Polygon zkEVM PIL编译器——pilcom 代码解析

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); // 以`pol commit`表示的多项式总数
    console.log("Q Pol Commitmets: " + out.nQ); // 以多项式本身为粒度，若degree为2，则nQ++，如`pol next = l1*l1 + l2*l2;`，需nQ++。
    console.log("Constant Pols: " + out.nConstants); // 以`pol constant`表示的多项式总数
    console.log("Im Pols: " + out.nIm); // 仅以`pol`，而非`pol constant`或`pol commit`表示的多项式总数
    console.log("plookupIdentities: " + out.plookupIdentities.length); // 即pil中的`in`表示的约束总数
    console.log("permutationIdentities: " + out.permutationIdentities.length); // 即pil中的`is`表示的约束总数
    console.log("connectionIdentities: " + out.connectionIdentities.length); // 即pil中的`connect`表示的约束总数
    console.log("polIdentities: " + out.polIdentities.length); // 即pil中的`=`表示的约束总数

    await fs.promises.writeFile(outputFile.trim(), JSON.stringify(out, null, 1) + "\n", "utf8");

相应的json文件输出为：

• 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$1$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": { # namespace.polyName
   "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