Intuiting Pratt Parsing

The article 'Intuiting Pratt Parsing' by Louis Baragwanath aims to demystify Pratt parsing, a technique used by compilers to accurately interpret the order of operations in programming code. It starts by acknowledging the common understanding of operator precedence (e.g., multiplication before addition) and poses the challenge of encoding this knowledge for machines, typically through Abstract Syntax Trees (ASTs) where operators sit above their operands.

Key takeaways from the article include:

• The AST as a Structure: An AST inherently encodes the order of evaluation, making it programmatically convenient, but the challenge lies in deriving this structure from linear text.
• Simplifying Precedence: The author simplifies the problem by first considering cases of only increasing or decreasing precedence, which naturally lead to either right-leaning or left-leaning ASTs, respectively.
• Associativity: It clarifies that left-to-right evaluation for equal precedence (left associativity) results in left-leaning trees, while right associativity (like in C assignment) requires a different structure.
• Extending to Mixed Precedence: The core insight arrives when transitioning from increasing to decreasing precedence. The visual explanation shows that when precedence drops, the parser must 'walk back up' the existing right-leaning spine to find the correct insertion point for a new, lower-precedence operator, initiating a left-leaning subtree.
• Pratt Parsing in Pseudocode: The article illustrates this 'walk-back' procedure with pseudocode, showing how a recursive parse() function evolves from handling purely right-leaning trees to accommodating left-leaning structures via a while loop that repeatedly binds operators of suitable precedence.
• Binding Power: It introduces the concept of Left Binding Power (LBP) and Right Binding Power (RBP) to precisely handle operator associativity, where rbp = lbp - 1 for right-associative operators ensures they are consumed deeper in the recursion.