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//! Core concepts of OpenDP.
//!
//! This module provides the central building blocks used throughout OpenDP:
//! * Measurement
//! * Transformation
//! * Domain
//! * Metric/Measure
//! * Function
//! * StabilityMap/PrivacyMap
// Generic legend
// M: Metric and Measure
// Q: Metric and Measure Carrier/Distance
// D: Domain
// T: Domain Carrier
// *I: Input
// *O: Output
// Ordering of generic arguments
// DI, DO, MI, MO, TI, TO, QI, QO
#[cfg(feature = "ffi")]
mod ffi;
#[cfg(feature = "ffi")]
pub use ffi::*;
use std::rc::Rc;
use crate::error::*;
use crate::traits::{DistanceConstant, InfCast, InfMul, TotalOrd};
use std::fmt::Debug;
/// A set which constrains the input or output of a [`Function`].
///
/// Domains capture the notion of what values are allowed to be the input or output of a `Function`.
///
/// # Proof Definition
/// A type `Self` implements `Domain` iff it can represent a set of values that make up a domain.
pub trait Domain: Clone + PartialEq + Debug {
/// The underlying type that the Domain specializes.
/// This is the type of a member of a domain, where a domain is any data type that implements this trait.
///
/// On any type `D` for which the `Domain` trait is implemented,
/// the syntax `D::Carrier` refers to this associated type.
///
/// For example, consider `D` to be `AtomDomain<T>`, the domain of all non-null values of type `T`.
/// The implementation of this trait for `AtomDomain<T>` designates that `type Carrier = T`.
/// Thus `AtomDomain<T>::Carrier` is `T`.
///
/// # Proof Definition
/// `Self::Carrier` can represent all values in the set described by `Self`.
type Carrier;
/// Predicate to test an element for membership in the domain.
/// Not all possible values of `::Carrier` are a member of the domain.
///
/// # Proof Definition
/// For all settings of the input parameters,
/// returns `Err(e)` if the member check failed,
/// or `Ok(out)`, where `out` is true if `val` is a member of `self`, otherwise false.
///
/// # Notes
/// It generally suffices to treat `Err(e)` as if `val` is not a member of the domain.
/// It can be useful, however, to see richer debug information via `e` in the event of a failure.
fn member(&self, val: &Self::Carrier) -> Fallible<bool>;
}
/// A mathematical function which maps values from an input [`Domain`] to an output [`Domain`].
pub struct Function<TI, TO> {
pub function: Rc<dyn Fn(&TI) -> Fallible<TO>>,
}
impl<TI, TO> Clone for Function<TI, TO> {
fn clone(&self) -> Self {
Function {
function: self.function.clone(),
}
}
}
impl<TI, TO> Function<TI, TO> {
pub fn new(function: impl Fn(&TI) -> TO + 'static) -> Self {
Self::new_fallible(move |arg| Ok(function(arg)))
}
pub fn new_fallible(function: impl Fn(&TI) -> Fallible<TO> + 'static) -> Self {
Self {
function: Rc::new(function),
}
}
pub fn eval(&self, arg: &TI) -> Fallible<TO> {
(self.function)(arg)
}
}
impl<TI: 'static, TO: 'static> Function<TI, TO> {
pub fn make_chain<TX: 'static>(
function1: &Function<TX, TO>,
function0: &Function<TI, TX>,
) -> Function<TI, TO> {
let function0 = function0.function.clone();
let function1 = function1.function.clone();
Self::new_fallible(move |arg| function1(&function0(arg)?))
}
}
/// A representation of the distance between two elements in a set.
///
/// # Proof Definition
/// A type `Self` has an implementation for `Metric` iff it can represent a metric for quantifying distances between values in a set.
pub trait Metric: Default + Clone + PartialEq + Debug {
/// # Proof Definition
/// `Self::Distance` is a type that represents distances in terms of a metric `Self`.
type Distance;
}
/// A representation of the distance between two distributions.
///
/// # Proof Definition
/// A type `Self` has an implementation for `Measure` iff it can represent a measure for quantifying distances between distributions.
pub trait Measure: Default + Clone + PartialEq + Debug {
/// # Proof Definition
/// `Self::Distance` is a type that represents distances in terms of a measure `Self`.
type Distance;
}
/// A map evaluating the privacy of a [`Measurement`].
