Per JDK-8042285, the JLS rules for functional interface comparison during most-specific testing failed to account for generic function types. This can be addressed in the same way as overriding: ensuring the two signatures have equivalent type parameters (same number, equivalent bounds), and then alpha-renaming from one to the other. (See JDK-8042285 comments for details.)

javac does nothing with any type parameters in the signatures, and should be updated.

interface F1 { <X> Object apply(X arg); }
interface F2 { <Y> String apply(Y arg); }
interface F3 { <X> Object apply(Object arg); }
interface F4 { String apply(Object arg); }

static void m1(F1 p) { System.out.println("F1"); }
static void m1(F2 f) { System.out.println("F2"); }
static void m2(F3 p) { System.out.println("F3"); }
static void m2(F4 f) { System.out.println("F4"); }

static String foo(Object in) { return "abc"; }

static void test(boolean cond) {
  m1(ThisTestClass::foo); // expected: ok; actual: error
  m2(ThisTestClass::foo); // expected: error; actual: ok
}