semigroupoids- Semigroupoids: Category sans id

Copyright(C) 2011-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <>
Safe HaskellSafe-Inferred






class Functor f => Alt f where Source


<!> is associative:             (a <!> b) <!> c = a <!> (b <!> c)
<$> left-distributes over <!>:  f <$> (a <!> b) = (f <$> a) <!> (f <$> b)

If extended to an Alternative then <!> should equal <|>.

Ideally, an instance of Alt also satisfies the "left distributon" law of MonadPlus with respect to <.>:

<.> right-distributes over <!>: (a <!> b) <.> c = (a <.> c) <!> (b <.> c)

But Maybe, IO, Either a, ErrorT e m, and STM satisfy the alternative "left catch" law instead:

pure a <!> b = pure a

However, this variation cannot be stated purely in terms of the dependencies of Alt.

When and if MonadPlus is successfully refactored, this class should also be refactored to remove these instances.

The right distributive law should extend in the cases where the a Bind or Monad is provided to yield variations of the right distributive law:

(m <!> n) >>- f = (m >>- f) <!> (m >>- f)
(m <!> n) >>= f = (m >>= f) <!> (m >>= f)

Minimal complete definition



(<!>) :: f a -> f a -> f a infixl 3 Source

<|> without a required empty

some :: Applicative f => f a -> f [a] Source

many :: Applicative f => f a -> f [a] Source


Alt [] 
Alt IO

This instance does not actually satisfy the (<.>) right distributive law It instead satisfies the Left-Catch law

Alt Maybe 
Alt IntMap 
Alt Seq 
Alt Option 
Alt NonEmpty 
Alt (Either a) 
MonadPlus m => Alt (WrappedMonad m) 
Alt f => Alt (IdentityT f) 
Ord k => Alt (Map k) 
Alt f => Alt (Reverse f) 
Alt f => Alt (Backwards f) 
(Bind f, Monad f) => Alt (MaybeT f) 
Apply f => Alt (ListT f) 
Alt f => Alt (Lift f) 
Alternative f => Alt (WrappedApplicative f) 
ArrowPlus a => Alt (WrappedArrow a b) 
(Alt f, Alt g) => Alt (Product f g) 
(Alt f, Functor g) => Alt (Compose f g) 
Alt f => Alt (WriterT w f) 
Alt f => Alt (WriterT w f) 
(Bind f, Monad f) => Alt (ErrorT e f) 
(Bind f, Monad f, Semigroup e) => Alt (ExceptT e f) 
Alt f => Alt (StateT e f) 
Alt f => Alt (StateT e f) 
Alt f => Alt (ReaderT e f) 
Alt f => Alt (Static f a) 
Alt f => Alt (RWST r w s f) 
Alt f => Alt (RWST r w s f)