November 18, 2019

Monad: Reader

This summary follows the minimum useable principle.

Readings

Monadic Semantics

Several functions depend on the same env information. In other words, they are all readers of the same environment information. Many Readers composed together by >>= or >=> to be a functional unit. The env information is being passed implicitly through the chain of computation.

type ReaderT r m a = ReaderT { runReaderT :: r -> m a }

Function ask introduce the env information into the Reader Monad
local (withReaderT) alter the env information temporarily.
asks convert a function from env to other type to a Reader Monad.
Usually, one ask will related to one Reader Monad that represent a function depends on env information.

ask

ask :: (Monad m) => ReaderT r m r
ask = ReaderT return
    -- return :: r -> m r , return in this case is defined for 'Monad m'

local

local
local
    :: (r -> r)         -- ^ The function to modify the environment.
    -> ReaderT r m a    -- ^ Computation to run in the modified environment.
    -> ReaderT r m a
local = withReaderT

withReaderT

withReaderT
    :: (r' -> r)        -- ^ The function to modify the environment.
    -> ReaderT r m a    -- ^ Computation to run in the modified environment.
    -> ReaderT r' m a
withReaderT f m = ReaderT $ runReaderT m . f

asks

asks
asks :: (Monad m)
    => (r -> a)         -- ^ The selector function to apply to the environment.
    -> ReaderT r m a
asks f = ReaderT (return . f)
{-# INLINE asks #-}

Common usage

use ask to introduce the env into computation (toy models).
use asks, Has type class , MonadReader and ReaderT pattern.
so we could construct functions of type a -> Reader r b or just Reader r b. (compulsory)
local or withReaderT alter environment (optional)
runReader or runreaderT to unwrap functions. (compulsory)
Feed the env information (compulsory)

Intuition:

Pass Env/Context/Configuration information through a chain of operations that depend on same set of configurations.

terms

function chain (composition):
A sequence of functions that compose.
- A :: a -> b
- B :: b -> c
- C :: c -> d
- D :: d-> e
  
  A chain of functions above:
  D . C . B . A :: a -> e

intuitation recap

pass environment information env through all components of a function chain.
every functions in this function chain use this env or part of this env.
Common usage include:

ask :: introducing env into function chain.
local :: temporarily change env value or type.
asks :: swiftly turn a function of type env -> result into this monad.
runreaderT :: Get the functions (chain of operations), so it can be evaluated by feeding in a env.

Examples

0.necessary imports

-- Example One imports
import           Control.Monad.Trans.Reader
import           GHC.Float

-- Example Two imports
import           Control.Monad.IO.Class
import           Control.Monad    -- for the use of kleisli arrow ( >=> )

-- Staging Example imports
import           GHC.Float
import           Data.Store

1.Example one

A chain of Core functions.
Intuition:
- an initial input -> a chain of functions
  which inputs and outputs aligned and represented by a Reader Monad.
- Every operation in this function chain shares the same env informatoin.
  - CoreInputType -> Reader Env ChainOutputType
  - The env being passed down through the core operation chain.

core function 1 :: Int -> Int

a1 :: Int -> Reader Int Int
a1 n = do
    env <- ask           -- get Enviroment information
    return $ n + env

core function 2 :: Int -> Float

a2 :: Int -> Reader Int Float
a2 n = do
    env <- ask          -- get Enviroment information
    let fn = fromIntegral n
    return $ fromIntegral env / fn

core function 3 :: Float -> Double

a3 :: Float -> Reader Int Double
a3 f = do
    env <- ask          -- get Enviroment information
    let fn = fromIntegral env
    return $ float2Double $ fn * f

A Chain of core functions.

Input is a1 of type Int
chain output is a3 of type Double
Only when input and env being provided, the result can be produced.

chainA :: Int -> Reader Int Double
chainA n = do
    t1 <- a1 n          -- core operaiton 1
    t2 <- a2 t1         -- core operaiton 2
    a3 t2               -- core operation 3

alternative: kleisli arrow

chainA' :: Int -> Reader Int Double
chainA' = a1 >=> a2 >=> a3

example output

> let p1 = chainA 10
> runReader p1 $ 2
> 0.3333333432674408

In this example env is 2 and n (the initial input) is 10 so :

t1 = 10 + 2 , t2 = 2 / 12,  t3 = 2* (2 / 12)  =  0.33333333

2.Example Two

A chian of functions depend only on Env information.
Intuition :
- Sequence operation depends only on Environment.

