chained-functional-commitment.lurk

;; First, we define a stateful function that adds its input to an internal counter, initialized to 0.

;; The function returns a new counter value and a commitment to a replacement function wrapping the new counter.

!(commit (letrec ((add (lambda (counter x)
                          (let ((counter (+ counter x)))
                            (cons counter (commit (add counter)))))))
            (add 0)))

;; We chain a next commitment by applying the committed function to a value of 9.

!(chain 0x2b444b40b27bac0dff8416c0f3c708a505a636d86ba66bdbe86497c515afb651 9)

;; The new counter value is 9, and the function returns a new functional commitment.

;; This new commitment is now the head of the chain.

;; Next, we ccreate a proof of this transition.

!(prove)

;; We can verify the proof.

!(verify "supernova_bn256_10_0f54f9e56fa6c436618597c971daa7b525ad80ac48be11226284fd4f8167e60a")

;; Now let's chain another call to the new head, adding 12 to the counter.

!(chain (comm 0x1d10fb6dea15a5865565d571efbcaf535750ab93ba4d9018bd6b7b803e86d986) 12)

;; Now the counter is 21, and we have a new head commitment.

;; Prove it.

!(prove)

;; And verify.

!(verify "supernova_bn256_10_281771b7af2f96cac51cb7579d94f0a6f56e9a9d951b753f8514b2b4ec6ce4db")

;; One more time, we'll add 14 to the head commitment's internal state.

!(chain 0x1a95f14fa34e01ce6cf44b4eb419c59e8b50978618139d9314304979cad1770f 14)

;; 21 + 14 = 35, as expected.

;; Prove.

!(prove)

;; Verify.

!(verify "supernova_bn256_10_22ab68c1fa6e75f54d213a3ada71edd21331bf58826263a79e3fdd32f1c4c62d")

;; Repeat indefinitely.

;; At every step, we have proof that the head commitment was correctly derived from the previous and some input.