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Nodes API

Warning

In this version of Oraqle, the API is still prone to changes. Paths and names can change between any version.

Boolean operations

AND operation

And

Bases: CommutativeUniqueReducibleNode

Performs an AND operation over several operands. The user must ensure that the operands are Booleans.

__init__(operands, gf)

Initialize a node with the given set as the operands. None of the operands can be a constant.

apply_function_to_operands(function)

replace_operands_using_function(function)

evaluate(actual_inputs)

clear_cache(already_cleared)

Clears any cached values of the node and any of its operands.

to_graph(graph_builder)

Adds this node to the graph as well as its edges.

Returns:

  • int –

    The identifier of this Node in the DotFile.

__hash__()

is_equivalent(other)

eliminate_common_subexpressions(terms)

Eliminates duplicate subexpressions that are equivalent (as defined by a node's __eq__ and __hash__ method).

Returns:

  • Node –

    A Node that must replace the previous expression.

count_parents()

Counts the total number of nodes in this subcircuit.

reset_parent_count()

Resets the cached number of nodes in this subcircuit to 0.

arithmetize(strategy)

arithmetize_depth_aware(cost_of_squaring)

to_arithmetic()

Outputs this node's equivalent ArithmeticNode. Errors if this node does not have a direct arithmetic equivalent.

Raises:

  • Exception –

    If there is no direct arithmetic equivalent.

add(other, flatten=True)

Performs a summation between self and other, possibly flattening any sums.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Sum node or a Constant representing self & other.

__add__(other)

__radd__(other)

mul(other, flatten=True)

Performs a multiplication between self and other, possibly flattening any products.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Product node or a Constant representing self & other.

__mul__(other)

bool_or(other, flatten=True)

Performs an OR operation between self and other, possibly flattening the result into an OR operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Or node or a Constant representing self & other.

__or__(other)

bool_and(other, flatten=True)

Performs an AND operation between self and other, possibly flattening the result into an AND operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened And node or a Constant representing self & other.

__and__(other)

__lt__(other)

__gt__(other)

__le__(other)

__ge__(other)

__neg__()

__invert__()

__pow__(other)

__sub__(other)

__rsub__(other)

__eq__(other)

and_flatten(other)

Performs an AND operation with other, flattening the And node if either of the two is also an And and absorbing Constants.

Returns:

  • Node –

    An And node containing the flattened AND operation, or a Constant node.

OR operation

Or

Bases: CommutativeUniqueReducibleNode

Performs an OR operation over several operands. The user must ensure that the operands are Booleans.

__init__(operands, gf)

Initialize a node with the given set as the operands. None of the operands can be a constant.

apply_function_to_operands(function)

replace_operands_using_function(function)

evaluate(actual_inputs)

clear_cache(already_cleared)

Clears any cached values of the node and any of its operands.

to_graph(graph_builder)

Adds this node to the graph as well as its edges.

Returns:

  • int –

    The identifier of this Node in the DotFile.

__hash__()

is_equivalent(other)

eliminate_common_subexpressions(terms)

Eliminates duplicate subexpressions that are equivalent (as defined by a node's __eq__ and __hash__ method).

Returns:

  • Node –

    A Node that must replace the previous expression.

count_parents()

Counts the total number of nodes in this subcircuit.

reset_parent_count()

Resets the cached number of nodes in this subcircuit to 0.

arithmetize(strategy)

arithmetize_depth_aware(cost_of_squaring)

to_arithmetic()

Outputs this node's equivalent ArithmeticNode. Errors if this node does not have a direct arithmetic equivalent.

Raises:

  • Exception –

    If there is no direct arithmetic equivalent.

add(other, flatten=True)

Performs a summation between self and other, possibly flattening any sums.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Sum node or a Constant representing self & other.

__add__(other)

__radd__(other)

mul(other, flatten=True)

Performs a multiplication between self and other, possibly flattening any products.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Product node or a Constant representing self & other.

__mul__(other)

bool_or(other, flatten=True)

Performs an OR operation between self and other, possibly flattening the result into an OR operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Or node or a Constant representing self & other.

