Scanner & Pratt Parser

1. Zero-Allocation Scanner

SmartCal's scanner reads the character stream without creating intermediate object arrays.

Features:

• Detection of 2-character operators (<=, >=, ==, !=, &&, ||) via simple charCodeAt pair comparison.
• Support for strings with spaces ("Hello world").
• Support for extended Unicode range (U+0080 to U+FFFF) to allow international identifiers.

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2. The Pratt Parser (Top-Down Operator Precedence)

Invented by Vaughan Pratt in 1973, the Pratt Parser associates precedence not with grammar rules, but with tokens themselves via two functions:

1. NUD (Null Denotation): What a token does when it appears at the start of an expression (e.g., literal number, identifier, opening parenthesis, unary - sign).
2. LED (Left Denotation): What a token does when it appears between two expressions (e.g., addition +, multiplication *, ternary ?).

Binding Power

Each operator has a left and right binding power (lbp, rbp):

Operator	Binding Power (lbp, rbp)	Associativity
+, -	(50, 51)	Left-associative (lbp < rbp)
*, /, %	(60, 61)	Left-associative
^ (Power)	(71, 70)	Right-associative (lbp > rbp)
? : (Ternary)	(20, 19)	Right-associative

// Core Pratt parsing algorithm
parseExpression(rbp = 0): ASTNode {
  let token = this.scanner.next();
  let left = this.nud(token);

  while (this.getLbp(this.scanner.peek()) > rbp) {
    token = this.scanner.next();
    left = this.led(token, left);
  }

  return left;
}

This elegant mechanism guarantees strictly linear parsing time $O(N)$ over the expression length.