Intuiting Pratt Parsing: A New Perspective on an Elegant Algorithm

A new blog post by Louis Stowasser offers an intuitive explanation of Pratt parsing, one of the most elegant yet underappreciated algorithms in computer science. The post reframes how we think about operator precedence and associativity by visualizing the resulting parse trees.

The Problem

How do you encode that a + b * c + d should be evaluated as a + (b * c) + d? This is the classic problem of operator precedence in parsing. The most common solution is to build an Abstract Syntax Tree (AST) where each operator sits above its operands.

  +
 / \
 +   d
/ \
a   *
    / \
   b   c

A Visual Intuition

Stowasser's key insight is to think about parsing not in terms of grammars and parser generators, but in terms of tree shapes:

• Decreasing precedence produces a left-leaning tree — like a * b + c * d where multiplication binds tighter
• Increasing precedence produces a right-leaning tree — like a + b * c + d where addition binds looser on the left
• Equal precedence with left associativity behaves like decreasing precedence

Why Pratt Parsing?

Traditional approaches use parser generators (ANTLR, yacc) with complex grammar rules. Pratt parsing handles operator precedence with just two simple ideas:

1. Binding power: Each operator has a numeric binding power
2. Null denotation and left denotation: Functions that handle prefix and infix positions

The algorithm is remarkably simple to implement — typically under 50 lines of code — yet handles all standard operator precedence patterns.

Modern Relevance

Pratt parsing is gaining renewed attention in the programming language community:

• Used in Go's standard library for template parsing
• Popular in scripting language implementations for its simplicity
• Increasingly taught as an alternative to recursive descent for expression parsing
• Relevant to anyone building DSLs (domain-specific languages)

The Broader Point

Stowasser's contribution isn't just about Pratt parsing specifically — it's about the value of finding intuitive, visual explanations for complex algorithms. Too often, computer science education jumps to formal notation before building the mental models that make the formalism meaningful.

Source: Louis Stowasser Blog, Hacker News