__or__(other)

bool_and(other, flatten=True)

Performs an AND operation between self and other, possibly flattening the result into an AND operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened And node or a Constant representing self & other.

__and__(other)

__lt__(other)

__gt__(other)

__le__(other)

__ge__(other)

__neg__()

__invert__()

__pow__(other)

__sub__(other)

__rsub__(other)

__eq__(other)

or_flatten(other)

Performs an OR operation with other, flattening the Or node if either of the two is also an Or and absorbing Constants.

Returns:

  • Node –

    An Or node containing the flattened OR operation, or a Constant node.

NEG operation

Neg

Bases: UnivariateNode

A node that negates a Boolean input.

__init__(node, gf)

Initialize a univariate node.

apply_function_to_operands(function)

replace_operands_using_function(function)

evaluate(actual_inputs)

clear_cache(already_cleared)

Clears any cached values of the node and any of its operands.

to_graph(graph_builder)

__hash__()

is_equivalent(other)

Check whether self is semantically equivalent to other.

This function may have false negatives but it should never return false positives.

`True` if `self` is semantically equivalent to `other`, `False` if they are not or that they cannot be shown to be equivalent.

eliminate_common_subexpressions(terms)

Eliminates duplicate subexpressions that are equivalent (as defined by a node's __eq__ and __hash__ method).

Returns:

  • Node –

    A Node that must replace the previous expression.

count_parents()

Counts the total number of nodes in this subcircuit.

reset_parent_count()

Resets the cached number of nodes in this subcircuit to 0.

arithmetize(strategy)

arithmetize_depth_aware(cost_of_squaring)

to_arithmetic()

Outputs this node's equivalent ArithmeticNode. Errors if this node does not have a direct arithmetic equivalent.

Raises:

  • Exception –

    If there is no direct arithmetic equivalent.

add(other, flatten=True)

Performs a summation between self and other, possibly flattening any sums.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Sum node or a Constant representing self & other.

__add__(other)

__radd__(other)

mul(other, flatten=True)

Performs a multiplication between self and other, possibly flattening any products.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Product node or a Constant representing self & other.

__mul__(other)

bool_or(other, flatten=True)

Performs an OR operation between self and other, possibly flattening the result into an OR operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Or node or a Constant representing self & other.

__or__(other)

bool_and(other, flatten=True)

Performs an AND operation between self and other, possibly flattening the result into an AND operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened And node or a Constant representing self & other.

__and__(other)

__lt__(other)

__gt__(other)

__le__(other)

__ge__(other)

__neg__()

__invert__()

__pow__(other)

__sub__(other)

__rsub__(other)

__eq__(other)

operands()

set_operands(operands)

operation(operands)

Arithmetic operations

These operations are fundamental arithmetic operations, so they will stay the same when they are arithmetized.

High-level arithmetic operations

Subtraction

Subtraction

Bases: NonCommutativeBinaryNode

Represents a subtraction, which can be arithmetized using addition and constant-multiplication.

__init__(left, right, gf)

Initialize a Node that performs an operation between two operands that is not commutative.

apply_function_to_operands(function)

replace_operands_using_function(function)

evaluate(actual_inputs)

clear_cache(already_cleared)

Clears any cached values of the node and any of its operands.

to_graph(graph_builder)

__hash__()

is_equivalent(other)

eliminate_common_subexpressions(terms)

Eliminates duplicate subexpressions that are equivalent (as defined by a node's __eq__ and __hash__ method).

Returns:

  • Node –

    A Node that must replace the previous expression.

count_parents()

Counts the total number of nodes in this subcircuit.

reset_parent_count()

Resets the cached number of nodes in this subcircuit to 0.

arithmetize(strategy)

arithmetize_depth_aware(cost_of_squaring)

to_arithmetic()

Outputs this node's equivalent ArithmeticNode. Errors if this node does not have a direct arithmetic equivalent.

Raises:

  • Exception –

    If there is no direct arithmetic equivalent.

add(other, flatten=True)

Performs a summation between self and other, possibly flattening any sums.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Sum node or a Constant representing self & other.

