License	BSD-style (see the file LICENSE)
Maintainer	sjoerd@w3future.com
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Functor.Free

Contents

Coproducts
Internal
Orphan instances

Description

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

Synopsis

newtype Free c a = Free {
- runFree :: forall b. c b => (a -> b) -> b
}
deriveInstances :: Name -> Q [Dec]
unit :: a -> Free c a
rightAdjunct :: c b => (a -> b) -> Free c a -> b
counit :: c a => Free c a -> a
leftAdjunct :: (Free c a -> b) -> a -> b
transform :: (forall r. c r => (b -> r) -> a -> r) -> Free c a -> Free c b
unfold :: (b -> Coproduct c b a) -> b -> Free c a
convert :: (c (f a), Applicative f) => Free c a -> f a
convertClosed :: c r => Free c Void -> r
newtype Extract a = Extract {
- getExtract :: a
}
newtype Duplicate f a = Duplicate {
- getDuplicate :: f (f a)
}
type Coproduct c m n = Free c (Either m n)
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
data ShowHelper a where
- ShowUnit :: a -> ShowHelper a
- ShowRec :: Show (f (ShowHelper a)) => f (ShowHelper a) -> ShowHelper a

Documentation

newtype Free c a Source #

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) Source #
Instance details Defined in Data.Functor.Free.Internal Methods algebra :: f (Free c a) -> Free c a #
Monad (Free c) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 #

deriveInstances :: Name -> Q [Dec] Source #

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

For example:

deriveInstances ''Num

unit :: a -> Free c a Source #

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 Source #

rightAdjunct is the destructor of Free c values.

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

counit = rightAdjunct id

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

leftAdjunct f = f . unit

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

transform f as = as >>= f unit

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

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

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 Source #

convert = rightAdjunct pure

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

convertClosed = rightAdjunct absurd

newtype Extract a Source #

Constructors

Extract
Fields getExtract :: a

newtype Duplicate f a Source #

Constructors

Duplicate
Fields getDuplicate :: f (f a)

Coproducts

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

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 Source #

inL :: m -> Coproduct c m n Source #

inR :: n -> Coproduct c m n Source #

type InitialObject c = Free c Void Source #

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

Internal

data ShowHelper a where Source #

Constructors

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

Instances

Show (f (ShowHelper a)) => Algebra f (ShowHelper a) Source #
Instance details Defined in Data.Functor.Free.Internal Methods algebra :: f (ShowHelper a) -> ShowHelper a #
Show a => Floating (ShowHelper a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Functor.Free Methods mempty :: ShowHelper a # mappend :: ShowHelper a -> ShowHelper a -> ShowHelper a # mconcat :: [ShowHelper a] -> ShowHelper a #

Orphan instances

Show a => Floating (ShowHelper a) Source #
Instance details 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) Source #
Instance details Methods (/) :: ShowHelper a -> ShowHelper a -> ShowHelper a # recip :: ShowHelper a -> ShowHelper a # fromRational :: Rational -> ShowHelper a #
Show a => Num (ShowHelper a) Source #
Instance details 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 => Semigroup (ShowHelper a) Source #
Instance details 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) Source #
Instance details Methods mempty :: ShowHelper a # mappend :: ShowHelper a -> ShowHelper a -> ShowHelper a # mconcat :: [ShowHelper a] -> ShowHelper a #
(forall x. c x :=> Floating x) => Floating (Free c a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 #
(forall x. c x :=> Semigroup x) => Semigroup (Free c a) Source #
Instance details 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) Source #
Instance details Methods mempty :: Free c a # mappend :: Free c a -> Free c a -> Free c a # mconcat :: [Free c a] -> Free c a #
(Applicative f, forall x. c x :=> Floating x) => Floating (LiftAFree c f a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 #