module Pandora.Paradigm.Structure.Ability.Monotonic where

import Pandora.Pattern.Category ((#))
import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (-.#..-))

class Monotonic a e where
	{-# MINIMAL reduce #-}
	reduce :: (a -> r -> r) -> r -> e -> r

	-- | Version of `reduce` which ignores accumulator
	resolve :: (a -> r) -> r -> e -> r
	resolve g = reduce # g -.#..- (!.)

instance Monotonic a a where
	reduce f r x = f x r