__add__(other)

__radd__(other)

mul(other, flatten=True)

Performs a multiplication between self and other, possibly flattening any products.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Product node or a Constant representing self & other.

__mul__(other)

bool_or(other, flatten=True)

Performs an OR operation between self and other, possibly flattening the result into an OR operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Or node or a Constant representing self & other.

__or__(other)

bool_and(other, flatten=True)

Performs an AND operation between self and other, possibly flattening the result into an AND operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened And node or a Constant representing self & other.

__and__(other)

__lt__(other)

__gt__(other)

__le__(other)

__ge__(other)

__neg__()

__invert__()

__pow__(other)

__sub__(other)

__rsub__(other)

__eq__(other)

operands()

set_operands(operands)

operation(operands)

Exponentiation

Power

Bases: UnivariateNode

Represents an exponentiation: x ** constant.

apply_function_to_operands(function)

replace_operands_using_function(function)

evaluate(actual_inputs)

clear_cache(already_cleared)

Clears any cached values of the node and any of its operands.

to_graph(graph_builder)

__hash__()

is_equivalent(other)

Check whether self is semantically equivalent to other.

This function may have false negatives but it should never return false positives.

`True` if `self` is semantically equivalent to `other`, `False` if they are not or that they cannot be shown to be equivalent.

eliminate_common_subexpressions(terms)

Eliminates duplicate subexpressions that are equivalent (as defined by a node's __eq__ and __hash__ method).

Returns:

  • Node –

    A Node that must replace the previous expression.

count_parents()

Counts the total number of nodes in this subcircuit.

reset_parent_count()

Resets the cached number of nodes in this subcircuit to 0.

arithmetize(strategy)

arithmetize_depth_aware(cost_of_squaring)

to_arithmetic()

Outputs this node's equivalent ArithmeticNode. Errors if this node does not have a direct arithmetic equivalent.

Raises:

  • Exception –

    If there is no direct arithmetic equivalent.

add(other, flatten=True)

Performs a summation between self and other, possibly flattening any sums.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Sum node or a Constant representing self & other.

__add__(other)

__radd__(other)

mul(other, flatten=True)

Performs a multiplication between self and other, possibly flattening any products.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Product node or a Constant representing self & other.

__mul__(other)

bool_or(other, flatten=True)

Performs an OR operation between self and other, possibly flattening the result into an OR operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Or node or a Constant representing self & other.

__or__(other)

bool_and(other, flatten=True)

Performs an AND operation between self and other, possibly flattening the result into an AND operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened And node or a Constant representing self & other.

__and__(other)

__lt__(other)

__gt__(other)

__le__(other)

__ge__(other)

__neg__()

__invert__()

__pow__(other)

__sub__(other)

__rsub__(other)

__eq__(other)

operands()

set_operands(operands)

operation(operands)

__init__(node, exponent, gf)

Initialize a Power node that exponentiates node with exponent.

Polynomial evaluation

Univariate polynomial evaluation

UnivariatePoly

Bases: UnivariateNode

Evaluation of a univariate polynomial.

apply_function_to_operands(function)

replace_operands_using_function(function)

evaluate(actual_inputs)

clear_cache(already_cleared)

Clears any cached values of the node and any of its operands.

to_graph(graph_builder)

__hash__()

is_equivalent(other)

Check whether self is semantically equivalent to other.

This function may have false negatives but it should never return false positives.

`True` if `self` is semantically equivalent to `other`, `False` if they are not or that they cannot be shown to be equivalent.

eliminate_common_subexpressions(terms)

Eliminates duplicate subexpressions that are equivalent (as defined by a node's __eq__ and __hash__ method).

Returns:

  • Node –

    A Node that must replace the previous expression.

count_parents()

Counts the total number of nodes in this subcircuit.

reset_parent_count()

Resets the cached number of nodes in this subcircuit to 0.

arithmetize(strategy)

arithmetize_depth_aware(cost_of_squaring)

to_arithmetic()

Outputs this node's equivalent ArithmeticNode. Errors if this node does not have a direct arithmetic equivalent.

