Control.Compose

Contents

• Value transformers
• Specialized semantic editor combinators
• Contravariant functors
• Unary/unary composition
• Type composition
  • Unary/binary
  • (->)/unary
• Monoid constructors
• Flip a binary constructor's type arguments
• Type application
• Identity
• Constructor pairing
  • Unary
• Binary
• Arrow between two constructor applications
• Augment other modules

Description

Synopsis

• type Unop a = a -> a
• type Binop a = a -> a -> a
• result :: Category cat => (b `cat` b') -> (a `cat` b) -> a `cat` b'
• argument :: Category cat => (a' `cat` a) -> (a `cat` b) -> a' `cat` b
• (~>) :: Category cat => (a' `cat` a) -> (b `cat` b') -> (a `cat` b) -> a' `cat` b'
• (~>*) :: (Functor p, Functor q) => (a' -> a) -> (b -> b') -> (p a -> q b) -> p a' -> q b'
• (<~) :: Category cat => (b `cat` b') -> (a' `cat` a) -> (a `cat` b) -> a' `cat` b'
• (*<~) :: (Functor p, Functor q) => (b -> b') -> (a' -> a) -> (p a -> q b) -> p a' -> q b'
• class ContraFunctor h where
  • contraFmap :: (a -> b) -> h b -> h a
• bicomap :: ContraFunctor f => (a :<->: b) -> f a :<->: f b
• newtype (g :. f) a = O (g (f a))
• type O = (:.)
• unO :: (g :. f) a -> g (f a)
• biO :: g (f a) :<->: (g :. f) a
• convO :: Functor g => (b :<->: g c) -> (c :<->: f a) -> b :<->: (g :. f) a
• coconvO :: ContraFunctor g => (b :<->: g c) -> (c :<->: f a) -> b :<->: (g :. f) a
• inO :: (g (f a) -> g' (f' a')) -> (g :. f) a -> (g' :. f') a'
• inO2 :: (g (f a) -> g' (f' a') -> g'' (f'' a'')) -> (g :. f) a -> (g' :. f') a' -> (g'' :. f'') a''
• inO3 :: (g (f a) -> g' (f' a') -> g'' (f'' a'') -> g''' (f''' a''')) -> (g :. f) a -> (g' :. f') a' -> (g'' :. f'') a'' -> (g''' :. f''') a'''
• oPure :: Applicative g => f a -> (g :. f) a
• oFmap :: Functor g' => (f a -> f' a') -> (g' :. f) a -> (g' :. f') a'
• oLiftA2 :: Applicative g'' => (f a -> f' a' -> f'' a'') -> (g'' :. f) a -> (g'' :. f') a' -> (g'' :. f'') a''
• oLiftA3 :: Applicative g''' => (f a -> f' a' -> f'' a'' -> f''' a''') -> (g''' :. f) a -> (g''' :. f') a' -> (g''' :. f'') a'' -> (g''' :. f''') a'''
• fmapFF :: (Functor g, Functor f) => (a -> b) -> (g :. f) a -> (g :. f) b
• fmapCC :: (ContraFunctor g, ContraFunctor f) => (a -> b) -> (g :. f) a -> (g :. f) b
• contraFmapFC :: (Functor g, ContraFunctor f) => (b -> a) -> (g :. f) a -> (g :. f) b
• contraFmapCF :: (ContraFunctor g, Functor f) => (b -> a) -> (g :. f) a -> (g :. f) b
• class DistribM m n where
  • distribM :: n (m a) -> m (n a)
• joinDistribM :: (Monad m, Monad n, DistribM m n) => (m :. n) ((m :. n) a) -> (m :. n) a
• bindDistribM :: (Functor m, Functor n, Monad m, Monad n, DistribM m n) => (m :. n) a -> (a -> (m :. n) b) -> (m :. n) b
• returnDistribM :: (Monad m, Monad n) => a -> (m :. n) a
• joinMMT :: (Monad m, Monad n, Traversable n, Applicative m) => m (n (m (n a))) -> m (n a)
• joinComposeT :: (Monad m, Monad n, Traversable n, Applicative m) => (m :. n) ((m :. n) a) -> (m :. n) a
• newtype OO f j a b = OO {
  • unOO :: f (a `j` b)
  }
• newtype FunA h a b = FunA {
  • unFunA :: h a -> h b
  }
• inFunA :: ((h a -> h b) -> h' a' -> h' b') -> FunA h a b -> FunA h' a' b'
• inFunA2 :: ((h a -> h b) -> (h' a' -> h' b') -> h'' a'' -> h'' b'') -> FunA h a b -> FunA h' a' b' -> FunA h'' a'' b''
• class FunAble h where
  • arrFun :: (a -> b) -> h a -> h b
  • firstFun :: (h a -> h a') -> h (a, b) -> h (a', b)
  • secondFun :: (h b -> h b') -> h (a, b) -> h (a, b')
  • (***%) :: (h a -> h b) -> (h a' -> h b') -> h (a, a') -> h (b, b')
  • (&&&%) :: (h a -> h b) -> (h a -> h b') -> h a -> h (b, b')
• class Monoid_f m where
  • mempty_f :: forall a. m a
  • mappend_f :: forall a. m a -> m a -> m a
• newtype Flip j b a = Flip {
  • unFlip :: a `j` b
  }
• biFlip :: (a `j` b) :<->: Flip j b a
• inFlip :: ((a `j` b) -> a' `k` b') -> Flip j b a -> Flip k b' a'
• inFlip2 :: ((a `j` b) -> (a' `k` b') -> a'' `l` b'') -> Flip j b a -> Flip k b' a' -> Flip l b'' a''
• inFlip3 :: ((a `j` b) -> (a' `k` b') -> (a'' `l` b'') -> a''' `m` b''') -> Flip j b a -> Flip k b' a' -> Flip l b'' a'' -> Flip m b''' a'''
• type OI = Flip (->) (IO ())
• class ToOI sink where
  • toOI :: sink b -> OI b
• newtype f :$ a = App {
  • unApp :: f a
  }
• type App = (:$)
• biApp :: f a :<->: App f a
• inApp :: (f a -> f' a') -> App f a -> App f' a'
• inApp2 :: (f a -> f' a' -> f'' a'') -> App f a -> App f' a' -> App f'' a''
• newtype Id a = Id a
• unId :: Id a -> a
• biId :: a :<->: Id a
• inId :: (a -> b) -> Id a -> Id b
• inId2 :: (a -> b -> c) -> Id a -> Id b -> Id c
• newtype (f :*: g) a = Prod {
  • unProd :: (f a, g a)
  }
• (*:*) :: f a -> g a -> (f :*: g) a
• biProd :: (f a, g a) :<->: (f :*: g) a
• convProd :: (b :<->: f a) -> (c :<->: g a) -> (b, c) :<->: (f :*: g) a
• (***#) :: (a -> b -> c) -> (a' -> b' -> c') -> (a, a') -> (b, b') -> (c, c')
• ($*) :: (a -> b, a' -> b') -> (a, a') -> (b, b')
• inProd :: ((f a, g a) -> (f' a', g' a')) -> (f :*: g) a -> (f' :*: g') a'
• inProd2 :: ((f a, g a) -> (f' a', g' a') -> (f'' a'', g'' a'')) -> (f :*: g) a -> (f' :*: g') a' -> (f'' :*: g'') a''
• inProd3 :: ((f a, g a) -> (f' a', g' a') -> (f'' a'', g'' a'') -> (f''' a''', g''' a''')) -> (f :*: g) a -> (f' :*: g') a' -> (f'' :*: g'') a'' -> (f''' :*: g''') a'''
• newtype (f ::*:: g) a b = Prodd {
  • unProdd :: (f a b, g a b)
  }
• (*::*) :: f a b -> g a b -> (f ::*:: g) a b
• inProdd :: ((f a b, g a b) -> (f' a' b', g' a' b')) -> (f ::*:: g) a b -> (f' ::*:: g') a' b'
• inProdd2 :: ((f a b, g a b) -> (f' a' b', g' a' b') -> (f'' a'' b'', g'' a'' b'')) -> (f ::*:: g) a b -> (f' ::*:: g') a' b' -> (f'' ::*:: g'') a'' b''
• newtype Arrw j f g a = Arrw {
  • unArrw :: f a `j` g a
  }
• type (:->:) = Arrw (->)
• biFun :: (f a -> g a) :<->: (f :->: g) a
• convFun :: (b :<->: f a) -> (c :<->: g a) -> (b -> c) :<->: (f :->: g) a
• inArrw :: ((f a `j` g a) -> f' a' `j` g' a') -> Arrw j f g a -> Arrw j f' g' a'
• inArrw2 :: ((f a `j` g a) -> (f' a' `j` g' a') -> f'' a'' `j` g'' a'') -> Arrw j f g a -> Arrw j f' g' a' -> Arrw j f'' g'' a''
• inArrw3 :: ((f a `j` g a) -> (f' a' `j` g' a') -> (f'' a'' `j` g'' a'') -> f''' a''' `j` g''' a''') -> Arrw j f g a -> Arrw j f' g' a' -> Arrw j f'' g'' a'' -> Arrw j f''' g''' a'''
• biConst :: a :<->: Const a b
• inConst :: (a -> b) -> Const a u -> Const b v
• inConst2 :: (a -> b -> c) -> Const a u -> Const b v -> Const c w
• inConst3 :: (a -> b -> c -> d) -> Const a u -> Const b v -> Const c w -> Const d x
• biEndo :: (a -> a) :<->: Endo a
• inEndo :: (Unop a -> Unop a') -> Endo a -> Endo a'