///
/// A `PrivacyMap` is implemented as a function that takes an input [`Metric::Distance`]
/// and returns the smallest upper bound on distances between output distributions on neighboring input datasets.
pub struct PrivacyMap<MI: Metric, MO: Measure>(
pub Rc<dyn Fn(&MI::Distance) -> Fallible<MO::Distance>>,
);
impl<MI: Metric, MO: Measure> Clone for PrivacyMap<MI, MO> {
fn clone(&self) -> Self {
PrivacyMap(self.0.clone())
}
}
impl<MI: Metric, MO: Measure> PrivacyMap<MI, MO> {
pub fn new(map: impl Fn(&MI::Distance) -> MO::Distance + 'static) -> Self {
PrivacyMap(Rc::new(move |d_in: &MI::Distance| Ok(map(d_in))))
}
pub fn new_fallible(map: impl Fn(&MI::Distance) -> Fallible<MO::Distance> + 'static) -> Self {
PrivacyMap(Rc::new(map))
}
pub fn new_from_constant(c: MO::Distance) -> Self
where
MI::Distance: Clone,
MO::Distance: DistanceConstant<MI::Distance>,
{
PrivacyMap::new_fallible(move |d_in: &MI::Distance| {
MO::Distance::inf_cast(d_in.clone())?.inf_mul(&c)
})
}
pub fn eval(&self, input_distance: &MI::Distance) -> Fallible<MO::Distance> {
(self.0)(input_distance)
}
}
impl<MI: 'static + Metric, MO: 'static + Measure> PrivacyMap<MI, MO> {
pub fn make_chain<MX: 'static + Metric>(
map1: &PrivacyMap<MX, MO>,
map0: &StabilityMap<MI, MX>,
) -> Self {
let map1 = map1.0.clone();
let map0 = map0.0.clone();
PrivacyMap(Rc::new(move |d_in: &MI::Distance| map1(&map0(d_in)?)))
}
}
/// A map evaluating the stability of a [`Transformation`].
///
/// A `StabilityMap` is implemented as a function that takes an input [`Metric::Distance`],
/// and returns the smallest upper bound on distances between output datasets on neighboring input datasets.
pub struct StabilityMap<MI: Metric, MO: Metric>(
pub Rc<dyn Fn(&MI::Distance) -> Fallible<MO::Distance>>,
);
impl<MI: Metric, MO: Metric> Clone for StabilityMap<MI, MO> {
fn clone(&self) -> Self {
StabilityMap(self.0.clone())
}
}
impl<MI: Metric, MO: Metric> StabilityMap<MI, MO> {
pub fn new(map: impl Fn(&MI::Distance) -> MO::Distance + 'static) -> Self {
StabilityMap(Rc::new(move |d_in: &MI::Distance| Ok(map(d_in))))
}
pub fn new_fallible(map: impl Fn(&MI::Distance) -> Fallible<MO::Distance> + 'static) -> Self {
StabilityMap(Rc::new(map))
}
pub fn new_from_constant(c: MO::Distance) -> Self
where
MI::Distance: Clone,
MO::Distance: DistanceConstant<MI::Distance>,
{
StabilityMap::new_fallible(move |d_in: &MI::Distance| {
MO::Distance::inf_cast(d_in.clone())?.inf_mul(&c)
})
}
pub fn eval(&self, input_distance: &MI::Distance) -> Fallible<MO::Distance> {
(self.0)(input_distance)
}
}
impl<MI: 'static + Metric, MO: 'static + Metric> StabilityMap<MI, MO> {
pub fn make_chain<MX: 'static + Metric>(
map1: &StabilityMap<MX, MO>,
map0: &StabilityMap<MI, MX>,
) -> Self {
let map1 = map1.0.clone();
let map0 = map0.0.clone();
StabilityMap(Rc::new(move |d_in: &MI::Distance| map1(&map0(d_in)?)))
}
}
/// A randomized mechanism with certain privacy characteristics.
