Nested Conditional blocks may be incorrectly lifted

[swernli]

Describe the bug

When a conditional includes nested conditionals that modify variables defined outside of the outer conditional scope, the outer conditional may incorrectly be lifted into a generated callable by the ConditionallyControlled rewrite step. See discussion with concrete examples in comments here #767 (comment).

To Reproduce

The easiest way to reproduce this is to use ClassicallyControlledSupportTests.qs from the qsharp-runtime repo. Add the following operation to the file:

    operation MutableWithNesting() : Unit {
        mutable x = 0;
        if (x == 0) {
            if (x < 1) {
                set x = 1;
            }
        }
        Message($"{x}");
    }

And then recompile the repo. The compilation will succeed and produce generated C# files in the obj/qsharp/src folder. Investigate ClassicallyControlledSupportTests.g.cs, and observe that the outer if-statement is lifted into a callabe that is passed the x variable as a read-only argument even though the generated body performs an update of that variable. The C# will compile, but the behavior at runtime will be wrong, as the variable x will have the value zero after execution instead of the expected value of 1.

Expected behavior

Both the inner if-statement and the outer one should be recognized as not valid for lifting, so no lifted callables should be generated.

[bettinaheim]

@ScottCarda-MS Could you please look into this bug?

[bettinaheim]

@ScottCarda-MS The chases to double check/fix are the following:

1. the case given in the description above is purely classical and should not be lifted
2. the following test case that is quantum, should behave correctly:

    operation MutableWithNesting(cond: Bool) : Unit {

        use q = Qubit();
        H(q);
        if (cond) {
            if (M(q) == Zero) {
                mutable x = 0;
                set x = 1;
            }
        }
        if (M(q) == Zero) {
            mutable x = 0;
            if (x < 1) {
                set x = 1;
            }
        }
        if (M(q) == Zero) {
            mutable x = 0;
            if (x < 1) {
                if (x < 2) {
                    set x = 1;
                }
            }
        }
        if (cond) {
            if (M(q) == Zero) {
                mutable x = 0;
                if (x < 1) {
                    if (x < 2) {
                        set x = 1;
                    }
                }
            }
        }
    }