If you run `foo | bar`, what starts running first? Does foo start and push its output into bar, or does bar start first and pull its input from foo? Does foo ru

If you run `foo | bar`, what starts running first? Does foo start and push its output into bar, or does bar start first and pull its input from foo? Does foo run to completion then bar to completion, do they take it in turns, or run at the same time on different processors? Does it matter?