Function lambda_calculus::arithmetic::leq

pub fn leq() -> Term

Applied to two Church-encoded numbers it returns a Church-encoded boolean indicating whether its first argument is less than or egual to the second one.

LEQ := λmn.IS_ZERO (SUB m n) = λ λ IS_ZERO (SUB 2 1)

Examples

use lambda_calculus::arithmetic::leq;
use lambda_calculus::booleans::{tru, fls};
use lambda_calculus::reduction::beta_full;

assert_eq!(beta_full(leq().app(0.into()).app(0.into())), tru());
assert_eq!(beta_full(leq().app(1.into()).app(1.into())), tru());
assert_eq!(beta_full(leq().app(0.into()).app(1.into())), tru());
assert_eq!(beta_full(leq().app(1.into()).app(0.into())), fls());