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この記事の文脈

https://twitter.com/inamiy/status/1489256068995710976

準備

この記事では、補助的な関数として以下のものを用いる。

-- Special case of Control.Arrow.&&&

viercc

#!/usr/bin/env cabal
{- cabal:
build-depends: base, vector
-}
module Main where

import Data.Foldable (foldl')
import Control.Monad (guard)

import qualified Data.Vector.Unboxed as V

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{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleContexts #-}
module Logistic where

import Data.Kind ( Type )
import Data.Functor.Const
import Data.Functor.Contravariant

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Q: Is there an instance Monad ZipList compatible with Applicative ZipList?

A: No.

Proof.

Use these definitions

(<&>) :: Functor f => f a -> (a -> b) -> f b

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{-# LANGUAGE DeriveTraqversable #-}
import Witherable

newtype T a = MkT [a]
  deriving (Show, Eq, Functor, Foldable, Traversable)

instance Filterable T where
  -- ひとつでもNothingがあれば空リスト、
  -- すべてJustならJustを除いた元のリスト
  catMaybes tpa = case sequenceA tpa of

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{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE StandaloneKindSignatures #-}
{-# LANGUAGE GADTs #-}
module CoerceUnder where

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sum''''' :: Num a => [a] -> a
sum''''' xs = snd $ foldr h (\s -> ((), s)) xs 0
  where
    h :: Num a => a -> (a -> b) -> a -> b
    h x k = \s -> k (s + x)

{-

snd $ foldr h (\s -> ((), s)) xs 0

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$ ghc-9.0.1 -fno-code -ddump-to-file -dsuppress-module-prefixes -dsuppress-type-applications -ddump-ds -ddump-splices Main.hs
[1 of 2] Compiling THPatTest        ( THPatTest.hs, /tmp/ghc31722_0/ghc_4.o, /tmp/ghc31722_0/ghc_4.dyn_o )
[2 of 2] Compiling Main             ( Main.hs, /tmp/ghc31722_0/ghc_2.o, /tmp/ghc31722_0/ghc_2.dyn_o )
$ runghc Main.hs
(2,2,2)
(1,2,1)

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module Lib
    ( largestPowersInt ) where

class Eq a => Iterable a where
    zer :: a
    inc :: a -> a
    dec :: a -> a

instance Iterable Int where
    zer = 0

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module Summation where

import Data.List (sortBy)
import Data.Ord (comparing)
import qualified Data.Vector.Unboxed as V

type Query = (Int, Int, Int)

test1 :: [Query]
test1 =