Lambda Calculus

Abstract

Let us remind ourselves once again what “combinatory algebra” means: for each term t(x ₁,…, x _n) there exists an element T in D _A , so that for arbitrary M ₁,…,M _n ∈ D _A we have

$$ T{M_1}{M_2} \ldots {M_n} = t\left( {{M_1}, \ldots {M_n}} \right); $$

the algorithmic rule becomes a concrete object. It lies in the nature of the subject, that by applications we always pass from a term t to an object T.