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Symbolic differentiation (#4)

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This commit is contained in:
Patrick Stevens
2023-03-24 21:10:36 +00:00
committed by GitHub
parent c3bfeb0762
commit adff7ac3fd
4 changed files with 275 additions and 0 deletions
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115
Cargo.lock generated
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@@ -2,6 +2,121 @@
# It is not intended for manual editing. # It is not intended for manual editing.
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1
Cargo.toml
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@@ -6,3 +6,4 @@ edition = "2021"
# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
[dependencies] [dependencies]
immutable-chunkmap = "1.0.5"

157
src/expr_syntax_tree.rs Normal file
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@@ -0,0 +1,157 @@
#![allow(dead_code)]
use immutable_chunkmap::map;
use std::ops::{Add, Mul};
/*
An untyped syntax tree for an expression whose constants are all of type `A`.
*/
#[derive(Clone, Debug)]
pub enum Expr<A> {
Const(A),
Sum(Box<Expr<A>>, Box<Expr<A>>),
Variable(u32),
// The first `Expr` here is a function, which may reference the input variable `Variable(i)`.
// For example, `(fun x y -> x + y) 3 4` is expressed as:
// Apply(0, Apply(1, Sum(Variable(0), Variable(1)), Const(4)), Const(3))
Apply(u32, Box<Expr<A>>, Box<Expr<A>>),
Mul(Box<Expr<A>>, Box<Expr<A>>),
}
impl<A> Expr<A> {
fn eval_inner<const SIZE: usize>(e: &Expr<A>, ctx: &map::Map<u32, A, SIZE>) -> A
where
A: Clone + Add<Output = A> + Mul<Output = A>,
{
match &e {
Expr::Const(x) => x.clone(),
Expr::Sum(x, y) => Expr::eval_inner(x, ctx) + Expr::eval_inner(y, ctx),
Expr::Variable(id) => ctx
.get(id)
.unwrap_or_else(|| panic!("No binding found for free variable {}", id))
.clone(),
Expr::Apply(variable, func, arg) => {
let arg = Expr::eval_inner(arg, ctx);
let (updated_context, _) = ctx.insert(*variable, arg);
Expr::eval_inner(func, &updated_context)
}
Expr::Mul(x, y) => Expr::eval_inner(x, ctx) * Expr::eval_inner(y, ctx),
}
}
pub fn eval<const MAX_VAR_NUM: usize>(e: &Expr<A>) -> A
where
A: Clone + Add<Output = A> + Mul<Output = A>,
{
Expr::eval_inner(e, &map::Map::<u32, A, MAX_VAR_NUM>::new())
}
pub fn apply(var: u32, f: Expr<A>, arg: Expr<A>) -> Expr<A> {
Expr::Apply(var, Box::new(f), Box::new(arg))
}
pub fn sum(x: Expr<A>, y: Expr<A>) -> Expr<A> {
Expr::Sum(Box::new(x), Box::new(y))
}
pub fn mul(x: Expr<A>, y: Expr<A>) -> Expr<A> {
Expr::Mul(Box::new(x), Box::new(y))
}
pub fn differentiate(one: &A, zero: &A, var: u32, f: &Expr<A>) -> Expr<A>
where
A: Clone,
{
match f {
Expr::Const(_) => Expr::Const(zero.clone()),
Expr::Sum(x, y) => Expr::sum(
Expr::differentiate(one, zero, var, x),
Expr::differentiate(one, zero, var, y),
),
Expr::Variable(i) => {
if *i == var {
Expr::Const(one.clone())
} else {
Expr::Const(zero.clone())
}
}
Expr::Mul(x, y) => Expr::sum(
Expr::Mul(
Box::new(Expr::differentiate(one, zero, var, x.as_ref())),
(*y).clone(),
),
Expr::Mul(
Box::new(Expr::differentiate(one, zero, var, y.as_ref())),
(*x).clone(),
),
),
Expr::Apply(new_var, func, expr) => {
if *new_var == var {
panic!(
"cannot differentiate with respect to variable {} that's been assigned",
var
)
}
let expr_deriv = Expr::differentiate(one, zero, var, expr);
Expr::mul(
expr_deriv,
Expr::Apply(
*new_var,
Box::new(Expr::differentiate(one, zero, *new_var, func)),
(*expr).clone(),
),
)
}
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_expr() {
let expr = Expr::apply(
0,
Expr::apply(
1,
Expr::sum(Expr::Variable(0), Expr::Variable(1)),
Expr::Const(4),
),
Expr::Const(3),
);
assert_eq!(Expr::eval::<2>(&expr), 7);
}
#[test]
fn test_derivative() {
let add_four = Expr::sum(Expr::Variable(0), Expr::Const(4));
let mul_five = Expr::mul(Expr::Variable(1), Expr::Const(5));
{
let mul_five_then_add_four = Expr::apply(0, add_four.clone(), mul_five.clone());
let mul_then_add_diff = Expr::differentiate(&1, &0, 1, &mul_five_then_add_four);
for i in 3..10 {
// (5x + 4) differentiates to 5
assert_eq!(
Expr::eval::<2>(&Expr::apply(1, mul_then_add_diff.clone(), Expr::Const(i))),
5
);
}
}
{
let add_four_then_mul_five = Expr::apply(1, mul_five.clone(), add_four.clone());
let add_then_mul_diff = Expr::differentiate(&1, &0, 0, &add_four_then_mul_five);
for i in 3..10 {
// ((x + 4) * 5) differentiates to 5
assert_eq!(
Expr::eval::<2>(&Expr::apply(0, add_then_mul_diff.clone(), Expr::Const(i))),
5
);
}
}
}
}

2
src/main.rs
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@@ -1,3 +1,5 @@
mod expr_syntax_tree;
use std::iter::Sum; use std::iter::Sum;
use std::ops::{Mul, Sub}; use std::ops::{Mul, Sub};