# Calculator with Short-Circuit Evaluation — Alternative Solution

Setter idea: optional values carry deferred errors. Codex (GPT-6): complete parsing, safe integer evaluation, and the explicit-tree lazy alternative.

## Explicit syntax tree and lazy evaluation

Reuse the lexical and postfix conversion rules from the [standard solution](solution.en.md). Scan postfix tokens with a stack of node indices. Pop one, two, or three children to construct each operator node. No expression arithmetic occurs during construction.

Starting at the root, simulate recursion with explicit `(node, phase)` frames. Ordinary operators evaluate their operands and apply the safe arithmetic function. Logical operators visit the left subtree first: propagate its error immediately, or use its truth value to return directly or visit the right subtree. A conditional visits its condition, then pushes only the selected branch. Unused branches never enter the evaluation stack.

Store each completed node result separately. Phases resume the correct step after a child returns, without duplicate evaluation or premature conditional selection. Safe error propagation also handles any remaining ordinary-operator visits after an operand has failed.

## Correctness and Complexity

Postfix construction uses the standard parser's grouping. Evaluation frames exactly simulate the recursive semantics, including short-circuit branch selection. Induction over node completion proves each stored result correct and hence the root result correct.

Construction requires $O(n)$ time and space. Evaluation visits only required nodes, so total time remains $O(n)$ and explicit frames use at most $O(n)$ space. The tree requires extra storage but gives a direct lazy execution model that can accommodate expensive pure operations. Both programs share parsing and safe arithmetic; agreement alone is not independent parser verification. Tests additionally use a recursive precedence parser and truly lazy model. Codex (GPT-6) supplied this method and [alternative.cpp](alternative.cpp).

[Statement](statement.en.md) · [Formal test plan](tests/plan.json) · [Generator](tests/generate.py) · [Measurements](../../../docs/benchmark-R32.json)