Lesson 12 · Comparison operators - Build a Spreadsheet Engine

Comparison operators

Formulas compare values too, and comparisons bind more loosely than arithmetic so the sides are computed first. Today you add the comparison operators at the lowest precedence level, which IF will later depend on.

The goal

Parse the comparison operators at a precedence below arithmetic.

Start here - the target

TO DO

Scenario: Comparisons parse below arithmetic

Givena formula that compares two arithmetic expressions

Whenit is parsed

Thenparse('=1>0').String() is '(1 > 0)' and parse('=3<=4').String() is '(3 <= 4)'

Andparse('=1+2>3').String() is '((1 + 2) > 3)', showing the addition binds tighter than the comparison

Background

Spreadsheet formulas do not just compute numbers, they ask questions: is A1 greater than zero? The six comparison operators - >, <, >=, <=, = (equal), and <> (not equal) - slot straight into the precedence machinery you already have. The only decision is where they sit, and the answer is below arithmetic: they get the lowest binding power.

That ordering is what makes 1+2>3 mean “is the sum greater than three” rather than “is 1 plus the comparison”. With comparison at power 10 and + at 20, the parser folds the addition into a subtree first, then makes it the left side of the comparison - printing ((1 + 2) > 3). Comparisons produce a yes/no result, which is why we built the Bool value kind back in Chapter 1; the evaluator will turn these nodes into booleans later, and IF will branch on them.

Make it work

// comparisons get the LOWEST binding power so arithmetic groups first
func bp(k TokKind) int {
  switch k {
  case TStar, TSlash: return 30
  case TPlus, TMinus: return 20
  case TGt, TLt, TGe, TLe, TEq, TNe: return 10
  }
  return 0
}

CheckpointDONE

Comparisons parse at the lowest precedence, below arithmetic. Commit and stop here.