PhDP

import data.real.basic

#check ℝ

open nat

-- Links:
-- * Lean 3's big math library: https://github.com/leanprover-community/mathlib
-- * Number game: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/
-- * Agda's Unimath library: https://github.com/UniMath/agda-unimath

PhDP

def hello := "world"

open List

#check Nat.zero
#check Nat.succ
#check Nat.succ 0
#check Nat.add
#check Nat.add 1
#check Nat.add 2 2

PhDP

fn nth_primes(n: usize) -> usize {
    match n {
        0 => 1,
        1 => 2,
        2 => 3,
        _ => {
            let mut primes = vec![2, 3];
            let mut candidate = 5;
            loop {
                let max = (candidate as f64).sqrt() as usize;

PhDP

/// You need to add these lines to Cargo.toml's [dependencies]:
/// statrs = "0.15.0"
/// nalgebra = "0.29.0"

use statrs::distribution::{Binomial, Discrete};
use nalgebra::base::DVector;
use nalgebra::dvector;

// Builds a vector of evenly spaced floats within a closed interval [a, b].
pub fn linspace(a: f64, b: f64, n: usize) -> DVector<f64> {

PhDP

Installing Rust

Most editors/IDEs have good Rust support at this point, but I recommend Visual Code with Rust Analyzer.

Linux or OSX

Simply copy and paste the command from the rustup website (here) in a terminal. Rustup will install the rustc compiler and, just as importantly, the cargo package manager.

PhDP

# A graph as a vector of sorted vectors. This is very similar to the way sparse matrices
# are represented except each vertex has its own sorted vector (making it much faster to
# add/remove edges). Using BTrees instead of sorted vector would improve performance for
# adding/removing edges.

#WeightedGraph = Vector{Vector{(UInt32, Float64)}}
Graph = Vector{Vector{UInt32}} # Make more generic...

# There has to be a better way (map?):
function make_graph(order)

PhDP

/**
 * @file grammatical_evolution.h
 * @brief Functions to use grammatical evolution to evolve programs, mathematical
 * functions, sentences, whatever you want, just use your imagination!
 */
#ifndef RAW_GRAMMATICAL_EVOLUTION_H_
#define RAW_GRAMMATICAL_EVOLUTION_H_

#include "raw/common.h"
#include "raw/grammar.h"

PhDP

<expr>      ::= dS/dt = <formula>\ndI/dt = <formula>\ndR/dt = <formula>
<formula>   ::= <unary><formula> | <formula> <operator> <formula> | <formula> <operator> <variable> | <variable> <operator> <formula> | <variable>
<unary>     ::= -
<operator>  ::= - | *
<variable>  ::= a | b | I | S

PhDP

Codon size: 100
0: dS/dt = a\ndI/dt = I\ndR/dt = S
1: dS/dt = S - S - b * S - a\ndI/dt = S * I - I - a * S * a * -I * b - I * a * S * a * b * a - I - a\ndR/dt = --a - --I - a * b * -a * ---S - S * a * a - a * a
4: dS/dt = -a - I - b\ndI/dt = S - b - --b - a * -b * a * b - S - S - I\ndR/dt = a * a * S * b - I
7: dS/dt = a\ndI/dt = S * a\ndR/dt = b - I
9: dS/dt = b * S * S\ndI/dt = I * I - b * S * a\ndR/dt = -b - I - b * S - S * S * a * b
12: dS/dt = I * b * S\ndI/dt = -a - I - a * a - S\ndR/dt = S * S * b * -S - S - -S - a - -b - -a - b - a - b - S - S * I - ---b - a - S * S - I * b * S - -a - I - a * a - a * I - b * S * b * -S - S - -S - a - -b - -a - b - a - b - S
15: dS/dt = -I - S\ndI/dt = --a - -b - b\ndR/dt = -a - b - S * b - a - S * -S * -b - S
16: dS/dt = a * b\ndI/dt = -b * b\ndR/dt = b - I - a * b - a * I
17: dS/dt = I * I * a - I\ndI/dt = a * a - -S - ----S - -a * --b - b - S * I - a * b - a\ndR/dt = S - a

PhDP

// C++17

#include <iostream>
#include <array>
#include <initializer_list>

// Column-major matrix based on std::array.
template<size_t ROW, size_t COL, typename T>
class matrix {
 public: