purify::Expr Class Reference

Symbolic affine expression over indexed variables and field coefficients. More...

#include <expr.hpp>

Public Types
using	Term = std::pair<Symbol, FieldElement>

Public Member Functions
	Expr ()
	Constructs the zero expression.
	Expr (const FieldElement &value)
	Constructs a pure constant expression from a field element.
	Expr (std::int64_t value)
	Constructs a pure constant expression from a signed integer.
const FieldElement &	constant () const
	Returns the constant term of the affine expression.
std::vector< Term > &	linear ()
	Returns mutable access to the sorted linear term list.
const std::vector< Term > &	linear () const
	Returns read-only access to the sorted linear term list.
std::string	to_string () const
	Formats the expression in a stable human-readable form used for debugging and serialization.
std::optional< FieldElement >	evaluate (const WitnessAssignments &values) const
	Evaluates the expression against a possibly partial transcript witness assignment.
std::pair< Expr, Expr >	split () const
	Splits the expression into a pure constant and a pure linear component.

Static Public Member Functions
static Expr	variable (Symbol symbol)
	Returns a single-variable expression with coefficient one.

Friends
Expr	operator+ (const Expr &lhs, const Expr &rhs)
	Adds two affine expressions and merges like terms.
Expr	operator+ (const Expr &lhs, std::int64_t rhs)
	Adds an integer constant to an affine expression.
Expr	operator+ (std::int64_t lhs, const Expr &rhs)
	Adds an affine expression to an integer constant.
Expr	operator- (const Expr &lhs, const Expr &rhs)
	Subtracts one affine expression from another.
Expr	operator- (const Expr &lhs, std::int64_t rhs)
	Subtracts an integer constant from an affine expression.
Expr	operator- (std::int64_t lhs, const Expr &rhs)
	Subtracts an affine expression from an integer constant.
Expr	operator- (const Expr &value)
	Negates every coefficient in the affine expression.
Expr	operator* (const Expr &expr, const FieldElement &scalar)
	Scales an affine expression by a field element.
Expr	operator* (const FieldElement &scalar, const Expr &expr)
	Scales an affine expression by a field element.
Expr	operator* (const Expr &expr, std::int64_t scalar)
	Scales an affine expression by an integer constant.
Expr	operator* (std::int64_t scalar, const Expr &expr)
	Scales an affine expression by an integer constant.
bool	operator== (const Expr &lhs, const Expr &rhs)
	Compares two affine expressions structurally.
bool	operator< (const Expr &lhs, const Expr &rhs)
	Orders affine expressions structurally for cache keys.

Detailed Description

This type is used while deriving circuit relations before they are lowered into native multiplication gates and linear constraints.

Definition at line 71 of file expr.hpp.

Member Typedef Documentation

Term

using purify::Expr::Term = std::pair<Symbol, FieldElement>

Definition at line 73 of file expr.hpp.

Constructor & Destructor Documentation

Expr() [1/3]

purify::Expr::Expr

(

)

Definition at line 92 of file expr.cpp.

Referenced by operator*, operator*, operator*, operator*, operator+, operator+, operator+, operator-, operator-, operator-, operator-, operator<, operator==, split(), and variable().

Expr() [2/3]

purify::Expr::Expr ( const FieldElement & value )

explicit

Definition at line 94 of file expr.cpp.

Expr() [3/3]

purify::Expr::Expr ( std::int64_t value )

explicit

Definition at line 96 of file expr.cpp.

Member Function Documentation

constant()

const FieldElement & purify::Expr::constant ( ) const

inline

Definition at line 86 of file expr.hpp.

Referenced by purify::ExprBuilder::add(), purify::ExprBuilder::add_scaled(), purify::ExprLess::operator()(), purify::BulletproofTranscript::replace_and_insert(), and purify::ExprBuilder::subtract().

evaluate()

std::optional< FieldElement > purify::Expr::evaluate

(

const WitnessAssignments &

values

)

const

Definition at line 125 of file expr.cpp.

References purify::Witness.

Referenced by purify::Transcript::boolean(), purify::Transcript::div(), purify::Transcript::equal(), purify::Transcript::evaluate(), and purify::Transcript::mul().

linear() [1/2]

std::vector< Term > & purify::Expr::linear ( )

inline

Definition at line 91 of file expr.hpp.