b1 :: (MonadIO m) => ReaderT String m Int
b1 = do
    env <- ask           -- get Environment information
    n   <- liftIO getLine
    let n1 = read env
        n2 = read n
    return $ n1 + n2

b2 :: (MonadIO m) => ReaderT String m Float
b2 = do
    env <- ask          -- get Environment information
    n   <- liftIO getLine
    let n1 = read env
        n2 = read n
    return $ n1 / n2

b3 :: (MonadIO m) => ReaderT String m Double
b3 = do
    env <- ask          -- get Enviroment information
    n   <- liftIO getLine
    let n1 = read env
        n2 = read n
    return $ n1 * n2

function b1, b2, b3 depend on same env of type String

tryB :: ReaderT String IO Float
tryB = do
    t1 <- b1
    t2 <- b2
    t3 <- b3
    return $ fromIntegral t1 + t2 + double2Float t3

runReaderT tryB –> function that take a Env and produce the result of this composition chain.

> :info tryB
>   tryB :: ReaderT String IO Float
> let f = runReaderT tryB
> :info f
>   f :: String -> IO Float 	-- Defined at <interactive>:6:5

> runReaderT :: ReaderT  --> function :: Env -> Result
> let p = runReaderT tryB
> r <- p "10"
> 1
> 2
> 3
>  r
> 46.0

In this example env is 10 and it is of type string. Each function take another input from the commond line.

1+10 + 10/2 + 3*10 = 46

3.Example Three

local :: (r -> r) -> ReaderT r m a -> ReaderT r m a
withReaderT :: (r' -> r) -> ReaderT r m a -> ReaderT r' m a

Intuition :
- local change env to the same type .
- withReaderT change env to another type .
IMPORTANT: The modification only effects temporarily. That is the reason why the name is local.

changeEnv :: String -> Float
changeEnv s = read s + 100

This reader c1 is different from b1 or b2 or b3. Its env information is of type Float.

c1 :: (Monad m) => ReaderT Float m Float
c1 = do
    env <- ask
    return $ env * 5

tryC :: ReaderT String IO Float
tryC = do
    t1  <- b1
    t2  <- b2
    tc1 <- withReaderT changeEnv c1
    t3  <- b3
    return $ fromIntegral t1 + t2 + double2Float t3 + tc1

> let p = runReaderT tryC
> r <- p "10"   -- env is "10"
>1        -- b1 readin 1  
>2        -- b2 readin 2  ; computation c1 
>3        -- b3 readin 3 
> r
-- 346.0

The result is t1+t2+t3+tc1

1+10 + 10/2 + 10*3 + (10+100)*5 = 596

local modify the value of Env temporarily.

withReaderT is more general, it could modify the type of Env. The definition of withReaderT guarantee the computation stays in the original env context.

ReaderT r' m a
local
    :: (r -> r)         -- ^ The function to modify the environment.
    -> ReaderT r m a    -- ^ Computation to run in the modified environment.
    -> ReaderT r m a
local = withReaderT

withReaderT
    :: (r' -> r)        -- ^ The function to modify the environment.
    -> ReaderT r m a    -- ^ Computation to run in the modified environment.
    -> ReaderT r' m a
withReaderT f m = ReaderT $ runReaderT m . f

4.Example Four

asks :: (Monad m) => (r -> a) -> ReaderT r m a 
asks f = ReaderT (return . f)

Intuition:
- convert an simple function into ReaderT.

simpleFunc :: String -> Float
simpleFunc s = 1000 + read s

tryD :: ReaderT String IO Float
tryD = do
    t1  <- b1
    t2  <- b2
    tc1 <- withReaderT changeEnv c1
    t3  <- b3
    td1 <- asks simpleFunc
    return $ fromIntegral t1 + t2 + double2Float t3 + tc1 + td1

> let p = runReaderT tryD 
> r <- p "10"
>1
>2
>3
> r
>1606.0

This example is: t1 + t2 + t3 + tc1 + td1

1+10 + 10/2 +  10*3 + 110 * 5 + (10+1000)= 1606

Notes

Given a function of type :: r -> a, we could use asks to convert it monad ReaderT r m a. However, it is not certainly applicable the other way around.
It could be impossible to factorize a function of type ReaderT r m a as combinations of asks and f.
- The implementation of asks is asks f = ReaderT (return . f)
- In ReaderT r m a, if m is Either or IO, there will be no hope for return . f to produce Computational Context Information of m.
- In this case, m usually related to more than one Type and each Type contains more than one possible value.

