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class Arrow a =>
ArrowChoice (a :: Type -> Type -> Type)rebase Rebase.Prelude Choice, for arrows that support it. This class underlies the if and case constructs in arrow notation. Instances should satisfy the following laws:
left (arr f) = arr (left f)
left (f >>> g) = left f >>> left g
f >>> arr Left = arr Left >>> left f
left f >>> arr (id +++ g) = arr (id +++ g) >>> left f
left (left f) >>> arr assocsum = arr assocsum >>> left f
assocsum (Left (Left x)) = Left x assocsum (Left (Right y)) = Right (Left y) assocsum (Right z) = Right (Right z)
The other combinators have sensible default definitions, which may be overridden for efficiency.class Arrow a =>
ArrowLoop (a :: Type -> Type -> Type)rebase Rebase.Prelude The loop operator expresses computations in which an output value is fed back as input, although the computation occurs only once. It underlies the rec value recursion construct in arrow notation. loop should satisfy the following laws:
- extension loop (arr f) = arr (\ b -> fst (fix (\ (c,d) -> f (b,d))))
- left tightening loop (first h >>> f) = h >>> loop f
- right tightening loop (f >>> first h) = loop f >>> h
- sliding loop (f >>> arr (id *** k)) = loop (arr (id *** k) >>> f)
- vanishing loop (loop f) = loop (arr unassoc >>> f >>> arr assoc)
- superposing second (loop f) = loop (arr assoc >>> second f >>> arr unassoc)
assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c)
newtype
ArrowMonad (a :: Type -> Type -> Type) brebase Rebase.Prelude The ArrowApply class is equivalent to Monad: any monad gives rise to a Kleisli arrow, and any instance of ArrowApply defines a monad.
ArrowMonad :: a () b -> ArrowMonad (a :: Type -> Type -> Type) brebase Rebase.Prelude No documentation available.
class ArrowZero a =>
ArrowPlus (a :: Type -> Type -> Type)rebase Rebase.Prelude A monoid on arrows.
class Arrow a =>
ArrowZero (a :: Type -> Type -> Type)rebase Rebase.Prelude No documentation available.
class Arrow a =>
ArrowApply (a :: Type -> Type -> Type)base-prelude BasePrelude Some arrows allow application of arrow inputs to other inputs. Instances should satisfy the following laws:
first (arr (\x -> arr (\y -> (x,y)))) >>> app = id
first (arr (g >>>)) >>> app = second g >>> app
first (arr (>>> h)) >>> app = app >>> h
class Arrow a =>
ArrowChoice (a :: Type -> Type -> Type)base-prelude BasePrelude Choice, for arrows that support it. This class underlies the if and case constructs in arrow notation. Instances should satisfy the following laws:
left (arr f) = arr (left f)
left (f >>> g) = left f >>> left g
f >>> arr Left = arr Left >>> left f
left f >>> arr (id +++ g) = arr (id +++ g) >>> left f
left (left f) >>> arr assocsum = arr assocsum >>> left f
assocsum (Left (Left x)) = Left x assocsum (Left (Right y)) = Right (Left y) assocsum (Right z) = Right (Right z)
The other combinators have sensible default definitions, which may be overridden for efficiency.class Arrow a =>
ArrowLoop (a :: Type -> Type -> Type)base-prelude BasePrelude The loop operator expresses computations in which an output value is fed back as input, although the computation occurs only once. It underlies the rec value recursion construct in arrow notation. loop should satisfy the following laws:
- extension loop (arr f) = arr (\ b -> fst (fix (\ (c,d) -> f (b,d))))
- left tightening loop (first h >>> f) = h >>> loop f
- right tightening loop (f >>> first h) = loop f >>> h
- sliding loop (f >>> arr (id *** k)) = loop (arr (id *** k) >>> f)
- vanishing loop (loop f) = loop (arr unassoc >>> f >>> arr assoc)
- superposing second (loop f) = loop (arr assoc >>> second f >>> arr unassoc)
assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c)
newtype
ArrowMonad (a :: Type -> Type -> Type) bbase-prelude BasePrelude The ArrowApply class is equivalent to Monad: any monad gives rise to a Kleisli arrow, and any instance of ArrowApply defines a monad.