Is my rec function tail recursive?

Question

Is this function tail-recursive ?

let rec rec_algo1 step J = 
    if step = dSs then J
    else
        let a = Array.init (Array2D.length1 M) (fun i ->         


        

Answer 1

You asked how we can formally check this so I'll have a stab. We first have to define what it means for a function to be tail-recursive. A recursive function definition of the form

let rec f x_1 ... x_n = e

is tail recursive if all calls of f inside e are tail calls - ie. occur in a tail context. A tail context C is defined inductively as a term with a hole []:

C ::= []
    | e
    | let p = e in C
    | e; C
    | match e with p_1 -> C | ... | p_n -> C
    | if e then C else C

where e is an F# expression, x is a variable and p is a pattern. We ought to expand this to mutually recursive function definitions but I'll leave that as an exercise.

Lets now apply this to your example. The only call to rec_algo1 in the body of the function is in this context:

if step = dSs then J
else
    let a = Array.init (Array2D.length1 M) (fun i -> minby1J i M J)
    let argmin = a|> Array.minBy snd |> fst
    []

And since this is a tail context, the function is tail-recursive. This is how functional programmers eyeball it - scan the body of the definition for recursive calls and then verify that each occurs in a tail context. A more intuitive definition of a tail call is when nothing else is done with the result of the call apart from returning it.