Burn contract

$X = (n u ll i f i er, c m_{x}^{v a l u e}, c m_{y}^{v a l u e}, c m^{t o k e n}, roo t, d a t a, s p e n d Hoo k, s i g na t u r e_{x}^{p u b l i c}, s i g na t u r e_{y}^{p u b l i c})$

$W = (v a l u e, t o k e n, b l in d^{v a l u e}, b l in d^{t o k e n}, s n, s p e n d Hoo k, d a t a, b l in d^{d a t a}, s k, p os, p a t h, s i g na t u r e^{secre t})$

$L = {X : (W, W) \in R}$

Burning a coin

Publish coin's nullifier to avoid double-spending.
Commit to coin's value $(c m_{x}^{v a l u e}, c m_{y}^{v a l u e})$
Commit to tokenId
Add coin to merkle tree, and set it's root it as instance.
Set spendHook as instance
Calculate $S i g na t u r e^{p u b l i c}$ , and set it as instance.

Public Input	Description
nullifier	coin nullifier
$c m_{x}^{v a l u e}$	x coordinate of value point commitment
$c m_{y}^{v a l u e}$	y coordinate of value point commitment
$c m^{t o k e n}$	[commitment](../crypto/commitment.md] of tokenId as field element
root	root of coin commitments merkle tree
data	data read during execution of burn spendHook contract
spendHook	burn related contract
$s i g na t u r e_{x}^{p u b l i c}$	signature public x coordinate
$s i g na t u r e_{y}^{p u b l i c}$	signature public y coordinate

Witnesses	Description
value	burn value
token	tokenId
$b l in d^{v a l u e}$	blinding term for burn value commitment
$b l in d^{t o k e n}$	blinding term for tokenId commitment
sn	serial number for burn coin
spendHook	contract related contract
data	data read during spendHook execution
$b l in d^{d a t a}$	blinding term for data commitment
sk	coin private key
pos	coin commitment leaf position in the merkle tree
path	coin commitment path in the merkle tree
$s i g na t u r e^{secre t}$	signature secret key

Circuit checks

If the coin has value zero, then coin is set to zero, with leaf position 0 in the sparse merkle tree, the aim is prevent burning zero value coins.