Product() of empty slice should be 1 (not 0).

[your-diary]

PR #566 introduced Product() but I believe its return value for an empty slice is incorrect: it currently returns 0 but it should be 1.

Operations such as Sum() and Product() are so-called fold operations with the initial value mathematically called identity element. Normally, the identity element of product operation is 1, so Product(<empty slice>) should return 1 (not 0).

Supporting evidence:

• Empty product - Wikipedia and Fold (higher-order function) - Wikipedia say the value of empty product is 1.

• Rust's Iterator::product() returns 1 for an empty slice.

  fn main() {
      println!("{}", Vec::<usize>::new().into_iter().product::<usize>()); //=> 1
  }

• Haskell's product returns 1 for an empty list.

  module Main where
  
  main :: IO ()
  main = do
      print $ product ([] :: [Int]) -- 1

[samber]

I agree. Thanks for the feedback.

I'm going to fix that.