Monotone.hs

module Data.MediaBus.Basics.Monotone
    ( LocalOrd(..)
    ) where

import           Data.Word
import           Data.Int

-- | Class of numbers that are monotone increasing having only a relative order,
-- that is not necessarily transitive.
--
-- For example, a series of 'Word8' values: @0 64 128 192 0 64 128 ...@ could be
-- interpreted as a monotone series of consecutive increasing values, that wrap
-- around after 255. But note that the 'Ord' instance is not sufficient to
-- express that @0@ `succeeds` @192@, since 'Ord' ensures complete transitivity
-- and therefore @0 < 192@.
class LocalOrd a where
    succeeds :: a -> a -> Bool
    default succeeds :: (Bounded a, Integral a) => a -> a -> Bool
    x `succeeds` y = (x - y) < ((maxBound - minBound) `div` 2)

instance LocalOrd Word8

instance LocalOrd Word16

instance LocalOrd Word32

instance LocalOrd Word64

instance LocalOrd Int8

instance LocalOrd Int16

instance LocalOrd Int32

instance LocalOrd Int64

instance LocalOrd Int