Consensus3

Define a function with type:

consensus3 : ('a -> 'b) * ('a -> 'b) * ('a -> 'b) -> 'a -> 'b option

The function takes as input 3 functions with the same type, and it outputs a function with type:

'a -> 'b

By applying consensus3 to a triple of functions (f0,f1,f2), the output function f satisfies the following properties:

f n is undefined if at least one of the 3 input functions is undefined on the input n
f n = Some v if at least 2 out of 3 input functions give v as output on the input n
f n = None otherwise.

For instance:

assert (consensus3 ((fun x -> x), (fun y -> y+4), (fun z -> 5/z)) 1 = Some 5);;
assert (consensus3 ((fun x -> x), (fun y -> y+4), (fun z -> 5/z)) 2 = Some 2);;
assert (consensus3 ((fun x -> x), (fun y -> y+4), (fun z -> 5/z)) 3 = None);;
assert (
  try
    consensus3 ((fun x -> x), (fun y -> y+4), (fun z -> 5/z)) 0
    |> ignore; false
  with _ -> true);;