Scope progression

In imperative programming, we usually have code that looks the following way:

func addOneToSlice(xs []int) []int {
  rs := make([]int, len(xs))
  for i, value := range xs {
    rs[i] = value + 1
  }
  return rs
}

However, notice the following about the for loop:

• Each iteration has a specific purpose, which is to add one to the current element.
• However, each iteration has no constraint on which element it can operate.
• Operating with xs[i+2] and rs[i+3] wouldn't fundamentally alter the structure of the code we have, while making the end result incorrect.

Compare how the same task would be done in F#:

let rec addOneToList =
  function
  | [] -> []
  | x :: xs -> x + 1 :: addOneToList xs

Now consider the following:

• We have a list as a function argument.
• A list in functional languages is a linked list.
• The efficient and standard operations on linked lists are:
  • Separating the head x from its tail xs
  • Doing something to the head x
  • Comparing the list passed as a parameter with the empty list []

Given these restrictions, adding 1 to any element y not at the head of the list would significantly alter the structure of our function.

Now compare how the computation progresses in both styles:

• In the functional style, we create a new scope with new values, which involves making a recursive call in the example above.
• In the imperative style, we mutate an existing value without changing the scope.

In functional style, marrying both scope with computational progress has the following consequences:

• We avoid mutation.
• The execution flow is explicit.
• The structure we are dealing with becomes clear.