InputWithAddAction.elm

module InputWithAddAction (Model, Action, view, update, init) where

import Html exposing (div, input, button, text)
import Html.Events exposing (onClick, on, targetValue)
import Html.Attributes exposing (value)
import Signal


type Action = UpdatedValue String


type alias Model = String


init : Model
init = ""


update : Action -> Model -> Model
update action model =
  case action of
    UpdatedValue str
      -> str

{- the first parameter here is the callback -}
view addAction address model =
  div []
      [ input
        [ value model
        , on "input" targetValue (Signal.message address << UpdatedValue)
        ]
        []
      , button
        [ on "click" targetValue (addAction model) ]
        [ text "Add to list" ]
      ]

Main.elm

module Main where

import Html exposing (div, text, ul, li, Html)
import InputWithAddAction


type Action = Add String | Delete String | InputAction InputWithAddAction.Action | NoOp

--- MODEL ---

type alias Model =
  { stuffList : List String
  , inputModel : InputWithAddAction.Model
  }

-- initial model
init : Model
init =
  { stuffList = ["initial", "stuff"]
  , inputModel = InputWithAddAction.init
  }

-- mailbox of actions
actions = Signal.mailbox NoOp


update : Action -> Model -> Model
update action model =
  case action of
    Add str
      -> { model | stuffList = str :: model.stuffList } 
    Delete str
      -> { model | stuffList = (List.filter ((/=) str) model.stuffList) }
    InputAction act
      -> { model | inputModel = (InputWithAddAction.update act model.inputModel) } 
    NoOp -> model


view : Model -> Html
view model =
  div []
      [ (InputWithAddAction.view
                           {- here we construct a function that the child view can use to
                              send actions to parent -}
                             (\textToAdd _ -> Signal.message actions.address (Add textToAdd))
                             (Signal.forwardTo actions.address InputAction)
                             model.inputModel)
      , ul []
        (List.map (\m -> li [] [text m]) model.stuffList)
      ]


signals = Signal.foldp update init actions.signal

main : Signal Html
main = Signal.map view signals

The callback is interesting. I'd remove the ignored second parameter and invoke it as (always (addAction model)).