Data.Functor.Free.Internal

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

(forall x. c x => Class' f x) => Algebra f (Free c a)

Defined in Data.Functor.Free.Internal

Methods

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

Monad (Free c)

Defined in Data.Functor.Free.Internal

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

fail :: String -> Free c a

Functor (Free c)

Defined in Data.Functor.Free.Internal

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.Internal

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 (LiftAFree c f x)) => Foldable (Free c)

Defined in Data.Functor.Free.Internal

Methods

fold :: Monoid m => Free c m -> 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 (LiftAFree c f x)) => Traversable (Free c)

Defined in Data.Functor.Free.Internal

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.Internal

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

(forall x. c x :=> Floating x) => 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

(forall x. c x :=> Fractional x) => 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

(forall x. c x :=> Num x) => 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, Show (Signature c (ShowHelper a)), c (ShowHelper a)) => Show (Free c a)

Defined in Data.Functor.Free.Internal

Methods

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

show :: Free c a -> String

showList :: [Free c a] -> ShowS

(forall x. c x :=> Semigroup x) => 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

(forall x. c x :=> Monoid x) => 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

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)

newtype Extract a

Constructors

Extract

Fields

• getExtract :: a

newtype Duplicate f a

Constructors

Duplicate

Fields

• getDuplicate :: f (f a)

class Class f x => Class' f x where

Methods

evaluate' :: AlgebraSignature f => f x -> x

Instances

Class f x => Class' f x

Defined in Data.Functor.Free.Internal

Methods

evaluate' :: f x -> x

newtype LiftAFree c f a

Constructors

LiftAFree

Fields

• getLiftAFree :: f (Free c a)

Instances

(Applicative f, forall x. c x => Class' s x) => Algebra s (LiftAFree c f a)

Defined in Data.Functor.Free.Internal

Methods

algebra :: s (LiftAFree c f a) -> LiftAFree c f a

(Applicative f, forall x. c x :=> Floating x) => Floating (LiftAFree c f a)

Defined in Data.Functor.Free

Methods

pi :: LiftAFree c f a

exp :: LiftAFree c f a -> LiftAFree c f a

log :: LiftAFree c f a -> LiftAFree c f a

sqrt :: LiftAFree c f a -> LiftAFree c f a

(**) :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

logBase :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

sin :: LiftAFree c f a -> LiftAFree c f a

cos :: LiftAFree c f a -> LiftAFree c f a

tan :: LiftAFree c f a -> LiftAFree c f a

asin :: LiftAFree c f a -> LiftAFree c f a

acos :: LiftAFree c f a -> LiftAFree c f a

atan :: LiftAFree c f a -> LiftAFree c f a

sinh :: LiftAFree c f a -> LiftAFree c f a

cosh :: LiftAFree c f a -> LiftAFree c f a

tanh :: LiftAFree c f a -> LiftAFree c f a

asinh :: LiftAFree c f a -> LiftAFree c f a

acosh :: LiftAFree c f a -> LiftAFree c f a

atanh :: LiftAFree c f a -> LiftAFree c f a

log1p :: LiftAFree c f a -> LiftAFree c f a

expm1 :: LiftAFree c f a -> LiftAFree c f a

log1pexp :: LiftAFree c f a -> LiftAFree c f a

log1mexp :: LiftAFree c f a -> LiftAFree c f a

(Applicative f, forall x. c x :=> Fractional x) => Fractional (LiftAFree c f a)

Defined in Data.Functor.Free

Methods

(/) :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

recip :: LiftAFree c f a -> LiftAFree c f a

fromRational :: Rational -> LiftAFree c f a

(Applicative f, forall x. c x :=> Num x) => Num (LiftAFree c f a)

Defined in Data.Functor.Free

Methods

(+) :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

(-) :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

(*) :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

negate :: LiftAFree c f a -> LiftAFree c f a

abs :: LiftAFree c f a -> LiftAFree c f a

signum :: LiftAFree c f a -> LiftAFree c f a

fromInteger :: Integer -> LiftAFree c f a

(Applicative f, forall x. c x :=> Semigroup x) => Semigroup (LiftAFree c f a)

