reader.elm

module Reader exposing
  ( return
  , ask
  , runReader
  , local
  , fmap
  , chain
  )

type Reader r a = Reader (r -> a)

id x = x

constant a = \_ -> a

return a = Reader (constant a)

ask = Reader id

runReader e reader =
  case reader of
    Reader r -> r(e)

local f reader = 
  Reader (\c -> runReader f(c) reader)

fmap f reader =
  Reader (\c -> f(runReader c reader))
    
chain f reader =
  Reader (\c -> runReader c (f(runReader c reader)))

-- fun to derive
map f reader =
  chain (\a -> pointed (f(a))) reader