5.Complex Example : Staging

Business logic :

Core functions:
- f1 :: a -> b
- f2 :: b -> c
- f3 :: c -> d
- f4 :: d -> e
- f5 :: e -> f
chainF :: a -> f
chainF = f5 . f4 . f3 . f2 . f1
Core Functions depends on Config information. So :
- f1 :: a -> e -> b
- f2 :: b -> e -> c
- f3 :: c -> e -> d
- f4 :: d -> e -> e
- f5 :: e -> e -> f
chainF :: e -> a -> f

We could rewrite f1 to f5 as:
- f1 :: a -> Reader e b
- f2 :: b -> Reader e c
- f3 :: c -> Reader e d
- f4 :: d -> Reader e e
- f5 :: e -> Reader e f
chainF :: a -> Reader e f
```
chainF a = do 
    e <- ask 
    b <- f1 a 
    c <- f1 b 
    d <- f1 c 
    e <- f1 d 
    f <- f1 e 
    return f
```
or

chainF = f1 >=> f2 >=> f3 >=> f4 >=> f5
The computation of each core function could be very complicated and time consuming, so I would like to save the result of every step on the disk. If corresponding config doesn’t change, the next time when chainF is running we can simple deserialize existed result and provide to the following functions.

4. ReaderT implementations:

The Env contains information for a chain of computations, functions for serialization and deserialization. This Env could be initialized from Conifg information.

type Serializer = forall a. (Store a) =>
                            a -> FilePath -> IO ()

type Deserializer = forall a. (Store a) =>
                              FilePath -> IO a

data Env = Env
  { sf1Env :: String
  , sf2Env :: Int
  , sf3Env :: Float
  , sf4Env :: Double
  , sf5Env :: Int
  , serializer :: Serializer
  , deserializer :: Deserializer
  }

StageCore function relies on env information
- type StageCore a = ReaderT Env IO a
Functions that fully or partially depends on env information.

-- sf1
--   :: (Monad m)
--   => ReaderT Env m Int
sf1 :: StageCore Int
sf1 = do
  env <- ask
  return $ length . sf1Env $ env

sf2 :: Int -> StageCore Float
sf2 arg2 = do
  env <- ask
  return $ fromIntegral $ sf2Env env + arg2

sf3 :: Float -> StageCore Double
sf3 arg3 = do
  env <- ask
  return $ float2Double $ sf3Env env + arg3

sf4 :: Double -> StageCore String
sf4 arg4 = do
  env <- ask
  return $ show $ sf4Env env + arg4

sf5 :: StageCore Int
sf5 = do
  env <- ask
  return $ 100 + sf5Env env

coreChain :: () -> ReaderT Env IO Int
coreChain = (\_ -> sf1) >=> sf2 >=> sf3 >=> sf4 >=> (\_ -> sf5)

Now we would like to:
1. Serialize the output of each core functions to the disk.
2. If env information is new , we do the calculation.
3. If previous calculation is new, we do this calculation.
4. otherwise, we deserialize what we saved on the disk.
we need to name each stage/computation type StageName = String
information need for core function a -> b now need to embellished with a Boolean type to indicate the serialization status.
type Core a = (a, Bool)
We use Data.Store to serialize output of each core function
StageName and Env defines this boolen value

checkSerialization :: StageName -> StageCore (Core FilePath)
checkSerialization = undefined

Function staging take:
1. a StageName to identify this computation.
2. a core function of type a -> StageCore b.
3. produce a new function ` Core a -> StageCore (Core b)
  This would be make more sense,
- embellish input/output of the original core-function with the Bool information (a, Bool) -> StageCore (b,Bool) == Core a -> StageCore (Core b)
- this bool information is being used for helping following operation to decide whether to do the computation or just desrialize from dist.
- a StageName being used to identify stage and influence the Boolean information.

staging
  :: (Store b)
  => StageName -> (a -> StageCore b) -> Core a -> StageCore (Core b)
staging stageName coreFunc (coreInput, preStatus) = do
  env <- ask
  let savetoDisk = serializer env
      readDisk = deserializer env
  (serializationPath, done) <- checkSerialization stageName
  if done && preStatus
    then do
      ds <- liftIO $ readDisk serializationPath
      return (ds, True)
    else do
      coreOutput <- coreFunc coreInput
      liftIO $ savetoDisk coreOutput serializationPath
      return (coreOutput, False)

Finally, Staging could be used like this:

stageChain =
  staging "stageFunction_1" (\_ -> sf1) >=>
  staging "stageFunction_2" sf2 >=>
  staging "stageFunction_3" sf3 >=> 
  staging "stageFunction_4" sf4 >=> 
  staging "stageFunction_5" (\_ -> sf5)

6. ReaderT Design Pattern

The famous 23 design pattern is almost perfect except for the suspicious number 23.

This number 23 is not as convincing as the number 42.

