module Pandora.Paradigm.Structure.Ability.Monotonic where

import Pandora.Pattern ((.|..))
import Pandora.Pattern.Category ((/))
import Pandora.Paradigm.Primary.Functor.Function ((!))

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 a -> r
g = (a -> r -> r) -> r -> e -> r
forall a e r. Monotonic a e => (a -> r -> r) -> r -> e -> r
reduce ((a -> r -> r) -> r -> e -> r) -> (a -> r -> r) -> r -> e -> r
forall (m :: * -> * -> *). Category m => m ~~> m
/ a -> r
g (a -> r) -> (((->) a :. (->) r) := a) -> a -> r -> r
forall (v :: * -> * -> *) a c d b.
(Category v, Covariant (v a)) =>
v c d -> ((v a :. v b) := c) -> (v a :. v b) := d
.|.. (!)

instance Monotonic a a where
	reduce :: (a -> r -> r) -> r -> a -> r
reduce a -> r -> r
f r
r a
x = a -> r -> r
f a
x r
r