lambda_calculus is a simple, zero-dependency implementation of pure lambda calculus in Safe Rust.
- a parser for lambda expressions, both in classic and De Bruijn index notation
- 7 β-reduction strategies
- a set of standard terms (combinators)
- lambda-encoded boolean, pair, tuple, option and result data types
- single-pair-encoded list
- Church-, Scott- and Parigot-encoded numerals and lists
- Stump-Fu (embedded iterators)- and binary-encoded numerals
- signed numbers
Include the library by adding the following to your Cargo.toml:
[dependencies]
lambda_calculus = "3"Compilation features:
backslash_lambda: changes the display of lambdas fromλto\encoding: builds the data encoding modules; default feature
Example feature setup in Cargo.toml:
[dependencies.lambda_calculus]
version = "3"
default-features = false # do not build the data encoding modules
features = ["backslash_lambda"] # use a backslash lambdacode:
use lambda_calculus::data::num::church::{succ, pred};
fn main() {
println!("SUCC := {0} = {0:?}", succ());
println!("PRED := {0} = {0:?}", pred());
}stdout:
SUCC := λa.λb.λc.b (a b c) = λλλ2(321)
PRED := λa.λb.λc.a (λd.λe.e (d b)) (λd.c) (λd.d) = λλλ3(λλ1(24))(λ2)(λ1)
code:
use lambda_calculus::*;
fn main() {
assert_eq!(
parse(&"λa.λb.λc.b (a b c)", Classic),
parse(&"λλλ2(321)", DeBruijn)
);
}code:
use lambda_calculus::*;
use lambda_calculus::data::num::church::pred;
fn main() {
let mut expr = app!(pred(), 1.into_church());
println!("{} order β-reduction steps for PRED 1 are:", NOR);
println!("{}", expr);
while expr.reduce(NOR, 1) != 0 {
println!("{}", expr);
}
}stdout:
normal order β-reduction steps for PRED 1 are:
(λa.λb.λc.a (λd.λe.e (d b)) (λd.c) (λd.d)) (λa.λb.a b)
λa.λb.(λc.λd.c d) (λc.λd.d (c a)) (λc.b) (λc.c)
λa.λb.(λc.(λd.λe.e (d a)) c) (λc.b) (λc.c)
λa.λb.(λc.λd.d (c a)) (λc.b) (λc.c)
λa.λb.(λc.c ((λd.b) a)) (λc.c)
λa.λb.(λc.c) ((λc.b) a)
λa.λb.(λc.b) a
λa.λb.b
code:
use lambda_calculus::*;
use lambda_calculus::data::num::church::fac;
fn main() {
let expr = app(fac(), 3.into_church());
println!("comparing normalizing orders' reduction step count for FAC 3:");
for &order in [NOR, APP, HNO, HAP].iter() {
println!("{}: {}", order, expr.clone().reduce(order, 0));
}
}stdout:
comparing normalizing orders' reduction step count for FAC 3:
normal: 46
applicative: 39
hybrid normal: 46
hybrid applicative: 39
code:
use lambda_calculus::*;
fn main() {
println!("comparing different encodings of number 3 (De Bruijn indices):");
println!(" Church encoding: {:?}", 3.into_church());
println!(" Scott encoding: {:?}", 3.into_scott());
println!(" Parigot encoding: {:?}", 3.into_parigot());
println!("Stump-Fu encoding: {:?}", 3.into_stumpfu());
println!(" binary encoding: {:?}", 3.into_binary());
}stdout:
comparing different encodings of number 3 (De Bruijn indices):
Church encoding: λλ2(2(21))
Scott encoding: λλ1(λλ1(λλ1(λλ2)))
Parigot encoding: λλ2(λλ2(λλ2(λλ1)1)(2(λλ1)1))(2(λλ2(λλ1)1)(2(λλ1)1))
Stump-Fu encoding: λλ2(λλ2(2(21)))(λλ2(λλ2(21))(λλ2(λλ21)(λλ1)))
binary encoding: λλλ1(13)