///
/// The trait bounds provided by the Rust type system guarantee that:
/// * `input_domain` and `output_domain` are valid domains
/// * `input_metric` is a valid metric
/// * `output_measure` is a valid measure
///
/// It is, however, left to constructor functions to prove that:
/// * `input_metric` is compatible with `input_domain`
/// * `privacy_map` is a mapping from the input metric to the output measure
pub struct Measurement<DI: Domain, TO, MI: Metric, MO: Measure>
where
(DI, MI): MetricSpace,
{
pub input_domain: DI,
pub function: Function<DI::Carrier, TO>,
pub input_metric: MI,
pub output_measure: MO,
pub privacy_map: PrivacyMap<MI, MO>,
}
impl<DI: Domain, TO, MI: Metric, MO: Measure> Clone for Measurement<DI, TO, MI, MO>
where
(DI, MI): MetricSpace,
{
fn clone(&self) -> Self {
Self {
input_domain: self.input_domain.clone(),
function: self.function.clone(),
input_metric: self.input_metric.clone(),
output_measure: self.output_measure.clone(),
privacy_map: self.privacy_map.clone(),
}
}
}
impl<DI: Domain, TO, MI: Metric, MO: Measure> Measurement<DI, TO, MI, MO>
where
(DI, MI): MetricSpace,
{
pub fn new(
input_domain: DI,
function: Function<DI::Carrier, TO>,
input_metric: MI,
output_measure: MO,
privacy_map: PrivacyMap<MI, MO>,
) -> Fallible<Self> {
(input_domain.clone(), input_metric.clone()).assert_compatible()?;
Ok(Self {
input_domain,
function,
input_metric,
output_measure,
privacy_map,
})
}
pub fn invoke(&self, arg: &DI::Carrier) -> Fallible<TO> {
self.function.eval(arg)
}
pub fn map(&self, d_in: &MI::Distance) -> Fallible<MO::Distance> {
self.privacy_map.eval(d_in)
}
pub fn check(&self, d_in: &MI::Distance, d_out: &MO::Distance) -> Fallible<bool>
where
MO::Distance: TotalOrd,
{
d_out.total_ge(&self.map(d_in)?)
}
}
pub trait MetricSpace {
fn check(&self) -> bool;
fn assert_compatible(&self) -> Fallible<()> {
if !self.check() {
fallible!(FailedFunction, "metric and domain are not compatible")
} else {
Ok(())
}
}
}
/// A data transformation with certain stability characteristics.
///
/// The trait bounds provided by the Rust type system guarantee that:
/// * `input_domain` and `output_domain` are valid domains
/// * `input_metric` and `output_metric` are valid metrics
///
/// It is, however, left to constructor functions to prove that:
/// * metrics are compatible with domains
/// * `function` is a mapping from the input domain to the output domain
/// * `stability_map` is a mapping from the input metric to the output metric
#[derive(Clone)]
pub struct Transformation<DI: Domain, DO: Domain, MI: Metric, MO: Metric>
where
(DI, MI): MetricSpace,
(DO, MO): MetricSpace,
{
pub input_domain: DI,
pub output_domain: DO,
pub function: Function<DI::Carrier, DO::Carrier>,
pub input_metric: MI,
pub output_metric: MO,
pub stability_map: StabilityMap<MI, MO>,
}
impl<DI: Domain, DO: Domain, MI: Metric, MO: Metric> Transformation<DI, DO, MI, MO>
where
(DI, MI): MetricSpace,
(DO, MO): MetricSpace,
{
pub fn new(
input_domain: DI,
output_domain: DO,
function: Function<DI::Carrier, DO::Carrier>,
input_metric: MI,
output_metric: MO,
stability_map: StabilityMap<MI, MO>,
) -> Fallible<Self> {
(input_domain.clone(), input_metric.clone()).assert_compatible()?;
(output_domain.clone(), output_metric.clone()).assert_compatible()?;
Ok(Self {
input_domain,
output_domain,
function,
input_metric,
output_metric,
stability_map,
})
}
pub fn invoke(&self, arg: &DI::Carrier) -> Fallible<DO::Carrier> {
self.function.eval(arg)
}
pub fn map(&self, d_in: &MI::Distance) -> Fallible<MO::Distance> {
self.stability_map.eval(d_in)
}
pub fn check(&self, d_in: &MI::Distance, d_out: &MO::Distance) -> Fallible<bool>
where
MO::Distance: TotalOrd,
{
d_out.total_ge(&self.map(d_in)?)
}
}
#[cfg(test)]
mod tests {
use crate::domains::AtomDomain;
use crate::metrics::AbsoluteDistance;
use super::*;
#[test]
fn test_identity() -> Fallible<()> {
let input_domain = AtomDomain::<i32>::default();
let output_domain = AtomDomain::<i32>::default();
let function = Function::new(|arg: &i32| arg.clone());
let input_metric = AbsoluteDistance::<i32>::default();
let output_metric = AbsoluteDistance::<i32>::default();
let stability_map = StabilityMap::new_from_constant(1);
let identity = Transformation::new(
input_domain,
output_domain,
function,
input_metric,
output_metric,
stability_map,
)?;
let arg = 99;
let ret = identity.invoke(&arg)?;
assert_eq!(ret, 99);
Ok(())
}
}