1. 引言
开源代码见：
- https://github.com/0xPolygonHermez/pilcom（JavaScript）
pilcom为polygon zkEVM的PIL（polynomial Identity Language）编译器。
以test/examples下的arrays.pil代码为例：
namespace Arrays2(2**16);
pol constant d[2];
pol commit c;
d[0]+d[1] = c*d[0]; //第6行
namespace Arrays1(2**16);
pol commit a, b[3], c;
a*b[0] = 1; //第11行
b[1]*b[1] = b[2]*Arrays2.d[1]; //第12行
b[1] {b[0], a} in Arrays2.d[0] { Arrays2.c, Arrays2.d[1]}; //第14行
$ node src/pil.js test/examples/arrays.pil -o zyd.json
Debugger attached.
Input Pol Commitmets: 6
Q Pol Commitmets: 0
Constant Pols: 2
Im Pols: 0
plookupIdentities: 1
permutationIdentities: 0
connectionIdentities: 0
polIdentities: 3
Waiting for the debugger to disconnect...
pil.js代码本质为调用compile将pil代码编译为JSON格式。
const out = await compile(F, fullFileName, null, config);
console.log("Input Pol Commitmets: " + out.nCommitments);
console.log("Q Pol Commitmets: " + out.nQ);
console.log("Constant Pols: " + out.nConstants);
console.log("Im Pols: " + out.nIm);
console.log("plookupIdentities: " + out.plookupIdentities.length);
console.log("permutationIdentities: " + out.permutationIdentities.length);
console.log("connectionIdentities: " + out.connectionIdentities.length);
console.log("polIdentities: " + out.polIdentities.length);
await fs.promises.writeFile(outputFile.trim(), JSON.stringify(out, null, 1) + "\n", "utf8");
- 1）常量多项式类型为“constP”，对应的values op为“const”，PIL代码内标记为
pol constant； - 2）隐私多项式commitment类型为“cmP”，对应的values op为“cm”，PIL代码内标记为
pol commit； - 3）中间（intermediate）多项式类型“imP”，不允许有offset，对应的values op为“exp”；
- 4）多项式identities对应的pil代码中的位置，在“polIdentities”中表示：【如本例，分别在第6、11、12行。】
"polIdentities": [ { "e": 0, "fileName": "arrays.pil", "line": 6 }, { "e": 1, "fileName": "arrays.pil", "line": 11 }, { "e": 2, "fileName": "arrays.pil", "line": 12 } ] - 5）约束中的常量值，如
1
1
1等，其op为“number”，json表示为：
{ "op": "number", "deg": 0, "value": "1" } - 6）运算见“expressions”中的“op”字段，支持的运算有：“neg”、“add”、“sub”、“mul”、“pow”。
- 7）plookup约束
b[1] {b[0], a} in Arrays2.d[0] { Arrays2.c, Arrays2.d[1]};，对应在“expressions”中的JSON表示为：【规则为先in的左侧，再右侧。】{ # b[0]。在expressions数组的index为3。 "op": "cm", "deg": 1, "id": 2, "next": false }, { # a。在expressions数组的index为4。 "op": "cm", "deg": 1, "id": 1, "next": false }, { # b[1]。在expressions数组的index为5。 "op": "cm", "deg": 1, "id": 3, "next": false }, { # c。在expressions数组的index为6。 "op": "cm", "deg": 1, "id": 0, "next": false }, { # d[1]。在expressions数组的index为7。 "op": "const", "deg": 1, "id": 1, "next": false }, { # d[0]。在expressions数组的index为8。 "op": "const", "deg": 1, "id": 0, "next": false } - 8）plookup约束对应的pil代码中的位置，在“plookupIdentities”中表示：【如本例，在第14行。“f”/“t”，以及"selF"和“selT”的值均为相应项在expression数组内的index值。】
