constant

Constant 0 · 0

Zero isn't a primitive in EML, it takes depth 3 to build. This is surprising and fundamental to how EML reshapes what 'simple' means.

depth 3
Domain: n/a
Definition
0 = eml(1, eml(eml(1, 1), 1))0 \ = \ \texttt{eml(1, eml(eml(1, 1), 1))}

Formula

eml(1, eml(eml(1, 1), 1))
Evaluate
0
EML tree
111111eml2.718311eml15.1543eml0

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Step-through evaluation
  1. 1.depth 1const 1
  2. 2.depth 3const 1
  3. 3.depth 3const 1
  4. 4.depth 2exp(1) − ln(1) = 2.718282
  5. 5.depth 2const 1
  6. 6.depth 1exp(2.718282) − ln(1) = 15.154262
  7. 7.depth 0exp(1) − ln(15.154262) = 0
Derivation
  1. 1.Goal: produce 0.
  2. 2.Inner: eml(1, 1) = e.
  3. 3.Next: eml(e, 1) = exp(e) − ln(1) = exp(e).
  4. 4.Outer: eml(1, exp(e)) = exp(1) − ln(exp(e)) = e − e = 0.