Lesson 16 · Evaluating arithmetic - Build a Spreadsheet Engine

Evaluating arithmetic

A parsed formula is a tree; evaluating it means walking that tree to a value. Today you build the evaluator's core - a recursive walk that computes arithmetic nodes into a numeric result.

The goal

Evaluate a number-and-operator AST into a numeric Value by walking the tree.

Start here - the target

TO DO

Scenario: An arithmetic tree evaluates to a number

Givena parsed arithmetic formula

Wheneval walks its tree

Theneval(parse('=1+2*3')) is the Number 7 and eval(parse('=(1+2)*3')) is the Number 9

Andeval(parse('=10-3-2')) is the Number 5, confirming the tree already encodes precedence and associativity

Background

Evaluation is a post-order walk: to evaluate a BinaryNode, first evaluate its left and right children to values, then apply the operator to them. A NumberNode is the base case - it just wraps its literal in a Number value. Because the parser already built the tree with the right shape, the evaluator does no precedence work at all: 1+2*3 is already 1 + (2*3), so walking it bottom-up naturally computes the multiply before the add and returns 7.

The operator application lives in a small helper, applyBin, that switches on the operator string and does the arithmetic on the two numbers. Keep it to the four arithmetic operators today; comparisons produce booleans and come later. Notice the evaluator is a method on the sheet even though it does not touch any cells yet - that is deliberate, because the very next lesson needs the sheet to resolve cell references, and having eval already be a sheet method means no signature change.

Make it work

func (s *Sheet) eval(e Expr) Value {
  switch n := e.(type) {
  case NumberNode:
    return Value{Kind: Number, Num: n.Val}
  case BinaryNode:
    l := s.eval(n.L); r := s.eval(n.R)
    return applyBin(n.Op, l, r) // + - * / on l.Num, r.Num
  }
  return Value{Kind: Empty}
}

CheckpointDONE

Arithmetic formulas evaluate to a numeric value. Commit and stop here.