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//! The Boolean circuit domain.
//!
//! As in the paper "Bootstrap Learning for Modular Concept Discovery" (2013).
//!
//! # Examples
//!
//! ```
//! use programinduction::domains::circuits;
//! use programinduction::{ECParams, EC};
//! use rand::{rngs::SmallRng, SeedableRng};
//!
//! let dsl = circuits::dsl();
//! let rng = &mut SmallRng::from_seed([1u8; 32]);
//! let tasks = circuits::make_tasks(rng, 250);
//! let ec_params = ECParams {
//! frontier_limit: 100,
//! search_limit_timeout: None,
//! search_limit_description_length: Some(9.0),
//! };
//!
//! let frontiers = dsl.explore(&ec_params, &tasks);
//! let hits = frontiers.iter().filter_map(|f| f.best_solution()).count();
//! assert!(40 < hits && hits < 80, "hits = {}", hits);
//! ```
use itertools::Itertools;
use polytype::{ptp, tp, Type, TypeScheme};
use rand::{
distributions::{Distribution, WeightedIndex},
Rng,
};
use std::iter;
use std::sync::Arc;
use crate::lambda::{Evaluator as EvaluatorT, Expression, Language};
use crate::Task;
/// The circuit representation, a [`lambda::Language`], only defines the binary `nand` operation.
///
/// ```compile_fails
/// "nand": ptp!(@arrow[tp!(bool), tp!(bool), tp!(bool)])
/// ```
///
/// [`lambda::Language`]: ../../lambda/struct.Language.html
pub fn dsl() -> Language {
Language::uniform(vec![(
"nand",
ptp!(@arrow[tp!(bool), tp!(bool), tp!(bool)]),
)])
}
/// All values in the circuits domain can be represented in this `Space`.
pub type Space = bool;
/// An [`Evaluator`] for the circuits domain.
///
/// # Examples
///
/// ```
/// use polytype::{ptp, tp};
/// use programinduction::domains::circuits;
/// use programinduction::{lambda, ECParams, EC};
///
/// let dsl = circuits::dsl();
///
/// let examples = vec![ // NOT
/// (vec![false], true),
/// (vec![true], false),
/// ];
/// let task = lambda::task_by_evaluation(
/// circuits::Evaluator,
/// ptp!(@arrow[tp!(bool), tp!(bool)]),
/// &examples,
/// );
/// let ec_params = ECParams {
/// frontier_limit: 1,
/// search_limit_timeout: None,
/// search_limit_description_length: Some(5.0),
/// };
///
/// let frontiers = dsl.explore(&ec_params, &[task]);
/// let (expr, _logprior, _loglikelihood) = frontiers[0].best_solution().unwrap();
/// assert_eq!(dsl.display(expr), "(λ (nand $0 $0))");
/// ```
///
/// [`Evaluator`]: ../../lambda/trait.Evaluator.html
#[derive(Copy, Clone)]
pub struct Evaluator;
impl EvaluatorT for Evaluator {
type Space = Space;
type Error = ();
fn evaluate(&self, primitive: &str, inp: &[Self::Space]) -> Result<Self::Space, Self::Error> {
match primitive {
"nand" => Ok(!(inp[0] & inp[1])),
_ => unreachable!(),
}
}
}
/// Randomly sample a number of circuits into [`Task`]s.
///
/// For a circuit, the number of inputs is sampled from 1 to 6 with weights 1, 2, 3, 4, 4, and 4
/// respectively. The number of gates is sampled from 1 to 3 with weights 1, 2, and 2 respectively.
/// The gates themselves are sampled from NOT, AND, OR, and MUX2 with weights 1, 2, 2, and 4,
/// respectively. All circuits are connected: every input is used and every gate's output is either
/// wired to another gate or to the circuits final output.
///
/// The task observations are outputs of the truth table in sequence, for example
///
/// ```text
/// --- INPUTS --- OUTPUTS
/// false, false, false => false
/// false, false, true => false
/// false, true, false => false
/// false, true, true => false
/// true, false, false => false
/// true, false, true => false
/// true, true, false => false
/// true, true, true => true
/// ```
///
/// [`Task`]: ../../struct.Task.html
pub fn make_tasks<R: Rng>(
rng: &mut R,
count: u32,
) -> Vec<impl Task<[bool], Representation = Language, Expression = Expression>> {
make_tasks_advanced(
rng,
count,
[1, 2, 3, 4, 4, 4, 0, 0],
[1, 2, 2, 0, 0, 0, 0, 0],
1,
2,
2,
4,
0,
)
}
/// Like [`make_tasks`], but with a configurable circuit distribution.
///
/// This works by randomly constructing Boolean circuits, consisting of some number of inputs and
/// some number of gates transforming those inputs into final output. The resulting truth table
/// serves the task's oracle, providing a log-likelihood of `0.0` for success
/// and `f64::NEG_INFINITY` for failure.
///
/// The `n_input_weights` and `n_gate_weights` arguments specify the relative distributions for the
/// number of inputs/gates respectively from 1 to 8. The `gate_` arguments are relative
/// weights for sampling the respective logic gate.
/// Sample circuits which are invalid (i.e. not connected) are rejected.
