Keep only rules that replace integers with other integers

Question

Let's say I have a list of replacement rules:

List1 = {2 -> 3, b -> 5.5, 6.57 -> 2, 3 -> 4.5, 1 -> -1, 0.03 -> 0.5, 9 -> a}

The desired output is {2 -> 3, 1 -> -1}.

I have tried the following, to no avail:

Cases[List1, _Integer -> _Integer]

Cases[List1, IntegerQ[#[[1]]] && IntegerQ[#[[2]]] &]

Cases[List1, Rule[Integer_, Integer_]]

How can I obtain the desired output?

Answer 1

You can name the pattern:

Cases[List1, r : (_Integer -> _Integer)]

{2 -> 3, 1 -> -1}

You can also wrap the pattern with PatternSequence

Cases[List1, PatternSequence[_Integer -> _Integer]]

{2 -> 3, 1 -> -1}

This also works:

Cases[List1, _[__Integer]]

{2 -> 3, 1 -> -1}

Answer 2

Use HoldPattern:

 Cases[List1, HoldPattern[_Integer -> _Integer]]

{2 -> 3, 1 -> -1}

Answer 3

You could use Verbatim

Cases[List1, Verbatim[Rule][_Integer, _Integer]]

{2 -> 3, 1 -> -1}