--
-- Monadic fixpoints.
--
--- For more details, see Levent Erkok's thesis,
--- /Value Recursion in Monadic Computations/, 2002.
+-- For a detailed discussion, see Levent Erkok's thesis,
+-- /Value Recursion in Monadic Computations/, Oregon Graduate Institute, 2002.
--
-----------------------------------------------------------------------------
import Prelude
import System.IO
--- | @'fix' f@ is the least fixed point of the function @f@.
+-- | @'fix' f@ is the least fixed point of the function @f@,
+-- i.e. the least defined @x@ such that @f x = x@.
fix :: (a -> a) -> a
fix f = let x = f x in x
--- | Monads having fixed points with a \`knot-tying\' semantics.
--- Instances of 'MonadFix' should satisfy the laws
+-- | Monads having fixed points with a \'knot-tying\' semantics.
+-- Instances of 'MonadFix' should satisfy the following laws:
--
--- [purity]
+-- [/purity/]
-- @'mfix' ('return' . h) = 'return' ('fix' h)@
--
--- [left shrinking (or tightening)]
--- @'mfix' (\x -> a >>= \y -> f x y) = \y -> 'mfix' (\x -> f x y)@
+-- [/left shrinking/ (or /tightening/)]
+-- @'mfix' (\\x -> a >>= \\y -> f x y) = \\y -> 'mfix' (\\x -> f x y)@
--
--- [sliding]
+-- [/sliding/]
-- @'mfix' ('Control.Monad.liftM' h . f) = 'Control.Monad.liftM' h ('mfix' (f . h))@,
-- for strict @h@.
--
--- [nesting]
--- @'mfix' (\x -> 'mfix' (\y -> f x y)) = 'mfix' (\x -> f x x)@
+-- [/nesting/]
+-- @'mfix' (\\x -> 'mfix' (\\y -> f x y)) = 'mfix' (\\x -> f x x)@
--
-- This class is used in the translation of the recursive @do@ notation
-- supported by GHC and Hugs.
class (Monad m) => MonadFix m where
-- | The fixed point of a monadic computation.
- -- @'mfix' f@ executes the action 'f' only once, with the eventual
+ -- @'mfix' f@ executes the action @f@ only once, with the eventual
-- output fed back as the input. Hence @f@ should not be strict,
-- for then @'mfix' f@ would diverge.
mfix :: (a -> m a) -> m a