Constants in Lambda Calculus
Constants can be added to the syntax of the Lambda Calculus: e.g., 0, 1, 2, …
However, in principle they are not necessary, because certain expressions can be used to represent them.
0 = ?x.?y.y A fn that returns an ident. fun.
1 = ?x.?y. (x y) A fn that applies a given fn. 1 time.
2 = ?x.?y. (x (x y)) A fn that applies a given fn. twice.
These are called Church numerals.
Other, symbolic, constants can also be added with the understanding that they, too, can be represented by some arbitrary L.C. expressions. E.g., Apple = ?x.?y.y (?x.?y.y)