Exploring the Reader functor

Readerfunc.hs

-- Reader / unReader syntax 

newtype Reader e a = Reader { unReader :: e -> a }

Prelude> :t Reader
Reader :: (e -> a) -> Reader e a             --  Reader and unReader are ...

Prelude> :t unReader
unReader :: Reader e a -> (e -> a)           --  inverse to each other


Prelude> :{
Prelude| instance Functor (Reader e) where
Prelude|   fmap f g = Reader (f . unReader g)
Prelude| :}

Prelude> plusone = \x -> x+1
Prelude> plusone 1
2

Prelude> timestwo = \x -> x * 2
Prelude> timestwo 1
2

Prelude> rdplusone = Reader plusone
Prelude> :t rdplusone
rdplusone :: Num a => Reader a a

Prelude> rdcompose = fmap timestwo rdplusone
Prelude> :t rdcompose
rdcompose :: Num b => Reader b b

Prelude> unReader rdplusone 1
2
Prelude> unReader rdcompose 1
4

-- Different syntax

newtype Reader e a = Reader (e -> a)

Prelude> :{
Prelude| instance Functor (Reader e) where
Prelude|    fmap f (Reader g) = Reader (f . g)         --  this syntax 'silently'  "unboxes g"  
Prelude| :}

Prelude> rdplusone = Reader plusone
Prelude> :t rdplusone
rdplusone :: Num a => Reader a a

Prelude> rdcompose = fmap timestwo rdplusone
Prelude> :t rdcompose
rdcompose :: Num b => Reader b b

Prelude> Reader plus = rdplusone
Prelude> plus 1
2
Prelude> Reader comp = rdcompose
Prelude> comp 1
4

ReaderScript.hs

-- Reader / unReader syntax 

newtype Reader e a = Reader { unReader :: e -> a }

:t Reader

:t unReader


:{
instance Functor (Reader e) where
   fmap f g = Reader (f . unReader g)
:}


plusone = \x -> x+1
plusone 1

timestwo = \x -> x * 2
timestwo 1

rdplusone = Reader plusone
:t rdplusone

rdcompose = fmap timestwo rdplusone
:t rdcompose

unReader rdplusone 1
unReader rdcompose 1

-- Different syntax

newtype Reader e a = Reader (e -> a)

:{
instance Functor (Reader e) where
   fmap f (Reader g) = Reader (f . g)
:}

rdplusone = Reader plusone
:t rdplusone

rdcompose = fmap timestwo rdplusone
:t rdcompose


Reader plus = rdplusone
plus 1

Reader comp = rdcompose
comp 1