Explanation of the associativity of nested conditional operators

I do know that conditional operators have right associativity, but can't understand how the flow of condition1 , condition2 , expression1 , expression2 , expression3 are all happening one after another. Or how the evaluation and flows are changing when we assume that associativity is left to right.

(condition1) ? (expression1) : ((condition2) ? (expression2) : (expression3)) ;

I asked Gemini and Copilot for an explanation, and they keep repeating the same thing: that condition1 is the rightmost expression, but couldn't understand how. Or how and why condition1 is the first one to get evaluated, irrespective of right or left associativity.

(I'll assume you're referring to the conditional operator in the C family of programming languages. Tag your question with a specific language if you want to focus on that language.)

Case 1: Base case

Let's start with the simplest case, a single conditional expression:

condition ? expression1 : expression2

To evaluate this expression, follow these steps:

1. Evaluate condition.
2. If the result of Step 1 is true (or "truthy", depending on the language), then ignore expression2 and evaluate expression1.
3. If the result of Step 1 is false (or "falsy", depending on the language), then ignore expression1 and evaluate expression2.
4. Return the result of Step 2 (the value of expression1) or Step 3 (the value of expression2), whichever applies.

Notice that the order of evaluation goes from left to right: condition is evaluated first, followed by either expression1 or expression2.

Case 2: condition is a conditional expression

If the condition in condition ? expression1 : expression2 is itself a conditional expression, then you get the following overall expression:

(subcondition ? subexpression1 : subexpression2) ? expression1 : expression2

To evaluate this expression, follow the same steps as in the base case but replace condition with subcondition ? subexpression1 : subexpression2. In Step 1, you'll recurse:

1. Evaluate subcondition ? subexpression1 : subexpression2. To do this, follow the same steps as in the base case:
   1. Evaluate subcondition.
   2. If the result of Step 1.1 is true, then ignore subexpression2 and evaluate subexpression1.
   3. If the result of Step 1.1 is false, then ignore subexpression1 and evaluate subexpression2.
   4. Return the result of Step 1.2 (the value of subexpression1) or Step 1.3 (the value of subexpression2), whichever applies.
2. If the result of Step 1 is true, then ignore expression2 and evaluate expression1.
3. If the result of Step 1 is false, then ignore expression1 and evaluate expression2.
4. Return the result of Step 2 (the value of expression1) or Step 3 (the value of expression2), whichever applies.

Notice that the order of evaluation goes from left to right: subcondition is evaluated first, followed by either subexpression1 or subexpression2, followed by either expression1 or expression2.

Case 3: expression2 is a conditional expression

If the expression2 in condition ? expression1 : expression2 is itself a conditional expression, then you get the following overall expression:

condition ? expression1 : (subcondition ? subexpression1 : subexpression2)

To evaluate this expression, follow the same steps as in the base case but replace expression2 with subcondition ? subexpression1 : subexpression2. In Step 3, you'll recurse:

1. Evaluate condition.
2. If the result of Step 1 is true, then ignore subcondition ? subexpression1 : subexpression2 and evaluate expression1.
3. If the result of Step 1 is false, then ignore expression1 and evaluate subcondition ? subexpression1 : subexpression2. To do this, follow the same steps as in the base case:
   1. Evaluate subcondition.
   2. If the result of Step 3.1 is true, then ignore subexpression2 and evaluate subexpression1.
   3. If the result of Step 3.1 is false, then ignore subexpression1 and evaluate subexpression2.
   4. Return the result of Step 3.2 (the value of subexpression1) or Step 3.3 (the value of subexpression2), whichever applies.
4. Return the result of Step 2 (the value of expression1) or Step 3 (the value of subcondition ? subexpression1 : subexpression2), whichever applies.

Notice that the order of evaluation goes from left to right: condition is evaluated first, followed by either expression1 or subcondition, followed by (in the subcondition case only) either subexpression1 or subexpression2.

Left versus right associativity

Now let's look at your original expression, but omitting all parentheses:

condition1 ? expression1 : condition2 ? expression2 : expression3

This could potentially be interpreted in two different ways:

1. Left associative: (condition1 ? expression1 : condition2) ? expression2 : expression3
   • This is Case 2 above.
2. Right associative: condition1 ? expression1 : (condition2 ? expression2 : expression3)
   • This is Case 3 above.

An important thing to understand is that associativity and order of evaluation are two completely different concepts. For the conditional operator, left or right associativity simply determines whether you're in Case 2 or Case 3. But in both cases, the order of evaluation goes from left to right, with condition1 evaluated first.