constraints.base

Base classes for constraint evaluation.

ConstraintContext provides a uniform interface for constraint evaluation that works for both prover (returns arrays) and verifier (returns scalars). The same constraint code can be used in both contexts thanks to galois broadcasting.

Example:

def eval_constraint(ctx: ConstraintContext):

a = ctx.col(‘a’) b = ctx.col(‘b’) return a * b - ctx.challenge(‘alpha’)

# Works for prover (arrays) prover_result = eval_constraint(ProverConstraintContext(prover_data))

# Works for verifier (scalars) verifier_result = eval_constraint(VerifierConstraintContext(verifier_data))

Attributes

FF3Poly
FFPoly

Classes

ConstraintContext	Uniform interface for constraint evaluation - works for prover and verifier.
ProverConstraintContext	Prover implementation - returns polynomial arrays.
VerifierConstraintContext	Verifier implementation - returns scalar evaluations.
ConstraintModule	Per-AIR constraint evaluation. Used by both prover and verifier.

Functions

compress_2col(→ primitives.field.FF3)

Compress 2-column expression: ((col2*α + col1)*α + busid) + γ.

Module Contents

constraints.base.FF3Poly

constraints.base.FFPoly

constraints.base.compress_2col(busid: int, col1: primitives.field.FF3, col2: primitives.field.FF3, alpha: primitives.field.FF3, gamma: primitives.field.FF3, n: int | None = None) → primitives.field.FF3

Compress 2-column expression: ((col2*α + col1)*α + busid) + γ.

class constraints.base.ConstraintContext

Bases: abc.ABC

Uniform interface for constraint evaluation - works for prover and verifier.

abstractmethod col(name: str, index: int = 0) → FF3Poly | primitives.field.FF3

Get column at current row.

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array of values at all domain points Verifier: scalar evaluation at xi

abstractmethod next_col(name: str, index: int = 0) → FF3Poly | primitives.field.FF3

Get column at next row (offset +1).

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array shifted by -1 (circular) Verifier: evaluation at xi * omega

abstractmethod prev_col(name: str, index: int = 0) → FF3Poly | primitives.field.FF3

Get column at previous row (offset -1).

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array shifted by +1 (circular) Verifier: evaluation at xi * omega^(-1)

abstractmethod const(name: str, index: int = 0) → FF3Poly | primitives.field.FF3

Get constant polynomial at current row (converted to extension field).

Args:

name: Constant name (e.g., ‘__L1__’ for Lagrange polynomial) index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array of constant values (as FF3 for arithmetic compatibility) Verifier: scalar evaluation at xi

abstractmethod next_const(name: str, index: int = 0) → FF3Poly | primitives.field.FF3

Get constant polynomial at next row (offset +1).

Args:

name: Constant name index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array shifted by -1 (circular) Verifier: evaluation at xi * omega

abstractmethod prev_const(name: str, index: int = 0) → FF3Poly | primitives.field.FF3

Get constant polynomial at previous row (offset -1).

Args:

name: Constant name index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array shifted by +1 (circular) Verifier: evaluation at xi * omega^(-1)

abstractmethod challenge(name: str) → primitives.field.FF3

Get Fiat-Shamir challenge (always scalar).

Args:

name: Challenge name (e.g., ‘std_alpha’)

Returns:

Scalar challenge value

abstractmethod airgroup_value(index: int) → primitives.field.FF3

Get airgroup value (accumulated result across AIR instances).

Args:

index: Airgroup value index

Returns:

Scalar airgroup value (FF3)

class constraints.base.ProverConstraintContext(data: protocol.data.ProverData)

Bases: ConstraintContext

Prover implementation - returns polynomial arrays.

The prover evaluates constraints at all domain points simultaneously, producing arrays of constraint evaluations.

col(name: str, index: int = 0) → FF3Poly

Get column at current row.

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array of values at all domain points Verifier: scalar evaluation at xi

next_col(name: str, index: int = 0) → FF3Poly

Get column at next row (offset +1).

