Scope progression

#functional #fsharp #go

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:

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