(def nand (a b) (r) (
    (let (a_and_b) (relay_default_off a b))
    (set r (relay_default_on a_and_b vin))
))

(def not (a) (r) (
    (set r (nand a a))
))

(def and (a b) (r) (
    (set r (not (nand a b)))
))

(def or (a b) (r) (
    (set r (nand (not a) (not b)))
))

(def xor (a b) (r) (
    (set r (and (or a b) (not (and a b))))
))

(def xor_optimized (a b) (r) (
    (let (c) (nand a b))
    (set r (nand (nand a c) (nand b c)))
))

(def half_add (a b) (r0 r1) (
    (set r0 (xor a b))
    (set r1 (and a b))
))

(def add (a b carry) (r0 r1) (
    (let (d0 d1) (half_add a b))
    (let (e0 e1) (half_add carry d0))
    (set r0 e0)
    (set r1 (or d1 e1))
))

(def add2 (a0 a1 b0 b1 carry_in) (r0 r1 carry_out) (
    (let (d0 d1) (add a0 b0 carry_in))
    (let (e0 e1) (add a1 b1 d1))
    (set r0 d0)
    (set r1 e0)
    (set carry_out e1)
))