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https://github.com/haraldmaida/lamcal

A lambda calculus parser, evaluator and repl
https://github.com/haraldmaida/lamcal

calculus evaluator lambda math parser repl sciene

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A lambda calculus parser, evaluator and repl

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README 

        

# Lamcal



[![Crates.io][crates_badge]][crate]

[![Docs.rs][docs_badge]][documentation]

[![Linux Build Status][travis_badge]][Travis CI]

[![Windows Build Status][appveyor_badge]][Appveyor CI]

[![codevoc.io][codecov_badge]][codecoverage]

[![Apache-2.0][license_badge]][Apache-2.0]



[crates_badge]: https://img.shields.io/crates/v/lamcal.svg

[docs_badge]: https://docs.rs/lamcal/badge.svg

[travis_badge]: https://travis-ci.org/haraldmaida/lamcal.svg?branch=master

[appveyor_badge]: https://ci.appveyor.com/api/projects/status/github/haraldmaida/lamcal?branch=master&svg=true

[codecov_badge]: https://codecov.io/gh/haraldmaida/lamcal/branch/master/graph/badge.svg

[license_badge]: https://img.shields.io/badge/license-Apache%2D%2D2%2E0-blue.svg



[crate]: https://crates.io/crates/lamcal

[documentation]: https://docs.rs/lamcal

[Travis CI]: https://travis-ci.org/haraldmaida/lamcal

[Appveyor CI]: https://ci.appveyor.com/project/innoave/lamcal

[codecoverage]: https://codecov.io/github/haraldmaida/lamcal?branch=master

[Apache-2.0]: https://www.apache.org/licenses/LICENSE-2.0

[license]: LICENSE

[lamcal]: https://github.com/haraldmaida/lamcal

[lamcal-repl]: https://github.com/haraldmaida/lamcal/tree/master/repl



[lamcal] is a [Lambda Calculus] parser and evaluator and a separate command line REPL application 

to play around with lambda expressions interactively. All code is written in [Rust].

 

Highlights:



* Implementation of the pure untyped lambda calculus

* Support for arbitrary huge terms by using trampolining instead of recursion in all functions

* Feature rich [command line REPL application]((https://github.com/haraldmaida/lamcal/tree/master/repl))

  ([separate crate](https://crates.io/crates/lamcal-repl))

 

The library can be used to

    

* parse lambda expressions in classic notation into terms, like `parse_str("(λx.(λy.x y) a) b")`

  
 or `parse_str("(\\x.(\\y.x y) a) b")`

* construct terms programmatically using functions, e.g. `lam("x", app(var("x"), var("y")))`

* construct a sequence of function applications using the macro `app!`, e.g.

  `app![var("a"), var("b"), var("c")]` which is equivalent to 

  `app(app(var("a"), var("b")), var("c))`

* evaluate lambda terms to replace variables with predefined terms bound to the variable's name in

  the environment  

* apply α-conversion to terms using different strategies, such as enumeration or appending the tick

  symbol

* apply β-reduction to terms using different strategies, such as call-by-name, normal-order or 

  call-by-value

* be extended by implementing user specific strategies for α-conversion and β-reduction.



The separate crate [lamcal-repl] 

([crate](https://crates.io/crates/lamcal-repl), 

 [github-repository](https://github.com/haraldmaida/lamcal/tree/master/repl)

)

provides the command line REPL (read-evaluate-print-loop) application to play around with lambda 

calculus terms and applying α-conversion and β-reduction interactively.



Features:



* Evaluation functions are provided in two variants: An associated function, e.g. `Term::reduce`,

  that mutates the term in place and a standalone function, e.g. `reduce`, that leaves the original

  term unchanged and returns the result as a new term.

* Strategies for α-conversion and β-reduction are defined as traits to easily implement custom

  strategies and use it with the functionality of this library.

* Inspection system to inspect every single intermediate state of a term during evaluation and 

  reduction and to stop processing depending on arbitrary conditions.

* No recursion in any of the functions dealing with the recursive data structure of `Term` to avoid

  stack overflow errors when applied on huge terms. Instead all functions follow the trampolining

  pattern.

* The parser gives detailed information about parse errors, like the position of the error in the 

  source stream and what would have been expected instead in a valid expression.

* Optional support for [`failure`] crate compatible error types.  



## Usage



To use [lamcal] as a library in your project add this to your `Cargo.toml` file:



```toml

[dependencies]

lamcal = "0.4"

```



and this to your crate root:



```rust

extern crate lamcal;

```



For details about the library see the [documentation] at crates.io.



This library optionally supports the [`failure`] crate. The support for the `failure` crate is a crate

feature. To enable it add the dependency to your `Cargo.toml` like so:



```toml

[dependencies]

lamcal = { version = "0.4", features = ["failure"] }

```



## License



Licensed under Apache License, Version 2.0


see [LICENSE] or http://www.apache.org/licenses/LICENSE-2.0 for details.



### Contribution



Unless you explicitly state otherwise, any contribution intentionally submitted

for inclusion in the work by you, as defined in the Apache-2.0 license, shall be

licensed as above, without any additional terms or conditions.



--------------------------------------------------------------------------------

[`failure`]: https://crates.io/crates/failure

[de bruijn index]: https://en.wikipedia.org/wiki/De_Bruijn_index

[krivine machine]: https://en.wikipedia.org/wiki/Krivine_machine

[lambda calculus]: https://en.wikipedia.org/wiki/Lambda_calculus

[lcss]: https://www.youtube.com/watch?v=GYCYq0lEFhE

[rust]: https://www.rust-lang.org

[SECD machine]: https://en.wikipedia.org/wiki/SECD_machine