lambda_calculus

license current version

lambda_calculus is a simple implementation of the untyped lambda calculus in Rust.

The data and operators follow the Church encoding. The terms are implemented using De Bruijn indices, but are displayed using the classic lambda notation and can be parsed both ways. Library functions utilizing the fixed-point combinator use its call-by-value variant and are built for compatibility with as many β-reduction strategies as possible.

The library contains:

The implementation tries to find a compromise between the spirit of the lambda calculus and Rust's best practices; the lambda Terms implemented by the library are produced by functions (in order to allow arbitrary application), but they are not Copyable and the methods they provide allow memory-friendly disassembly and referencing their internals.

Documentation

Example usage

code: ``` // SHOW_REDUCTIONS [@reduction.rs] = true;

[macro_use]

extern crate lambda_calculus;

use lambdacalculus::reduction::Order::*; use lambdacalculus::arithmetic::pred;

fn main() { let mut expr = app!(pred(), 1.into());

expr.beta(NOR, 0);

} stdout: β-reducing (λa.λb.λc.a (λd.λe.e (d b)) (λd.c) (λd.d)) (λa.λb.a b) [normal order]:

  1. (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)

  2. (λc.λd.c d) (λc.λd.d (c a)) => λc.(λd.λe.e (d a)) c

  3. (λc.(λd.λe.e (d a)) c) (λc.b) => (λc.λd.d (c a)) (λc.b)

  4. (λc.λd.d (c a)) (λc.b) => λc.c ((λd.b) a)

  5. (λc.c ((λd.b) a)) (λc.c) => (λc.c) ((λc.b) a)

  6. (λc.c) ((λc.b) a) => (λc.b) a

  7. (λc.b) a => b

result after 7 reductions: λa.λb.b ```

Status

The library is in a good shape and should soon begin to stabilize.

TODO