Referenced by purify::ExprBuilder::add(), purify::ExprBuilder::add_scaled(), purify::circuit_1bit(), purify::circuit_2bit(), purify::circuit_3bit(), purify::circuit_combine(), purify::circuit_ec_add(), purify::circuit_ec_add_x(), purify::ExprLess::operator()(), purify::BulletproofTranscript::replace_and_insert(), purify::BulletproofTranscript::replace_expr_v_with_bp_var(), and purify::ExprBuilder::subtract().

linear() [2/2]

const std::vector< Term > & purify::Expr::linear ( ) const

inline

Definition at line 96 of file expr.hpp.

split()

std::pair< Expr, Expr > purify::Expr::split

(

)

const

Definition at line 140 of file expr.cpp.

References Expr().

to_string()

std::string purify::Expr::to_string

(

)

const

Definition at line 104 of file expr.cpp.

References purify::FieldElement::one().

Referenced by purify::operator<<().

variable()

Expr purify::Expr::variable ( Symbol symbol )

static

Definition at line 98 of file expr.cpp.

References Expr(), and purify::FieldElement::one().

Referenced by purify::BulletproofTranscript::add_pubkey_and_out(), purify::BulletproofTranscript::from_transcript(), purify::NativeBulletproofCircuitTemplate::instantiate_packed(), purify::BulletproofTranscript::native_circuit(), and purify::Transcript::secret().

Friends And Related Symbol Documentation

operator* [1/4]

Expr operator* ( const Expr & expr, const FieldElement & scalar )

friend

Definition at line 311 of file expr.cpp.

References Expr(), purify::FieldElement::is_zero(), and operator*.

Referenced by operator*, operator*, operator*, and operator*.

operator* [2/4]

Expr operator* ( const Expr & expr, std::int64_t scalar )

friend

Definition at line 327 of file expr.cpp.

References Expr(), purify::FieldElement::from_int(), and operator*.

operator* [3/4]

Expr operator* ( const FieldElement & scalar, const Expr & expr )

friend

Definition at line 323 of file expr.cpp.

References Expr(), and operator*.

operator* [4/4]

Expr operator* ( std::int64_t scalar, const Expr & expr )

friend

Definition at line 331 of file expr.cpp.

References Expr(), and operator*.

operator+ [1/3]

Expr operator+ ( const Expr & lhs, const Expr & rhs )

friend

Definition at line 265 of file expr.cpp.

References Expr(), and operator+.

Referenced by operator+, operator+, and operator+.

operator+ [2/3]

Expr operator+ ( const Expr & lhs, std::int64_t rhs )

friend

Definition at line 287 of file expr.cpp.

References Expr(), and operator+.

operator+ [3/3]

Expr operator+ ( std::int64_t lhs, const Expr & rhs )

friend

Definition at line 291 of file expr.cpp.

References Expr(), and operator+.

operator- [1/4]

Expr operator- ( const Expr & lhs, const Expr & rhs )

friend

Definition at line 295 of file expr.cpp.

References Expr(), and operator-.

Referenced by operator-, operator-, operator-, and operator-.

operator- [2/4]

Expr operator- ( const Expr & lhs, std::int64_t rhs )

friend

Definition at line 299 of file expr.cpp.

References Expr(), and operator-.

operator- [3/4]

Expr operator- ( const Expr & value )

friend

Definition at line 307 of file expr.cpp.

References Expr(), purify::FieldElement::from_int(), and operator-.

operator- [4/4]

Expr operator- ( std::int64_t lhs, const Expr & rhs )

friend

Definition at line 303 of file expr.cpp.

References Expr(), and operator-.

operator<

bool operator< ( const Expr & lhs, const Expr & rhs )

friend

Definition at line 369 of file expr.cpp.

References Expr(), and operator<.

Referenced by operator<.

operator==

bool operator== ( const Expr & lhs, const Expr & rhs )

friend

Definition at line 335 of file expr.cpp.

References Expr(), and operator==.

Referenced by operator==.

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The documentation for this class was generated from the following files:

• include/purify/expr.hpp
• src/protocol/expr.cpp