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array shifted by -1 (circular) Verifier: evaluation at xi * omega

prev_col(name: str, index: int = 0) → FF3Poly

Get column at previous row (offset -1).

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array shifted by +1 (circular) Verifier: evaluation at xi * omega^(-1)

const(name: str, index: int = 0) → FF3Poly

Get constant polynomial at current row (converted to extension field).

Args:

name: Constant name (e.g., ‘__L1__’ for Lagrange polynomial) index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array of constant values (as FF3 for arithmetic compatibility) Verifier: scalar evaluation at xi

next_const(name: str, index: int = 0) → FF3Poly

Get constant polynomial at next row (offset +1).

Args:

name: Constant name index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array shifted by -1 (circular) Verifier: evaluation at xi * omega

prev_const(name: str, index: int = 0) → FF3Poly

Get constant polynomial at previous row (offset -1).

Args:

name: Constant name index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array shifted by +1 (circular) Verifier: evaluation at xi * omega^(-1)

challenge(name: str) → primitives.field.FF3

Get Fiat-Shamir challenge (always scalar).

Args:

name: Challenge name (e.g., ‘std_alpha’)

Returns:

Scalar challenge value

airgroup_value(index: int) → primitives.field.FF3

Get airgroup value (accumulated result across AIR instances).

Args:

index: Airgroup value index

Returns:

Scalar airgroup value (FF3)

class constraints.base.VerifierConstraintContext(data: protocol.data.VerifierData)

Bases: ConstraintContext

Verifier implementation - returns scalar evaluations.

The verifier evaluates constraints at a single random point xi, checking that the constraint polynomial evaluates to zero.

col(name: str, index: int = 0) → primitives.field.FF3

Get column at current row.

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array of values at all domain points Verifier: scalar evaluation at xi

next_col(name: str, index: int = 0) → primitives.field.FF3

Get column at next row (offset +1).

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array shifted by -1 (circular) Verifier: evaluation at xi * omega

prev_col(name: str, index: int = 0) → primitives.field.FF3

Get column at previous row (offset -1).

Args:

name: Column name index: Column index for multi-column polynomials (default 0)

Returns:

Prover: array shifted by +1 (circular) Verifier: evaluation at xi * omega^(-1)

const(name: str, index: int = 0) → primitives.field.FF3

Get constant polynomial at current row (converted to extension field).

Args:

name: Constant name (e.g., ‘__L1__’ for Lagrange polynomial) index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array of constant values (as FF3 for arithmetic compatibility) Verifier: scalar evaluation at xi

next_const(name: str, index: int = 0) → primitives.field.FF3

Get constant polynomial at next row (offset +1).

Args:

name: Constant name index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array shifted by -1 (circular) Verifier: evaluation at xi * omega

prev_const(name: str, index: int = 0) → primitives.field.FF3

Get constant polynomial at previous row (offset -1).

Args:

name: Constant name index: Column index for AIRs with multiple constants sharing a name

Returns:

Prover: array shifted by +1 (circular) Verifier: evaluation at xi * omega^(-1)

challenge(name: str) → primitives.field.FF3

Get Fiat-Shamir challenge (always scalar).

Args:

name: Challenge name (e.g., ‘std_alpha’)

Returns:

Scalar challenge value

airgroup_value(index: int) → primitives.field.FF3

Get airgroup value (accumulated result across AIR instances).

Args:

index: Airgroup value index

Returns:

Scalar airgroup value (FF3)

class constraints.base.ConstraintModule

Bases: abc.ABC

Per-AIR constraint evaluation. Used by both prover and verifier.

Each AIR (Algebraic Intermediate Representation) has its own constraint module that defines how constraints are evaluated. The same module works for both prover and verifier contexts.

abstractmethod constraint_polynomial(ctx: ConstraintContext) → FF3Poly | primitives.field.FF3

Evaluate all constraints combined into single polynomial.

Args:

ctx: ConstraintContext providing access to columns, constants, challenges

Returns:

Prover: array of constraint evaluations at all domain points Verifier: single constraint evaluation at xi