Function lambda_calculus::arithmetic::neq

pub fn neq() -> Term

Applied to two Church-encoded numbers it returns a Church-encoded boolean indicating whether its first argument is not egual to the second one.

NEQ := λab.OR (NOT (LEQ a b)) (NOT (LEQ b a)) = λ λ OR (NOT (LEQ 2 1)) (NOT (LEQ 1 2))

Examples

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

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