Please complete the indicated module in OCaml! Thank you!

module type STACK = sig

(** ['a t] is the type of stacks with element type ['a]. *)

type 'a t

(** [empty] is an empty stack. *)

val empty : 'a t

(** [is_empty] tests is an empty stack. *)

val is_empty : 'a t -> bool

(** [push x s] pushes an element [x] on top of

the stack [s] and returns the new stack. *)

val push : 'a -> 'a t -> 'a t

(** [peek s] peeks the top element of the stack [s].

If the stack is empty, [None] is returned. *)

val peek : 'a t -> 'a option

(** [pop s] pops the top element of the stack [s]

and returns the resulting stack. If the stack

was already empty, [None] is returned. *)

val pop : 'a t -> 'a t option

(** [size s] returns the number of elements in [s]. *)

val size : 'a t -> int

end

(** The type of recipes to build a stack. *)

type 'a build =

| Empty

(** [Empty] means calling [empty] to get a stack. *)

| Push of 'a * 'a build

(** [Push (x, b)] means building a stack [s] using [b],

and then calling [push x s] to get a stack. *)

| Pop of 'a build

(** [Pop b] means building a stack [s] using [b],

and then calling [pop s] to get a stack.

If [pop s] returns [None], the building fails

and an exception should be raised. +*)

(** The type of checks on a stack. *)

type 'a check =

| IsEmpty of bool

(** [IsEmpty b] means that calling [is_empty] on the

stack should get the answer [b]. *)

| Peek of ('a -> bool) option

(** [Peek None] means that calling [peek] on the stack

should get [None].

[Peek (Some p)] means that calling [peek] on the stack

should get [Some x] and [p x] should be true. *)

| Pop of unit option

(** [Pop None] means that calling [pop] on the stack

should get [None].

[Pop (Some ())] means that calling [pop] on the stack

should get [Some s] for some stack [s]. *)

| Size of int

(** [Size i] means that calling [size] on the stack

should get the answer [i]. *)

(** A functor to check the correctness

of an implementation of [STACK]. *)

module StackTester (Stack : STACK) :

sig

(** The exception that indicates that the building fails. *)

exception BuildFailure

(** [build b] builds a stack using the recipe [b].

For example, [build Empty] will give the stack

[Stack.empty].

@raise BuildFailure if the building fails

due to [Stack.pop] returning [None]. *)

val build : 'a build -> 'a Stack.t

(** [test s c] tests whether the stack [s] satisfies

the check [c].

For example, [test s (Size 10)] returns [true]

if and only if [Stack.size s] returns [10]. *)

val test : 'a Stack.t -> 'a check -> bool

end

=

struct

(* Complete this module. *)

end