Hundred Doors Exercise

As another exercise, I am going to be translating the 100 doors rosetta code example written in Standard ML.

datatype Door = Closed | Opened

fun toggle Closed = Opened

| toggle Opened = Closed

fun pass (steps, doors) = List.mapi (fn (k, door) => if (k+1) mod steps = 0 then toggle door else door) doors

(* [1..n] *)

fun runs n = List.tabulate (n, fn k => k+1)

fun run n =

let

val initialdoors = List.tabulate (n, fn _ => Closed)

val runs = runs n

in

foldl pass initialdoors runs

end

fun opened_doors n = List.mapPartiali (fn (k, Closed) => NONE | (k, Opened) => SOME (k+1)) (run n)

Door ?= Closed{} | Opened{}

toggle .= {Closed{}} => Opened()

toggle[+] .= {Opened{}} => Closed()

skip .= {Door? d} => d

pass .= {steps, doors} => (

[1::doors[@]] +> doors -> {k, door} =>

k %% steps @@ toggle door ~@ skip door

)

run .= {n} => (

initialDoors .= [1::n] -> Closed()

runs .= [1::n]

runs >- pass -> initialDoors

)

openedDoors .= {n} => (r .= run n; [1::r[@]] +> r) $> {k, Opened{}} => k