Chapter 12: The Principle of Computational Equivalence

Section 9: Implications for Mathematics and Its Foundations

Symbolic systems [and operator systems]

By introducing constants (0-argument operators) and interpreting as function application one can turn any symbolic system such as [x][y] x[x[y]] from page 103 into an algebraic system such as ( a) b a (a b). Doing this for the combinator system from page 711 yields the so-called combinatory algebra {((s a) b) c (a c) (b c), ( a) b a}.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]