Why can't KPHP overload functions

Imagine the following code:

$g1 = 0;
$g2 = 0.5;
 
function f($arg) {
  return $arg;
}
 
function setG1() {
  global $g1, $g2;
  $g1 = f($g2);
}
 
function setG2() {
  global $g1, $g2;
  $g2 = f($g1);
}

KPHP needs to infer types for $g1, $g2, $arg and f().

Now the algorithm works this way:

• $g1 :: lca(int, f($g2)); $g2 :: lca(double, f($g1)); $arg :: lca(int, double);
• $arg :: double
• f() :: double
• $g1 :: lca(int, double) = double
• $g2 :: lca(double, double) = double

If we want to automatically generate overloads for f() — so that f($g1) and f($g2) would be probably different functions f??($g1) and f?($g2) — we need to infer these overloads exactly.

• $g1 :: lca(int, f?($g2)); $g2 :: lca(double, f??($g1))
• f?($g2) :: lca(double, f??($g1))
• f??($g1) :: lca(int, f???($g2))
• f???($g2) :: lca(double, lca(int, lca(double, f????($g1)))
• f????($g1) :: lca(int, lca(double, lca(int, lca(double, lca(int, f?????($g2)))))
• f?????($g2) :: lca(double, lca(int, lca(double, lca(int, lca(double, lca(int, lca(double, f??????($g1)))))))
• …

In words: to infer the type of $g1, we need to know what overload of f($g2) to call, for this we need to know the type of $g2, for this we need to know what overload of f($g1) to call, for this we need to know the type of $g1. An infinite loop.

Type inferring assumes, that it is a convergent process. On every iteration, types become more concrete upwards the tree, while any types are changed.

In strictly typed languages we explicitly set types of arguments, returns, etc. — that exact apriori information. Heve we have PHP. Here we don't do it.
That's why type inferring exists, which is based on types generalization (lowest common ancestor — lca) and assuming it to be converged.