Recursive function basics

In this chapter, I want to introduce you to the basics of recursive functions, leaving more detailed consideration for the more advanced contexts. At this point, I want to show how the F# default treatment of functions as non-recursive differs from a forced one when the function is explicitly declared recursive using the let binding modifier, rec.

Take a look at the following far-fetched snippet (Ch3_8.fsx):

let cutter s = 
  let cut s = 
    printfn "imitator cut: %s" s 
  let cut (s: string) = 
    if s.Length > 0 then 
      printfn "real cut: %s" s 
      cut s.[1..] 
    else 
      printfn "finished cutting" 
  cut s 

The cutter function here provides a non-empty string that's supposed to cut it from the left-hand side, symbol by symbol, until the argument is gone. Within the cutter body, there are two definitions of the cut internal function, of which the second definition apparently shadows the first. Also, it's important that within the second cut definition...