/// m08 stream: an event stream as a pure automaton (a Mealy machine).
/// A step feeds one event and returns the (possibly empty) list of outputs it produced and the stream to use for
/// the next event. Nothing is mutated, so a stream value can be run any number of times with the same results.
module Snake.Stream

/// Something that happens to the program: time passing (ms since start) or a key going down or up, and from
/// Module 13 a mouse click at `(x, y)` in canvas pixels. Every stream ignores the kinds of event it does not use.
type Event =
    | Time of int64
    | KeyDown of string
    | KeyUp of string
    | Click of int * int

type Stream<'a> = Stream of (Event -> 'a list * Stream<'a>)

/// Feed one event to `s`: the outputs it produced and the stream for the next event.
let step (e: Event) (s: Stream<'a>) : 'a list * Stream<'a> = failwith "TODO m08"

/// Emits the `key` of every KeyDown event; ignores everything else.
/// (The stub is wrapped in `Stream` so the TODO only fires when the stream is stepped.)
let keyDowns: Stream<string> = Stream(fun _ -> failwith "TODO m08")

/// Emits the `key` of every KeyUp event; ignores everything else.
let keyUps: Stream<string> = Stream(fun _ -> failwith "TODO m08")

/// (m13) Emits the position `(x, y)` of every Click event; ignores everything else.
/// Given: nothing to write here. It is the third source, built exactly like your `keyDowns`.
let clicks: Stream<int * int> =
    let rec source () =
        Stream(fun e ->
            match e with
            | Click(x, y) -> [ (x, y) ], source ()
            | _ -> [], source ())

    source ()

/// On `Time t`, emits every multiple `k*ms` with `last < k*ms <= t`, ascending, where `last` starts at 0
/// and becomes `t` afterwards. A big time jump can emit several values. Ignores key events.
/// Hint: write a private helper that carries `last`.
let interval (ms: int64) : Stream<int64> = failwith "TODO m08"

/// Apply `f` to every output.
let map (f: 'a -> 'b) (s: Stream<'a>) : Stream<'b> = failwith "TODO m08"

/// Keep only the outputs for which `p` is true.
let filter (p: 'a -> bool) (s: Stream<'a>) : Stream<'a> = failwith "TODO m08"

/// Apply `f` to every output; `Some b` emits `b`, `None` is dropped (like `List.choose`).
let choose (f: 'a -> 'b option) (s: Stream<'a>) : Stream<'b> = failwith "TODO m08"

/// Both streams step on every event; the outputs of `a` come before the outputs of `b`.
let merge (a: Stream<'a>) (b: Stream<'a>) : Stream<'a> = failwith "TODO m08"

/// Fold the outputs into an accumulator, starting from `z`; emits each new accumulator (not `z` itself).
let scan (f: 'b -> 'a -> 'b) (z: 'b) (s: Stream<'a>) : Stream<'b> = failwith "TODO m08"

/// Emit `v` once, before the outputs of the first step; later steps are unaffected.
/// Note: streams only act when an event arrives, so if no event ever arrives, `v` is never emitted.
let startWith (v: 'a) (s: Stream<'a>) : Stream<'a> = failwith "TODO m08"

/// (m10) Limit how far one Time event can move the clock that `s` sees, so a long silence (a background tab)
/// does not turn into hundreds of beats at once.
/// `s` gets a clock of its own, starting at 0. On `Time t` that clock advances by `t - last`, but by at most `maxGap`
/// and never by less than 0 (time does not run backwards), where `last` is the `t` of the previous Time event
/// (0 at the start). `s` is then stepped with `Time clock`. Key and click events are passed to `s` unchanged.
/// Hint: a private helper that carries `last` and `clock`, like the one for `interval`.
let clampTime (maxGap: int64) (s: Stream<'a>) : Stream<'a> = failwith "TODO m10"

/// Feed all events through the stream and collect every output, in order. A pure fold.
let run (events: Event list) (s: Stream<'a>) : 'a list = failwith "TODO m08"