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. 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.