Raises:

  • Exception –

    If there is no direct arithmetic equivalent.

add(other, flatten=True)

Performs a summation between self and other, possibly flattening any sums.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Sum node or a Constant representing self & other.

__add__(other)

__radd__(other)

mul(other, flatten=True)

Performs a multiplication between self and other, possibly flattening any products.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Product node or a Constant representing self & other.

__mul__(other)

bool_or(other, flatten=True)

Performs an OR operation between self and other, possibly flattening the result into an OR operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Or node or a Constant representing self & other.

__or__(other)

bool_and(other, flatten=True)

Performs an AND operation between self and other, possibly flattening the result into an AND operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened And node or a Constant representing self & other.

__and__(other)

__lt__(other)

__gt__(other)

__le__(other)

__ge__(other)

__neg__()

__invert__()

__pow__(other)

__sub__(other)

__rsub__(other)

__eq__(other)

operands()

set_operands(operands)

operation(operands)

__init__(node, coefficients, gf)

Initialize a univariate polynomial with the given coefficients from least to highest order.

from_function(node, gf, function) classmethod

Interpolate a univariate polynomial for the given function.

Returns:

A UnivariatePoly whose coefficients compute the function on all inputs.

arithmetize_custom(strategy)

Compute an arithmetization along with a dictionary of precomputed powers.

Returns:

An arithmetization and a dictionary of previously computed powers.

arithmetize_depth_aware_custom(cost_of_squaring)

Compute a depth-aware arithmetization as well as a dictionary indexed by the depth of the nodes in the front. The dictionary stores precomputed powers.

Returns:

A CostParetoFront with the depth-aware arithmetization and a dictionary indexed by the depth of the nodes in the front, returning a dictionary with previously computed powers.

Control flow

If-else statement

IfElse

Bases: FixedNode

A node representing an if-else clause.

apply_function_to_operands(function)

replace_operands_using_function(function)

evaluate(actual_inputs)

clear_cache(already_cleared)

Clears any cached values of the node and any of its operands.

to_graph(graph_builder)

Adds this node to the graph as well as its edges.

Returns:

  • int –

    The identifier of this Node in the DotFile.

eliminate_common_subexpressions(terms)

Eliminates duplicate subexpressions that are equivalent (as defined by a node's __eq__ and __hash__ method).

Returns:

  • Node –

    A Node that must replace the previous expression.

count_parents()

Counts the total number of nodes in this subcircuit.

reset_parent_count()

Resets the cached number of nodes in this subcircuit to 0.

arithmetize(strategy)

arithmetize_depth_aware(cost_of_squaring)

to_arithmetic()

Outputs this node's equivalent ArithmeticNode. Errors if this node does not have a direct arithmetic equivalent.

Raises:

  • Exception –

    If there is no direct arithmetic equivalent.

add(other, flatten=True)

Performs a summation between self and other, possibly flattening any sums.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Sum node or a Constant representing self & other.

__add__(other)

__radd__(other)

mul(other, flatten=True)

Performs a multiplication between self and other, possibly flattening any products.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Product node or a Constant representing self & other.

__mul__(other)

bool_or(other, flatten=True)

Performs an OR operation between self and other, possibly flattening the result into an OR operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened Or node or a Constant representing self & other.

__or__(other)

bool_and(other, flatten=True)

Performs an AND operation between self and other, possibly flattening the result into an AND operation between many operands.

It is possible to disable flattening by setting flatten=False.

Returns:

  • Node –

    A possibly flattened And node or a Constant representing self & other.

__and__(other)

__lt__(other)

__gt__(other)

__le__(other)

__ge__(other)

__neg__()

__invert__()

__pow__(other)

__sub__(other)

__rsub__(other)

__eq__(other)

__init__(condition, positive, negative, gf)

Initialize an if-else node: If condition evaluates to true, then it outputs positive, otherwise it outputs negative.

__hash__()

is_equivalent(other)

operands()

set_operands(operands)

operation(operands)