Implementation of mutually recursive is_odd and is_even, splitting the definition across modules using OCaml 5.0 effect handlers

effectful_split_mutual_recursion.ml

module Base = struct
  type _ Effect.t +=
  | IsOdd: int -> bool Effect.t
  | IsEven: int -> bool Effect.t
end

module Odd = struct
  let is_odd n =
    if n=0 then false
    else Effect.perform (Base.IsEven (n-1))
end

module Even = struct
  let is_even n =
    if n=0 then true
    else Effect.perform (Base.IsOdd (n-1))
end

module M = struct
  module D = Effect.Deep
  let rec handler : 'a. 'a D.effect_handler =
  {
    D.effc = fun (type b) (eff : b Effect.t) ->
      match eff with
      | Base.IsEven n -> Some (fun (k: (b,_) D.continuation) ->
          D.continue k @@ D.try_with Even.is_even n handler)
      | Base.IsOdd n -> Some (fun (k: (b,_) D.continuation) ->
          D.continue k @@ D.try_with Odd.is_odd n handler)
      | _ -> None
  }
  let is_odd n = D.try_with Odd.is_odd n handler
  let is_even n = D.try_with Even.is_even n handler
end

let () = print_endline @@ string_of_bool @@ M.is_odd 72