#lang shplait

type Instruction
| left()
| right()
| forward(distance :: Int)


// Template for a program that take an `Instruction`:
#//
fun path_distance(i :: Instruction) :: Int:
  match i
  | left(): ....
  | right(): ....
  | forward(d): ....

fun path_distance(i :: Instruction) :: Int:
  match i
  | left(): 0
  | right(): 0
  | forward(d): d

check: path_distance(left())
       ~is 0
check: path_distance(right())
       ~is 0
check: path_distance(forward(5))
       ~is 5

// A list of Instructions
// (Listof Instruction)
//    [The "#//" below comments out the `define-type` form,
//     since `ListOf` is built-in]
#//
type Listof_Instruction
| empty()
| cons(i :: Instruction, rest :: Listof_Instruction)

// Template for a program that take a `(Listof Instruction)`:
#//
fun program_distance(li :: Listof(Instruction)) :: Int:
  match li
  | []: ....
  | cons(i, is): (path_distance i) .... (program_distance is)

fun program_distance(li :: Listof(Instruction)) :: Int:
  match li
  | []: 0
  | cons(i, is): path_distance(i) + program_distance(is)
                                                      
check: program_distance([])
       ~is 0
check: program_distance(cons(forward(5), (cons(left(),[]))))
       ~is 5
check: program_distance([forward(5), left()])
       ~is 5

fun does_turn(li :: Listof(Instruction)) :: Boolean:
  match li
  | []: #false
  | cons(i, is): is_turn(i) || does_turn(is)

fun is_turn(i :: Instruction) :: Boolean:
  match i
  | left(): #true
  | right(): #true
  | forward(d): #false
          
check: does_turn([])
       ~is #false
check: does_turn([forward(5), left()])
       ~is #true
check: does_turn([forward(3), forward(5)])
       ~is #false

check: is_turn(left())
       ~is #true
check: is_turn(right())
       ~is #true
check: is_turn(forward(4))
       ~is #false