Re: [Haskell-cafe] Parsec float

Jason Dusek wrote:

2009/05/30 Bartosz Wójcik :

...

...reading RWH I could not memorize what those liftM funtions meant.

The basic one, `liftM`, means `fmap`, though specialized for functors that are monads.

Prelude Control.Monad> :t liftM liftM :: forall a b (m :: * -> *). (Monad m) => (a -> b) -> m a -> m b Prelude Control.Monad> :t fmap fmap :: forall a b (f :: * -> *). (Functor f) => (a -> b) -> f a -> f b

Category theoretically, all the following are (or should be!) equal: fmap, (<$>), liftA, liftM. Type theoretically, they differ in whether they require Functor, Applicative, or Monad. Unfortunately there's a clash between the current types and their CT backing. That is, Monad doesn't require Applicative (or Functor), so people will often use liftM to avoid extra type constraints. Operationally, fmap and (<$>) are potentially more efficient. The liftA and liftM functions re-engineer fmap by using pure/(<*>) or return/ap, thanks to CT. The (<$>) function is just an alias for fmap. But the fmap function is part of a type class and so it may have a specific implementation which is more efficient than the generic one provided by CT. -- Live well, ~wren