创建一个Reader和Maybe Monad的组合（Applicative Functor）

Question

What I would like to do is make an Applicative Functor out of the Reader monad that does something like this:

data MyData = Int Int

get2Sum :: Reader [Int] Int
get2Sum = do
    myData <- ask
    let fst2 = take 2 myData
    case length fst2 of
        2 -> return $ sum fst2
        _ -> return 0

myDataFromApplicative = MyData <$> get2Sum <*> get2Sum

main = print $ runReader myDataFromApplicative [1,2]

However, if run something like

runReader myDataFromApplicative [1]

Instead of giving me MyData 0 0

I want it to give me Error

I was playing around with creating my own Reader Monad to accomplish this, but couldn't quite figure it out.

What I imagine is something like this (obviously this is just an outline

data SuccessReader r a = Interm {runSuccessReader :: r -> SuccessReader a} | Success a | Error
throwError :: SuccessReader ()


get2Sum :: Reader [Int] Int
get2Sum = do
    myData <- ask
    let fst2 = take 2 myData
    case length fst2 of
        2 -> return $ sum fst2
        _ -> throwError

myDataFromApplicative = MyData <$> get2Sum <*> get2Sum

main = do
    print $ runSuccessReader myDataFromApplicative [1,2]
    print $ runSuccessReader myDataFromApplicative [1]

which would output

Success MyData 3 3
Error

Answer 1

You don't need to write your own monad, as this is exactly the problem that monad transformers and monad stacks solve. Since you want a combination of a Reader and Maybe , you can use the ReaderT transformer with the Maybe monad. Eg

get2Sum :: ReaderT [Int] Maybe Int
get2Sum = do
    myData <- ask
    let fst2 = take 2 myData
    case length fst2 of
        2 -> return $ sum fst2
        _ -> lift Nothing

The type of get2Sum means that we have the outer monad Reader [Int] which contains the inner monad Maybe . In the implementation of get2Sum , lift is used to run operations in the inner monad (in this case, simply signalling error with Nothing ). Now when you run (note the T in runReaderT )

main = do
    print $ runReaderT myDataFromApplicative [1,2]
    print $ runReaderT myDataFromApplicative [1]

you get

Just (MyData 3 3)
Nothing

You could also hide the monad stack inside a custom newtype

{-# LANGUAGE GeneralizedNewtypeDeriving #-}

import Control.Applicative
import Control.Monad.Reader

data MyData = MyData Int Int deriving Show

newtype MyMonad a = MyMonad (ReaderT [Int] Maybe a)
    deriving (Functor, Applicative, Monad, MonadReader [Int])

runMyMonad :: MyMonad a -> [Int] -> Maybe a
runMyMonad (MyMonad m) = runReaderT m

myError :: MyMonad a
myError = MyMonad $ lift Nothing

get2Sum :: MyMonad Int
get2Sum = do
    myData <- ask
    let fst2 = take 2 myData
    case length fst2 of
        2 -> return $ sum fst2
        _ -> myError

myDataFromApplicative = MyData <$> get2Sum <*> get2Sum

main = do
    print $ runMyMonad myDataFromApplicative [1,2]
    print $ runMyMonad myDataFromApplicative [1]