Conversion from bool to int (true -> 1 and false -> 0) - f#

Question

Is there any built-in way in F# to convert from true to 1 and false to 0? This is simple in languages like C, C++ etc.
As a bit of background I am trying to solve an exercise in a textbook (exercise 2.4 in Functional Programming Using F#), which asks for an F# function occFromIth(str,i,ch) that returns the number of occurrences of character ch in positions j in the string str with j >= i.
My solution is
let rec occFromIth (str : string, i, ch) =
if i >= str.Length then 0
else if i < 0 || str.[i] <> ch then occFromIth(str, i+1, ch)
else 1 + occFromIth(str, i+1, ch)
but I don't like the code duplication so I wrote
let boolToInt = function
| true -> 1
| false -> 0
let rec occFromIth (str : string, i, ch) =
if i >= str.Length then 0
else boolToInt (not (i < 0 || str.[i] <> ch)) + occFromIth(str, i+1, ch)
I guess another alternative is to use if... then... else..., in the style of the C/C++ conditional operator
let rec occFromIth (str : string, i, ch) =
if i >= str.Length then 0
else (if (not (i < 0 || str.[i] <> ch)) then 1 else 0) + occFromIth(str, i+1, ch)
or
let rec occFromIth (str : string, i, ch) =
if i >= str.Length then 0
else (if (i < 0 || str.[i] <> ch) then 0 else 1) + occFromIth(str, i+1, ch)
What is the way to do this in F#?

Answer 1

System.Convert.ToInt32(bool) -- I'm not too familiar with F#, but I believe that using a function is the same whether it is built in or not: function(arg0, arg1, ...). So, in this case you'd simply call System.Convert.ToInt32(myBool).

Answer 2

You don't really need the bool to int or int to bool as you can achieve the result as:
let occFromIth (str : string, i, ch) =
str
|> Seq.mapi (fun j c -> (j,c))
|> Seq.filter (fun (j,c) -> j >= i && c = ch)
|> Seq.length

Answer 3

There is difference in making a function or using build in. The CPU instruction of any comparison return a result translated to the bit pattern for 1 and 0. This can be used to make branchless programming, which dependend on the situation are more effecient then branching. Comparison of to values can be found without branching
Int min(int a, int b) {
Int temp = a < b;
Return a*temp + b*(1-temp);
}