -> m) -> Free c a -> m

foldMap' :: Monoid m => (a -> m) -> Free c a -> m

foldr :: (a -> b -> b) -> b -> Free c a -> b

foldr' :: (a -> b -> b) -> b -> Free c a -> b

foldl :: (b -> a -> b) -> b -> Free c a -> b

foldl' :: (b -> a -> b) -> b -> Free c a -> b

foldr1 :: (a -> a -> a) -> Free c a -> a

foldl1 :: (a -> a -> a) -> Free c a -> a

toList :: Free c a -> [a]

null :: Free c a -> Bool

length :: Free c a -> Int

elem :: Eq a => a -> Free c a -> Bool

maximum :: Ord a => Free c a -> a

minimum :: Ord a => Free c a -> a

sum :: Num a => Free c a -> a

product :: Num a => Free c a -> a

(forall (f :: Type -> Type) x. Applicative f => c (Ap f (Free c x))) => Traversable (Free c)

Defined in Data.Functor.Free

Methods

traverse :: Applicative f => (a -> f b) -> Free c a -> f (Free c b)

sequenceA :: Applicative f => Free c (f a) -> f (Free c a)

mapM :: Monad m => (a -> m b) -> Free c a -> m (Free c b)

sequence :: Monad m => Free c (m a) -> m (Free c a)

(forall x. c (Extract x), forall x. c (Duplicate (Free c) x)) => Comonad (Free c)

Defined in Data.Functor.Free

Methods

extract :: Free c a -> a

duplicate :: Free c a -> Free c (Free c a)

extend :: (Free c a -> b) -> Free c a -> Free c b

c ~=> Floating => Floating (Free c a)

Defined in Data.Functor.Free

Methods

pi :: Free c a

exp :: Free c a -> Free c a

log :: Free c a -> Free c a

sqrt :: Free c a -> Free c a

(**) :: Free c a -> Free c a -> Free c a

logBase :: Free c a -> Free c a -> Free c a

sin :: Free c a -> Free c a

cos :: Free c a -> Free c a

tan :: Free c a -> Free c a

asin :: Free c a -> Free c a

acos :: Free c a -> Free c a

atan :: Free c a -> Free c a

sinh :: Free c a -> Free c a

cosh :: Free c a -> Free c a

tanh :: Free c a -> Free c a

asinh :: Free c a -> Free c a

acosh :: Free c a -> Free c a

atanh :: Free c a -> Free c a

log1p :: Free c a -> Free c a

expm1 :: Free c a -> Free c a

log1pexp :: Free c a -> Free c a

log1mexp :: Free c a -> Free c a

c ~=> Fractional => Fractional (Free c a)

Defined in Data.Functor.Free

Methods

(/) :: Free c a -> Free c a -> Free c a

recip :: Free c a -> Free c a

fromRational :: Rational -> Free c a

c ~=> Num => Num (Free c a)

Defined in Data.Functor.Free

Methods

(+) :: Free c a -> Free c a -> Free c a

(-) :: Free c a -> Free c a -> Free c a

(*) :: Free c a -> Free c a -> Free c a

negate :: Free c a -> Free c a

abs :: Free c a -> Free c a

signum :: Free c a -> Free c a

fromInteger :: Integer -> Free c a

(Show a, c ShowsPrec) => Show (Free c a)

Defined in Data.Functor.Free

Methods

showsPrec :: Int -> Free c a -> ShowS

show :: Free c a -> String

showList :: [Free c a] -> ShowS

c ~=> Semigroup => Semigroup (Free c a)

Defined in Data.Functor.Free

Methods

(<>) :: Free c a -> Free c a -> Free c a

sconcat :: NonEmpty (Free c a) -> Free c a

stimes :: Integral b => b -> Free c a -> Free c a

c ~=> Monoid => Monoid (Free c a)

Defined in Data.Functor.Free

Methods

mempty :: Free c a

mappend :: Free c a -> Free c a -> Free c a

mconcat :: [Free c a] -> Free c a

deriveFreeInstance :: Name -> Q [Dec]

Derive the instance of Free c a for the class c.

For example:

deriveFreeInstance ''Num

deriveInstances :: Name -> Q [Dec]

unit :: a -> Free c a

unit allows you to create Free c values, together with the operations from the class c.

rightAdjunct :: c b => (a -> b) -> Free c a -> b

rightAdjunct is the destructor of Free c values.

counit :: c a => Free c a -> a

counit = rightAdjunct id

leftAdjunct :: (Free c a -> b) -> a -> b

leftAdjunct f = f . unit

transform :: (forall r. c r => (b -> r) -> a -> r) -> Free c a -> Free c b

transform f as = as >>= f unit

transform f . transform g = transform (g . f)

unfold :: (b -> Coproduct c b a) -> b -> Free c a

unfold f = coproduct (unfold f) unit . f

inL and inR are useful here. For example, the following creates the list [1..10] as a Free Monoid:

unfold (b -> if b == 0 then mempty else inL (b - 1) <> inR b) 10

convert :: (c (f a), Applicative f) => Free c a -> f a

convert = rightAdjunct pure

convertClosed :: c r => Free c Void -> r

convertClosed = rightAdjunct absurd

newtype Extract a

Constructors

Extract

Fields

• getExtract :: a

newtype Duplicate f a

Constructors

Duplicate

Fields

• getDuplicate :: f (f a)

Coproducts

type Coproduct c m n = Free c (Either m n)

Products of Monoids are Monoids themselves. But coproducts of Monoids are not. However, the free Monoid applied to the coproduct is a Monoid, and it is the coproduct in the category of Monoids. This is also called the free product, and generalizes to any algebraic class.

coproduct :: c r => (m -> r) -> (n -> r) -> Coproduct c m n -> r

inL :: m -> Coproduct c m n

inR :: n -> Coproduct c m n

type InitialObject c = Free c Void

initial :: c r => InitialObject c -> r

Orphan instances

(Applicative f, Floating a) => Floating (Ap f a)

Methods

pi :: Ap f a

exp :: Ap f a -> Ap f a

log :: Ap f a -> Ap f a

sqrt :: Ap f a -> Ap f a

(**) :: Ap f a -> Ap f a -> Ap f a

logBase :: Ap f a -> Ap f a -> Ap f a

sin :: Ap f a -> Ap f a

cos :: Ap f a -> Ap f a

tan :: Ap f a -> Ap f a

asin :: Ap f a -> Ap f a

acos :: Ap f a -> Ap f a

atan :: Ap f a -> Ap f a

sinh :: Ap f a -> Ap f a

cosh :: Ap f a -> Ap f a

tanh :: Ap f a -> Ap f a

asinh :: Ap f a -> Ap f a

acosh :: Ap f a -> Ap f a

atanh :: Ap f a -> Ap f a

log1p :: Ap f a -> Ap f a

expm1 :: Ap f a -> Ap f a

log1pexp :: Ap f a -> Ap f a

log1mexp :: Ap f a -> Ap f a

(Applicative f, Fractional a) => Fractional (Ap f a)

Methods

(/) :: Ap f a -> Ap f a -> Ap f a

recip :: Ap f a -> Ap f a

fromRational :: Rational -> Ap f a