///
/// [`make_tasks`]: fn.make_tasks.html
#[allow(clippy::too_many_arguments)]
pub fn make_tasks_advanced<R: Rng>(
rng: &mut R,
count: u32,
n_input_weights: [u32; 8],
n_gate_weights: [u32; 8],
gate_not: u32,
gate_and: u32,
gate_or: u32,
gate_mux2: u32,
gate_mux4: u32,
) -> Vec<impl Task<[bool], Representation = Language, Expression = Expression>> {
let n_input_distribution =
WeightedIndex::new(n_input_weights).expect("invalid weights for number of circuit inputs");
let n_gate_distribution =
WeightedIndex::new(n_gate_weights).expect("invalid weights for number of circuit gates");
let gate_weights = WeightedIndex::new([gate_not, gate_and, gate_or, gate_mux2, gate_mux4])
.expect("invalid weights for circuit gates");
(0..count)
.map(move |_| {
let mut n_inputs = 1 + n_input_distribution.sample(rng);
let mut n_gates = 1 + n_gate_distribution.sample(rng);
while n_inputs / n_gates >= 3 {
n_inputs = 1 + n_input_distribution.sample(rng);
n_gates = 1 + n_gate_distribution.sample(rng);
}
let circuit = gates::Circuit::new(rng, &gate_weights, n_inputs as u32, n_gates);
let outputs: Vec<_> = iter::repeat(vec![false, true])
.take(n_inputs)
.multi_cartesian_product()
.map(|ins| circuit.eval(&ins))
.collect();
CircuitTask::new(n_inputs, outputs)
})
.collect()
}
struct CircuitTask {
n_inputs: usize,
expected_outputs: Vec<bool>,
tp: TypeScheme,
}
impl CircuitTask {
fn new(n_inputs: usize, expected_outputs: Vec<bool>) -> Self {
let tp = TypeScheme::Monotype(Type::from(vec![tp!(bool); n_inputs + 1]));
CircuitTask {
n_inputs,
expected_outputs,
tp,
}
}
}
impl Task<[bool]> for CircuitTask {
type Representation = Language;
type Expression = Expression;
fn oracle(&self, dsl: &Self::Representation, expr: &Self::Expression) -> f64 {
let evaluator = Arc::new(Evaluator);
let success = iter::repeat(vec![false, true])
.take(self.n_inputs)
.multi_cartesian_product()
.zip(&self.expected_outputs)
.all(|(inps, out)| {
if let Ok(o) = dsl.eval_arc(expr, &evaluator, &inps) {
o == *out
} else {
false
}
});
if success {
0f64
} else {
f64::NEG_INFINITY
}
}
fn tp(&self) -> &TypeScheme {
&self.tp
}
fn observation(&self) -> &[bool] {
&self.expected_outputs
}
}
mod gates {
use rand::{
distributions::{Distribution, WeightedIndex},
seq::index::sample,
Rng,
};
const GATE_CHOICES: [Gate; 5] = [Gate::Not, Gate::And, Gate::Or, Gate::Mux2, Gate::Mux4];
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
pub enum Gate {
Not,
And,
Or,
Mux2,
Mux4,
}
impl Gate {
fn n_inputs(self) -> u32 {
match self {
Gate::Not => 1,
Gate::And | Gate::Or => 2,
Gate::Mux2 => 3,
Gate::Mux4 => 6,
}
}
fn eval(self, inp: &[bool]) -> bool {
match self {
Gate::Not => !inp[0],
Gate::And => inp[0] & inp[1],
Gate::Or => inp[0] | inp[1],
Gate::Mux2 => [inp[0], inp[1]][inp[2] as usize],
Gate::Mux4 => {
[inp[0], inp[1], inp[2], inp[3]][((inp[5] as usize) << 1) + inp[4] as usize]
}
}
}
}
#[derive(Debug, PartialEq, Eq)]
pub struct Circuit {
n_inputs: u32,
operations: Vec<(Gate, Vec<u32>)>,
}
impl Circuit {
pub fn new<T: Rng>(
rng: &mut T,
gate_distribution: &WeightedIndex<u32>,
n_inputs: u32,
n_gates: usize,
) -> Self {
loop {
let mut operations = Vec::with_capacity(n_gates);
while operations.len() < n_gates {
let gate = GATE_CHOICES[gate_distribution.sample(rng)];
let n_lanes = n_inputs + (operations.len() as u32);
if gate.n_inputs() > n_lanes {
continue;
}
let args = sample(rng, n_lanes as usize, gate.n_inputs() as usize)
.into_iter()
.map(|x| x as u32)
.collect();
operations.push((gate, args));
}
let circuit = Circuit {
n_inputs,
operations,
};
if circuit.is_connected() {
break circuit;
}
}
}
/// A circuit is connected if every output except for the last one is an input for some
/// other gate.
fn is_connected(&self) -> bool {
let n_lanes = self.n_inputs as usize + self.operations.len();
let mut is_used = vec![false; n_lanes];
for (_, args) in &self.operations {
for i in args {
is_used[*i as usize] = true;
}
}
is_used.pop();
is_used.into_iter().all(|x| x)
}
pub fn eval(&self, inp: &[bool]) -> bool {
let mut lanes = inp.to_vec();
for (gate, args) in &self.operations {
let gate_inp: Vec<bool> = args.iter().map(|a| lanes[*a as usize]).collect();
lanes.push(gate.eval(&gate_inp));
}
lanes.pop().unwrap()
}
}
}