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Compiling using PILCOM

This document describes how Polynomial Identity Language programs are compiled by PILCOM.

Depending on the language used in implementation, every PIL code can be compiled into either a \(\texttt{JSON}\) file or a \(\texttt{C++}\) code by using a compiler called \(\bf{pilcom}\).

The \(\bf{pilcom}\) compiler package can be found at this Github repository here. Setup can be fired up at the command line with the usual \(\texttt{clone}\), \(\texttt{install}\) and \(\texttt{build}\) CLI commands.

Any PIL code can be compiled into a \(\texttt{JSON}\) file with the command,

node src/pil.js <input.pil> -o <output.pil.json>

which is a basic \(\texttt{JSON}\) representation of the PIL program (with some extra metadata) to be later consumed on by the pil-stark package in order to generate a STARK proof.

Similarly, any PIL code can be compiled into C++ code with this command,

node src/pil.js <input.pil> -c -n namespace

in which case the corresponding header files (.hpp) will be generated in the ./pols_generated folder.

Restriction on polynomial degrees

The current version of PIL can only handle quadratics. Simply put, given any set of polynomials; \(\texttt{a}\), \(\texttt{b}\) and \(\texttt{c}\); PIL can only handle products of two polynomials at a time,

\[ \mathtt{a * a},\ \ \mathtt{a * b}\ \ \text{and}\ \ \mathtt{a * c} \]

but not higher degrees such as,

\[ \mathtt{a * a * a},\ \ \mathtt{a * b * b},\ \ \mathtt{(1-a) * b * c}\ \ \text{ or }\ \ \mathtt{a * b * c * c} \]

These higher degree products are handled via an \(\texttt{intermediate}\) polynomial, conveniently dubbed \(\texttt{carry}\). Consider again the constraint of the optimized Multiplier program:

\[ \texttt{out}' = \texttt{RESET} * \texttt{freeIn}\ +\ (1 - \texttt{RESET}) (\texttt{freeIn} * \texttt{out}) \tag{Eqn. 6} \]

which involves the trinomial,

\[ (1 - \texttt{RESET}) (\texttt{freeIn} * \texttt{out}) . \]

A \(\texttt{carry}\) can be used in \(\text{Eqn. 6}\) as follows,

\[ \texttt{out}' = \texttt{RESET} * \texttt{freeIn}\ +\ (1 - \texttt{RESET})* \texttt{carry} \tag{Eqn. 7} \]

where in this case, \(\texttt{carry} = \texttt{freeIn} * \texttt{out}\).

In the same sense that keywords \(\texttt{commit}\) and \(\texttt{constant}\) can be thought of as \(\text{types}\) of polynomials, \(\texttt{intermediate}\) can also be regarded as a third type of polynomial in PIL.

PIL compilation

In order to compile the above PIL code to a JSON file, follow the following steps.

  • Create a subdirectory/folder for the Multiplier SM and call it multiplier_sm.

  • Switch directory to the new subdirectory multiplier_sm, and open a new file. Name it multiplier.pil , copy in it the text below and save;

    namespace Multiplier(2**10); 

// Constant Polynomials
pol constant RESET;

// Committed Polynomials
pol commit freeIn;
pol commit out;

// Intermediate Polynomials
pol carry = out*freeIn; 

// Constraints
out' = RESET*freeIn + (1-RESET)*carry;

  • Switch directory to \(\texttt{pilcom}/\) and run the below command,

    node src/pil.js ~/multiplier_sm/multiplier.pil -o multiplier-1st.json

If compilation is successful, the following debug message will be printed on the command line,

Input Pol Commitments: 2
Q Pol Commitmets: 1
Constant Pols: 1
Im Pols: 1
plookupIdentities: 0
permutationIdentities: 0
connectionIdentities: 0
polIdentities: 1

The debug message reflects the numbers of;

  • Input committed polynomials, denoted by \(\texttt{Input Pol Commitments}\),
  • Quadratic polynomials, denoted by \(\texttt{Q Pol Commitmets}\),
  • Constant polynomials, denoted by \(\texttt{Constant Pols}\),
  • Intermediate polynomials, denoted by \(\texttt{Im Pols}\),
  • The various identities that can be checked; the \(\texttt{Plookup}\), the \(\texttt{Permutation}\), the \(\texttt{connection}\) and the \(\texttt{Polynomial}\) identities.

The resulting \(\texttt{JSON}\) file into which the multiplier.pil code is compiled looks like this:

{
  "name": "multiplier_sm",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "scripts": {
    "test": "echo \"Error: no test specified\" && exit 1"
  },
  "keywords": [],
  "author": "",
  "license": "ISC"
}

This \(\texttt{JSON}\) file contains all the information needed by the proof/verification package called \(\texttt{pil-stark}\) for processing.