-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Step functions, staircase functions or piecewise constant functions
--   
@package step-function
@version 0.1.1.0


-- | Functions for dealing with step functions.
module Data.StepFunction

-- | A Transition, for a certain value on the x axis, there is a new y
--   value.
data Transition x y
Transition :: x -> y -> Bool -> Transition x y

-- | The x value where the transition happens.
x_val :: Transition x y -> x

-- | The new y value.
y_val :: Transition x y -> y

-- | If True, y_val is for all x >= x_val, otherwise for all x >
--   x_val.
left_closed :: Transition x y -> Bool

-- | A StepFunction is implemented as a default value and a sorted list of
--   Transitions.
data StepFunction x y

-- | Smart constructor sorts and simplifies the list of transitions.
mkStepFunction :: (Ord x, Eq y) => y -> [Transition x y] -> StepFunction x y

-- | Get the y value for a given x.
valAt :: Ord x => x -> StepFunction x y -> y

-- | The transitions.
transitions :: StepFunction x y -> [Transition x y]

-- | Merge two step function, such that the following should be true:
--   
--   <pre>
--   valAt x (merge f sf1 sf2) == f (valAt x sf1) (valAt x sf2)
--   </pre>
--   
--   The resulting step function will be simplified, transitions that don't
--   change the y value will be eliminated, and transitions that happen on
--   the same x position will be eliminated.
merge :: (Ord x, Eq c) => (a -> b -> c) -> StepFunction x a -> StepFunction x b -> StepFunction x c
instance (Eq x, Eq y) => Eq (Transition x y)
instance (Show x, Show y) => Show (Transition x y)
instance (Eq x, Eq y) => Eq (StepFunction x y)
instance (Show x, Show y) => Show (StepFunction x y)
instance (Ord x, Eq y) => Ord (Transition x y)
instance Functor (StepFunction x)
instance Functor (Transition x)