"plookupIdentities": [ { "f": [ 3, 4 ], "t": [ 6, 7 ], "selF": 5, "selT": 8, "fileName": "arrays.pil", "line": 14 } ] - 9）permutation约束对应在pil代码中的位置，在“permutationIdentities”中表示。
- 10）connection约束对应在pil代码中的位置，在“connectionIdentities”中表示。
{
"nCommitments": 6,
"nQ": 0,
"nIm": 0,
"nConstants": 2,
"publics": [],
"references": {
"Arrays2.d": {
"type": "constP",
"id": 0,
"polDeg": 65536,
"isArray": true,
"len": 2
},
"Arrays2.c": {
"type": "cmP",
"id": 0,
"polDeg": 65536,
"isArray": false
},
"Arrays1.a": {
"type": "cmP",
"id": 1,
"polDeg": 65536,
"isArray": false
},
"Arrays1.b": {
"type": "cmP",
"id": 2,
"polDeg": 65536,
"isArray": true,
"len": 3
},
"Arrays1.c": {
"type": "cmP",
"id": 5,
"polDeg": 65536,
"isArray": false
}
},
"expressions": [
{ # 对应约束为：d[0]+d[1]-d[0]*c=0
"op": "sub",
"deg": 2,
"values": [
{
"op": "add",
"deg": 1,
"values": [
{
"op": "const",
"deg": 1,
"id": 0,
"next": false
},
{
"op": "const",
"deg": 1,
"id": 1,
"next": false
}
]
},
{
"op": "mul",
"deg": 2,
"values": [
{
"op": "cm",
"deg": 1,
"id": 0,
"next": false
},
{
"op": "const",
"deg": 1,
"id": 0,
"next": false
}
]
}
]
},
{ # 对应约束为： a*b[0]-1=0
"op": "sub",
"deg": 2,
"values": [
{
"op": "mul",
"deg": 2,
"values": [
{
"op": "cm",
"deg": 1,
"id": 1,
"next": false
},
{
"op": "cm",
"deg": 1,
"id": 2,
"next": false
}
]
},
{
"op": "number",
"deg": 0,
"value": "1"
}
]
},
{ # 对应约束为：b[1]*b[1]-b[2]*d[1]=0
"op": "sub",
"deg": 2,
"values": [
{
"op": "mul",
"deg": 2,
"values": [
{
"op": "cm",
"deg": 1,
"id": 3,
"next": false
},
{
"op": "cm",
"deg": 1,
"id": 3,
"next": false
}
]
},
{
"op": "mul",
"deg": 2,
"values": [
{
"op": "cm",
"deg": 1,
"id": 4,
"next": false
},
{
"op": "const",
"deg": 1,
"id": 1,
"next": false
}
]
}
]
},
{ # b[0]
"op": "cm",
"deg": 1,
"id": 2,
"next": false
},
{ # a
"op": "cm",
"deg": 1,
"id": 1,
"next": false
},
{ # b[1]
"op": "cm",
"deg": 1,
"id": 3,
"next": false
},
{ # c
"op": "cm",
"deg": 1,
"id": 0,
"next": false
},
{ # d[1]
"op": "const",
"deg": 1,
"id": 1,
"next": false
},
{ # d[0]
"op": "const",
"deg": 1,
"id": 0,
"next": false
}
],
"polIdentities": [
{
"e": 0,
"fileName": "arrays.pil",
"line": 6
},
{
"e": 1,
"fileName": "arrays.pil",
"line": 11
},
{
"e": 2,
"fileName": "arrays.pil",
"line": 12
}
],
"plookupIdentities": [
{
"f": [
3,
4
],
"t": [
6,
7
],
"selF": 5,
"selT": 8,
"fileName": "arrays.pil",
"line": 14
}
],
"permutationIdentities": [],
"connectionIdentities": []
}
附录：polygon Hermez 2.0 zkEVM系列博客
- ZK-Rollups工作原理
- Polygon zkEVM——Hermez 2.0简介
- Polygon zkEVM网络节点
- Polygon zkEVM 基本概念
- Polygon zkEVM Prover
- Polygon zkEVM工具——PIL和CIRCOM
- Polygon zkEVM节点代码解析
- Polygon zkEVM的pil-stark Fibonacci状态机初体验
- Polygon zkEVM的pil-stark Fibonacci状态机代码解析
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