The lambda calculus is a universal computer language in the sense that each computable function can be represented by a lambda term. For example, we can represent numbers as follows: (Read zyas an abbreviation for x(x(x(x(.-- (xy).. .)), where xappears ntimes.) The above representation for numbers is referred to as Church numerals in the literature (after Alonzo Church, on of the founders of computer science and the inventor of the lambda calculus). With the above representation, we can define the successor function Succ as: Show, by applying the beta axiom that Succ n = n + 1 that is Succ (Xx. Xy. x"v) = (x . xy. xn+13 ) The lambda calculus is a universal computer language in the sense that each computable function can be represented by a lambda term. For example, we can represent numbers as follows: (Read zyas an abbreviation for x(x(x(x(.-- (xy).. .)), where xappears ntimes.) The above representation for numbers is referred to as Church numerals in the literature (after Alonzo Church, on of the founders of computer science and the inventor of the lambda calculus). With the above representation, we can define the successor function Succ as: Show, by applying the beta axiom that Succ n = n + 1 that is Succ (Xx. Xy. x"v) = (x . xy. xn+13 )