Value transformers

Specialized semantic editor combinators

Contravariant functors

Unary/unary composition

    -- standard Monoid instance for Applicative applied to Monoid
    instance (Applicative (g :. f), Monoid a) => Monoid ((g :. f) a) where
      { mempty = pure mempty; mappend = liftA2 mappend }
    -- Especially handy when g is a Monoid_f.
    instance Monoid (g (f a)) => Monoid ((g :. f) a) where
      { mempty = O mempty; mappend = inO2 mappend }

    instance (Applicative g, Monoid_f f) => Monoid_f (g :. f) where
      { mempty_f = O (pure mempty_f); mappend_f = inO2 (liftA2 mappend_f) }
    instance Monoid_f g => Monoid_f (g :. f) where
      { mempty_f = O mempty_f; mappend_f = inO2 mappend_f }

    instance (      Functor g,       Functor f) => Functor (g :. f) where fmap = fmapFF
    instance (ContraFunctor g, ContraFunctor f) => Functor (g :. f) where fmap = fmapCC

    instance (      Functor g, ContraFunctor f) => ContraFunctor (g :. f) where contraFmap = contraFmapFC
    instance (ContraFunctor g,       Functor f) => ContraFunctor (g :. f) where contraFmap = contraFmapCF

Type composition

Unary/binary

(->)/unary

Monoid constructors

   instance Monoid_f f where { mempty_f = mempty ; mappend_f = mappend }

Flip a binary constructor's type arguments

Type application

   instance (Applicative f, Monoid a) => Monoid (f a) where
     mempty  = pure mempty
     mappend = liftA2 mappend

Identity

Constructor pairing

Unary

Binary

Arrow between two constructor applications

Augment other modules