Defined in Data.Functor.Free

Methods

(<>) :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

sconcat :: NonEmpty (LiftAFree c f a) -> LiftAFree c f a

stimes :: Integral b => b -> LiftAFree c f a -> LiftAFree c f a

(Applicative f, forall x. c x :=> Monoid x) => Monoid (LiftAFree c f a)

Defined in Data.Functor.Free

Methods

mempty :: LiftAFree c f a

mappend :: LiftAFree c f a -> LiftAFree c f a -> LiftAFree c f a

mconcat :: [LiftAFree c f a] -> LiftAFree c f a

data ShowHelper a where

Constructors

ShowUnit :: a -> ShowHelper a

ShowRec :: Show (f (ShowHelper a)) => f (ShowHelper a) -> ShowHelper a

Instances

Show (f (ShowHelper a)) => Algebra f (ShowHelper a)

Defined in Data.Functor.Free.Internal

Methods

algebra :: f (ShowHelper a) -> ShowHelper a

Show a => Floating (ShowHelper a)

Defined in Data.Functor.Free

Methods

pi :: ShowHelper a

exp :: ShowHelper a -> ShowHelper a

log :: ShowHelper a -> ShowHelper a

sqrt :: ShowHelper a -> ShowHelper a

(**) :: ShowHelper a -> ShowHelper a -> ShowHelper a

logBase :: ShowHelper a -> ShowHelper a -> ShowHelper a

sin :: ShowHelper a -> ShowHelper a

cos :: ShowHelper a -> ShowHelper a

tan :: ShowHelper a -> ShowHelper a

asin :: ShowHelper a -> ShowHelper a

acos :: ShowHelper a -> ShowHelper a

atan :: ShowHelper a -> ShowHelper a

sinh :: ShowHelper a -> ShowHelper a

cosh :: ShowHelper a -> ShowHelper a

tanh :: ShowHelper a -> ShowHelper a

asinh :: ShowHelper a -> ShowHelper a

acosh :: ShowHelper a -> ShowHelper a

atanh :: ShowHelper a -> ShowHelper a

log1p :: ShowHelper a -> ShowHelper a

expm1 :: ShowHelper a -> ShowHelper a

log1pexp :: ShowHelper a -> ShowHelper a

log1mexp :: ShowHelper a -> ShowHelper a

Show a => Fractional (ShowHelper a)

Defined in Data.Functor.Free

Methods

(/) :: ShowHelper a -> ShowHelper a -> ShowHelper a

recip :: ShowHelper a -> ShowHelper a

fromRational :: Rational -> ShowHelper a

Show a => Num (ShowHelper a)

Defined in Data.Functor.Free

Methods

(+) :: ShowHelper a -> ShowHelper a -> ShowHelper a

(-) :: ShowHelper a -> ShowHelper a -> ShowHelper a

(*) :: ShowHelper a -> ShowHelper a -> ShowHelper a

negate :: ShowHelper a -> ShowHelper a

abs :: ShowHelper a -> ShowHelper a

signum :: ShowHelper a -> ShowHelper a

fromInteger :: Integer -> ShowHelper a

Show a => Show (ShowHelper a)

Defined in Data.Functor.Free.Internal

Methods

showsPrec :: Int -> ShowHelper a -> ShowS

show :: ShowHelper a -> String

showList :: [ShowHelper a] -> ShowS

Show a => Semigroup (ShowHelper a)

Defined in Data.Functor.Free

Methods

(<>) :: ShowHelper a -> ShowHelper a -> ShowHelper a

sconcat :: NonEmpty (ShowHelper a) -> ShowHelper a

stimes :: Integral b => b -> ShowHelper a -> ShowHelper a

Show a => Monoid (ShowHelper a)

Defined in Data.Functor.Free

Methods

mempty :: ShowHelper a

mappend :: ShowHelper a -> ShowHelper a -> ShowHelper a

mconcat :: [ShowHelper a] -> ShowHelper a

class a => b => a :=> b

Instances

a -> b => a :=> b

Defined in Data.Functor.Free.Internal

deriveInstances :: Name -> Q [Dec]

Derive the instances of Free c a for the class c, Show, Foldable and Traversable.

For example:

deriveInstances ''Num