OCaml polymorphic recursion errors

Question

Given the following types:

type _ task =
| Success : 'a -> 'a task
| Fail : 'a -> 'a task
| Binding : (('a task -> unit) -> unit) -> 'a task
| AndThen : ('a -> 'b task) * 'a task -> 'b task
| OnError : ('a -> 'b task) * 'a task -> 'b task

type _ stack =
| NoStack : 'a stack
| AndThenStack : ('a -> 'b task) * 'b stack -> 'a stack
| OnErrorStack : ('a -> 'b task) * 'b stack -> 'a stack

type 'a process = 
{ root: 'a task 
; stack: 'a stack 
}

let rec loop : 'a. 'a process -> unit = fun proc ->
match proc.root with
| Success value -> 
    let rec step = function
    | NoStack -> ()
    | AndThenStack (callback, rest) -> loop {proc with root = callback value; stack = rest }
    | OnErrorStack (_callback, rest) -> step rest  <-- ERROR HERE
    in
    step proc.stack
| Fail value -> 
    let rec step = function
    | NoStack -> ()
    | AndThenStack (_callback, rest) -> step rest
    | OnErrorStack (callback, rest) -> loop {proc with root = callback value; stack = rest }
    in
    step proc.stack
| Binding callback -> callback (fun task -> loop {proc with root = task} )
| AndThen (callback, task) -> loop {root = task; stack = AndThenStack (callback, proc.stack)}
| OnError (callback, task) -> loop {root = task; stack = OnErrorStack (callback, proc.stack)}

I get an error from the compiler:

Error: This expression has type b#1 stack but an expression was expected of type 'a stack The type constructor b#1 would escape its scope

In this line of code:

| Success value -> 
    let rec step = function
    | NoStack -> ()
    | AndThenStack (callback, rest) -> loop {proc with root = callback value; stack = rest }
    | OnErrorStack (_callback, rest) -> step rest  <-- ERROR HERE
    in
    step proc.stack

It's taken a while to get this far without running into an obscure error message that is inevitably corrected by using some helper types, but I can't seem to figure out how to correct this issue with a helper, or if I'm attempting to do something silly with my types.

What is the correct way to eliminate this error?

Answer 1

A second variable needed to be added to the task type definition to express separate success and failure values. Here is the complete solution:

type (_,_) task =
| Success : 'a -> ('a,_) task
| Fail : 'x -> (_,'x) task
| Binding : ((('a,'x) task -> unit) -> unit) -> ('a,'x) task
| AndThen : ('a -> ('b,'x) task) * ('a,'x) task -> ('b,'x) task
| OnError : ('x -> ('a,'y) task) * ('a,'x) task -> ('a,'y) task

type (_,_) stack =
| NoStack : (_,_) stack
| AndThenStack : ('a -> ('b,'x) task) * ('b,'x) stack -> ('a,'x) stack
| OnErrorStack : ('x -> ('a,'y) task) * ('a,'y) stack -> ('a,'x) stack

type ('a,'x) process = 
{ root: ('a,'x) task 
; stack: ('a,'x) stack 
}

let rec loop : type a x. (a, x) process -> unit = fun proc ->
match proc.root with
| Success value -> 
    let rec step : 'x. (a, 'x) stack -> unit = function
    | NoStack -> ()
    | AndThenStack (callback, rest) -> loop {root = callback value; stack = rest }
    | OnErrorStack (_callback, rest) -> step rest
    in
    step proc.stack
| Fail value -> 
    let rec step : 'a. ('a, x) stack -> unit = function
    | NoStack -> ()
    | AndThenStack (_callback, rest) -> step rest
    | OnErrorStack (callback, rest) -> loop {root = callback value; stack = rest }
    in
    step proc.stack
| Binding callback -> callback (fun task -> loop {proc with root = task})
| AndThen (callback, task) -> loop {root = task; stack = AndThenStack (callback, proc.stack)}
| OnError (callback, task) -> loop {root = task; stack = OnErrorStack (callback, proc.stack)}

Answer 2

I think there is something incoherent in these functions. Adding some annotations and removing irrelevant branches gives:

let rec loop (type s) (proc : s process) =
  match proc.root with
  | Success value -> 
      let rec step (type t) (x : t stack) =
        match x with
        | NoStack -> ()
        | AndThenStack (callback, rest) ->
            loop {proc with root = callback value; stack = rest }
                                          (*^^^^^*)
        | OnErrorStack (callback, rest) -> step rest
      in
      step proc.stack
  | _ -> ()

where the "underlined" variable is the subject of an error message:

Error: This expression has type s but an expression was expected of type t

What is supposed to happen if the first pass through step operates on an (OnErrorStack : unit stack), and then the second pass through step operates on an (AndThenStack : int stack)?

In other words, if the argument to loop is something like:

{ root = Success ();
  stack = OnErrorStack ((fun () -> Success 3),
                        AndThenStack ((fun x -> Success (float_of_int x)),
                                      (NoStack : float stack))) }

While (value : unit) will be compatible with the first step, it seems to me that nothing guarantees its compatibility with the second step, which acts rather on a value of the existential type within the OnErrorStack (int in the counter-example).