Symbolic systems [and operator systems]

By introducing constants (0-argument operators) and interpreting ∘ as function application one can turn any symbolic system such as ℯ[x][y]  x[x[y]] from page 103 into an algebraic system such as (ℯ ∘ 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}.