api.Cmp usage coupled with api.Select

[NikitaMasych]

Hi guys, assume we have the following logic c := api.Select(api.Cmp(a, b), d, e), where a, b, c, d, e are of type frontend.Variable. Select method according to docs will return second one (d) if the first argument is true, otherwise the third argument (e). api.Cmp returns -1, 0 or 1. But, in practice, using api.Println(c) I get <unsolved> being outputted. Even more, using api.AssertIsBoolean(api.Cmp(a,b)) I receive no errors. What am I missing and how can one achieve such a logic?

[gbotrel]

Not sure without seing the full snippet; but unsolved in a Println probably means that the solver didn't finish (couldn't finish really). That is, one of the constraint is unsatisfied, solver stopped; all the subsequent constraints are not solved so Println can't give you a value.

Can you print the error of the Prove or ccs.Solve method?

[NikitaMasych]

I'll provide full example of code, causing issues I mentioned:

package main

import (
	"github.com/consensys/gnark-crypto/ecc"
	"github.com/consensys/gnark/backend/groth16"
	"github.com/consensys/gnark/frontend"
	"github.com/consensys/gnark/frontend/cs/r1cs"
	"github.com/pkg/errors"
)

type circuit struct {
	A, B, C, D frontend.Variable
	Res        frontend.Variable
}

func (c *circuit) Define(api frontend.API) error {
	cmp := api.Cmp(c.A, c.B) // -1

	api.AssertIsBoolean(cmp) // assert does not fail, why?

	res := api.Select(cmp, c.C, c.D) // res should be D?

	api.AssertIsEqual(c.Res, res)

	return nil
}

func main() {
	ccs, err := frontend.Compile(ecc.BN254.ScalarField(), r1cs.NewBuilder, new(circuit))
	if err != nil {
		panic(errors.Wrap(err, "failed to compile circuit"))
	}

	pk, vk, err := groth16.Setup(ccs)
	if err != nil {
		panic(errors.Wrap(err, "failed to setup pk and vk"))
	}

	assignment := &circuit{
		A: 1,
		B: 2,
		C: 3,
		D: 4,

		Res: 4,
	}
	wit, err := frontend.NewWitness(assignment, ecc.BN254.ScalarField())
	if err != nil {
		panic(errors.Wrap(err, "failed to instantiate new witness"))
	}

	proof, err := groth16.Prove(ccs, pk, wit)
	if err != nil {
		panic(errors.Wrap(err, "failed to prove"))
	}

	publicWitness, err := wit.Public()
	if err != nil {
		panic(errors.Wrap(err, "failed to extract public witness"))
	}
	if err := groth16.Verify(proof, vk, publicWitness); err != nil {
		panic(errors.Wrap(err, "failed to verify proof"))
	}
}

[NikitaMasych]

As an output for execution of this program, I receive:

14:20:35 INF compiling circuit
14:20:35 INF parsed circuit inputs nbPublic=0 nbSecret=5
14:20:35 INF building constraint builder nbConstraints=3811
14:20:35 ERR error="unsatisfied constraint" backend=groth16 id=3808 nbConstraints=3811
panic: failed to prove: constraint #3808 is not satisfied: -1 ⋅ 2 != 0

[NikitaMasych]

This is tested with release gnark version v0.8.1

[NikitaMasych]

If I try with the following assignment:

assignment := &circuit{
  A: 2,
  B: 1,
  C: 3,
  D: 4,
  
  Res: 3,
}

cmp results in 1 and program successfully executes

[NikitaMasych]

Regarding api.Println, for this version:

package main

import (
	"github.com/consensys/gnark-crypto/ecc"
	"github.com/consensys/gnark/backend/groth16"
	"github.com/consensys/gnark/frontend"
	"github.com/consensys/gnark/frontend/cs/r1cs"
	"github.com/pkg/errors"
)

type circuit struct {
	A, B, C, D frontend.Variable
}

func (c *circuit) Define(api frontend.API) error {
	cmp := api.Cmp(c.A, c.B) // -1

	api.AssertIsBoolean(cmp) // assert does not fail, why?

	res := api.Select(cmp, c.C, c.D) // res should be D?

	api.Println(res)

	return nil
}

func main() {
	ccs, err := frontend.Compile(ecc.BN254.ScalarField(), r1cs.NewBuilder, new(circuit))
	if err != nil {
		panic(errors.Wrap(err, "failed to compile circuit"))
	}

	pk, vk, err := groth16.Setup(ccs)
	if err != nil {
		panic(errors.Wrap(err, "failed to setup pk and vk"))
	}

	assignment := &circuit{
		A: 1,
		B: 2,
		C: 3,
		D: 4,
	}
	wit, err := frontend.NewWitness(assignment, ecc.BN254.ScalarField())
	if err != nil {
		panic(errors.Wrap(err, "failed to instantiate new witness"))
	}

	proof, err := groth16.Prove(ccs, pk, wit)
	if err != nil {
		panic(errors.Wrap(err, "failed to prove"))
	}

	publicWitness, err := wit.Public()
	if err != nil {
		panic(errors.Wrap(err, "failed to extract public witness"))
	}
	if err := groth16.Verify(proof, vk, publicWitness); err != nil {
		panic(errors.Wrap(err, "failed to verify proof"))
	}
}

Output is:

14:27:51 INF compiling circuit
14:27:51 INF parsed circuit inputs nbPublic=0 nbSecret=4
14:27:51 INF building constraint builder nbConstraints=3810
14:27:51 ERR error="unsatisfied constraint" backend=groth16 id=3808 nbConstraints=3810
14:27:51 DBG main.go:22 > <unsolved>
panic: failed to prove: constraint #3808 is not satisfied: -1 ⋅ 2 != 0