Introduction Last time we discussed our mission, built a lexer and tree printer to be used throughout our experiments, and introduced the Recursive decent parser. Parsing mathematical expressions involves interpreting their structure, which can be complex due to the presence of operators with different precedence levels and associativity rules. In this article series, we delve into
In the context of Abstract Syntax Trees (ASTs) and parse trees, the terms “higher” and “lower” precedence, as well as tree “depth,” take on a different meaning due to the way parsers traverse the tree structure. In this context, “higher” precedence refers to nodes that are deeper in the tree, further away from the root. When parsers descend into the tree to evaluate expressions or execute algorithms, they typically start at the root and move downwards towards the leaves. Therefore, nodes that are deeper in the tree, or have a higher depth, are processed first, followed by nodes closer to the root. Conversely, nodes closer to the root have lower depth and are processed later in the parsing or evaluation process. This understanding is crucial for parsers and algorithms that rely on tree traversal to correctly interpret and evaluate expressions or perform other operations on tree structures. I have heard these terms used in reverse and for trees in general, this may be correct. I mention this because it can cause confusion, it is worth clarifying these terms when conversing with others.
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