{- Positions Function
   CSci 450/503, Fall 2016
   H. Conrad Cunningham
   2016-11-26: original version
   2016-11-27: revised to use composition
-}

import Html exposing (..)

-- Function zip is a typical function (e.g., in Haskell) that does not
-- seem to be defined in the current Elm library.  zip takes two lists and
-- returns the corresponding list of pairs. 

zip = List.map2 (,)

-- Function secondis takes a value x and a pair t and returns True if
-- and only if the second component of t is x.
-- 11-27: REPLACED secondis with (((==) x) << Tuple.second). This is
-- the compositon of the one-argument function Tuple.second and ((==)
-- x), which partially applies the equality function (==) to its left
-- operand x.

secondis : b -> (a,b) -> Bool
secondis x t = x == Tuple.second t 

-- Function positions takes a list xs and a value x and returns the
-- list of indexes at which x occurs in xs. This functions uses the
-- important higher order library functions map and filter.  (I
-- converted this from a Haskell comprehension as I was learning Elm.
-- There may be better ways of implementing this. One approach would
-- be to use a let expression to define the complext parts of the
-- expression into smaller steps.

positions : List a -> a -> List Int
positions xs x =
    List.map
       Tuple.first
       (List.filter 
          (((==) x) << Tuple.second) -- REPLACED: (secondis x)
          (zip (List.range 1 (List.length xs)) xs))


-- Function position takes a list xs and a value x and returns x's
-- index in xs.  It takes the head from the list returned by
-- positions. This value is a Maybe; by using withDefault, it converts
-- the returned Maybe value to 0.

position : List a -> a -> Int 
position xs x = 
   Maybe.withDefault 0 (List.head (positions xs x))

-- Simple Display Functions

newline = br [] []

displayLines : List String -> List (Html msg)
displayLines ss = 
   case ss of
      []      -> []
      x :: xs -> text x :: newline :: displayLines xs

display : List String -> Html msg
display ls = p [] (displayLines ls)

-- Some testing

names = ["Adam","Eve","Cain","Abel","Seth", "Adam"]

pos1 = positions names "Adam"
pos2 = positions names "Elijah"
pos3 = position names "Cain"

main =
  display 
     [ "Begin!"
     , "names == [Adam, Eve, Cain, Abel, Seth, Adam]"
     , "positions names Adam   == " ++ toString pos1
     , "positions names Elijah == " ++ toString pos2
     , "position  names Cain   == " ++ toString pos3
     , "End!"
     ]