map a list of functions to a single value

directions.hs

-- import Control.Monad (ap)
type Pos = (Int, Int)
type Direction = Pos -> Pos

direction :: Pos -> [Direction] -> [Pos]
direction p [] = []
direction p (x:xs) = x p : direction p xs
-- another way
-- direction p ds = ap ds [p] 


north (x,y) = (x-1,y)
south (x,y) = (x+1,y)
east (x,y) = (x,y+1)
west (x,y) = (x,y-1)
northeast (x,y) = (x-1,y+1)
southeast (x,y) = (x+1,y+1)
northwest (x,y) = (x-1,y-1)
southwest (x,y) = (x+1,y-1)

directions :: [Direction]
directions = [north, south, east, west, northeast, northwest, southeast, southwest]

-- application
-- direction (1,1) directions
-- [(0,1),(2,1),(1,2),(1,0),(0,2),(0,0),(2,2),(2,0)]

directions.scala

/*
The following can't be used in the REPL so do this:

> scalac directions.scala
> scala -cp directions
scala> import directions._
scala> directions (1,1)
res1: List[(Int, Int)] = List((0,1), (0,2), (1,2), (2,2), (2,1), (2,0), (1,0), (0,0))
*/

package object directions { //allows defining some type aliases
  type Pos = (Int, Int)
  type Direction = (Int,Int) => (Int,Int)
  
  //different roads to rome
  val north : Direction = (x,y) => (x-1,y) 
  val northeast  = (x:Int,y:Int) => (x-1,y+1)
  
  //choose one of the roads and minimize the pain 
  val east : Direction = (x,y) => (x,y+1)
  val southeast : Direction = (x,y) => (x+1, y+1)
  val south : Direction = (x,y) => (x+1,y)
  val southwest : Direction = (x,y) => (x+1,y-1)
  val west : Direction = (x,y)=>(x,y-1)
  val northwest : Direction = (x,y)=>(x-1,y-1)


  val alldirections = List(north.tupled, northeast.tupled, east.tupled, southeast.tupled, south.tupled, southwest.tupled, west.tupled, northwest.tupled) 
  //or alternative list creation 
  //val directions = north :: northeast :: east ...... :: Nil 

  def directions(p: Pos) = for(d <- alldirections) yield d(p)
  //you say even more compact
  def directionsTwo(p: Pos) = alldirections map (_(p))
}