With highly abstracted expression ability, the design patterns of Haskell iImplementation would be more like a personal preference or a hobby rather than some task specific best practices.

Readings

Desire

Want to know what is this function about from the type signature.

issues and solutions

Information in the function type signature:
- Obvious: core function is from Double to String
- Blur: The meaning of StageCore. Needs reference of StageCore
- No: which part of env affects this function.

    sf4 :: Double -> StageCore String     
    sf4 arg4 = do                              
      env <- ask                                                      
      return $ show $ sf4Env env + arg4

Use Has type class to constraint only necessary information to be used in env

  type NewStage r a = ReaderT r IO a    

  class HasEnv4 a  where
    getSF4env :: a -> Double

NewStage Double String enabling the use of Double in test. So we don’t need to construct a meaningless env .

  instance HasEnv4 Double where
    getSF4env = id

  instance HasEnv4 Env where
    getSF4env = sf4Env

 sf4N                                  
   :: (HasEnv4 r)                           
   => Double -> NewStage r String                                  
 sf4N arg4 = do                                                   
   env <- ask                                                   
   return $ show $ getSF4env env + arg4

Example

The above Complex example is the main body of ReaderT design pattern.
Initialize Env using configurator.
Each computation in the computation chain only relies on part of Env. Fix this by using Has typeclass.

data Env = Env
  { sf1Env :: String                --being used by sf1 only
  , sf2Env :: Int                   --being used by sf2 only
  , sf3Env :: Float                 --being used by sf3 only
  , sf4Env :: Double                --being used by sf4 only
  , sf5Env :: Int                   --being used by sf5 only
  , serializer :: Serializer
  , deserializer :: Deserializer
  }

1. Define type class

--TypeClass for retrieving sf1Env from Env
class HasEnv1 a  where
  getSF1env :: a -> String

instance HasEnv1 String where
  getSF1env = id

instance HasEnv1 Env where
  getSF1env = sf1Env

-- TypeClass for retrieving sf2Env from Env
class HasEnv2 a  where
  getSF2env :: a -> Int

instance HasEnv2 Int where
  getSF2env = id

instance HasEnv2 Env where
  getSF2env = sf2Env

-- TypeClass for retrieving sf3Env from Env
class HasEnv3 a  where
  getSF3env :: a -> Float

instance HasEnv3 Float where
  getSF3env = id

instance HasEnv3 Env where
  getSF3env = sf3Env


-- TypeClass for retrieving sf4Env from Env
class HasEnv4 a  where
  getSF4env :: a -> Double

instance HasEnv4 Double where
  getSF4env = id

instance HasEnv4 Env where
  getSF4env = sf4Env

-- TypeClass for retrieving sf5Env from Env
class HasEnv5 a  where        
  getSF5env :: a -> Int        

instance HasEnv5 Int where        
  getSF5env = id        

instance HasEnv5 Env where        
  getSF5env = sf5Env

Two instances were declared, with the help of the first function getEnv = id, we could test function depends on this typeclass easily (defined as follow).

2.define corresponding functions

-- | Then function sf1 to sf5 could rewrite as follow        


type NewStage r a = ReaderT r IO a        

sf1N        
  :: (HasEnv1 r)        
  => NewStage r Int        
sf1N = do        
  env <- ask        
  return $length . getSF1env $ env        

sf2N        
  :: (HasEnv2 r)
  => Int -> NewStage r Float
sf2N arg2 = do
  env <- ask
  return $ fromIntegral $ getSF2env env + arg2

sf3N
  :: (HasEnv3 r)
  => Float -> NewStage r Double
sf3N arg3 = do
  env <- ask
  return $ float2Double $ getSF3env env + arg3

sf4N
  :: (HasEnv4 r)
  => Double -> NewStage r String
sf4N arg4 = do
  env <- ask
  return $ show $ getSF4env env + arg4
sf5N
  :: (HasEnv5 r)
  => NewStage r Int
sf5N = do
  env <- ask
  return $ 100 + getSF5env env

In this case:

function associate with meaningful type signatures
It can be test very easily.
The type of the core computation could stay the same as before, but we updated the participant component with more flexibility.

3. new computation chain

Type signature stays the same as before

NewStage Env Int = StageCore Int = ReaderT Env IO Int

newCoreChain :: () -> NewStage Env Int
newCoreChain = (\_ -> sf1N) >=> sf2N >=> sf3N >=> sf4N >=> (\_ -> sf5N)
-- newCoreChain = (\_ -> sf1) >=> sf2 >=> sf3 >=> sf4 >=> (\_ -> sf5)

4. Refactor using Lens

TODO