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https://github.com/gurbaaz27/typeless
an interpreter for λ-calculus implemented in ruby
https://github.com/gurbaaz27/typeless
abstract-syntax-tree beta-reduction compiler interpreter lambda-calculus lexer-parser ll1-grammar ll1-parser parser ruby
Last synced: 3 months ago
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an interpreter for λ-calculus implemented in ruby
- Host: GitHub
- URL: https://github.com/gurbaaz27/typeless
- Owner: gurbaaz27
- License: mit
- Created: 2022-11-01T15:54:37.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-06-08T08:22:00.000Z (8 months ago)
- Last Synced: 2024-06-08T09:33:59.112Z (8 months ago)
- Topics: abstract-syntax-tree, beta-reduction, compiler, interpreter, lambda-calculus, lexer-parser, ll1-grammar, ll1-parser, parser, ruby
- Language: Ruby
- Homepage:
- Size: 226 KB
- Stars: 17
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Typeless
## λ-calculus interpreter
### Table of Contents
- [Description](#description)
- [Features](#features)
- [Code Structure](#code-structure)
- [Usage](#usage)
- [Demo Example](#demo-example)
- [Team Members](#team-members)
## Description
An interpreter for λ-calculus implemented in `ruby`, as part of our course project CS350A: Principles of Programming Languages under Prof. Satyadev Nandakumar, in Fall Semester 2022-23, IIT Kanpur.
The grammar specification is:
```
λ − term ::= variable |
(\variable · λ − term) |
[λ − term][λ − term]
The allowed variables are single lowercase English letters - a, b, c etc.
```
### Features
It supports the following features:
- [x] Lexer and grammar checker for lambda term expression using LL(1) parser
- [x] Determine free variables in given lambda term
- [x] Free variables substitution
- [x] Alpha Renaming and Beta Reduction
### Code Structure
```bash
.
├── assets/
├── lexer.rb
├── LICENSE
├── main.rb
├── parser.rb
├── README.md
├── reducer.rb
├── tests/
└── utils.rb
2 directories, 14 files
```
## Usage
Keep your λ-expression in a file and pass its filepath as an argument to `main.rb`.
```bash
Lambda Calculus Interpreter
===========================
Usage: main.rb [options]
-i, --input FILE Input file containing λ-expression
-o, --output FILE (Optional) Output file to store reduced λ-expression. Default: out.txt
```
### Demo Example
**Note** that we use the notation of `v{i}`, where `i := [1,2,3,...]` for our bound variables after the processing of alpha-renaming and beta-reduction. This helps in easily identifying the bound variables and keep their count in the final reduced form.
```bash
$ ruby main.rb -i tests/9.lc ## or
$ ruby main.rb --input=tests/9.lc
================
Course Project
Lambda Calculus Interpreter
Created by: Ayush, Gurbaaz and Kritin
================
Grammar checker :-
[ ( \ x . x ) ] [ y ] is a valid lambda term
================
Free variables :- y
================
α-renaming :- [ ( \ v0 . v0 ) ] [ y ]
================
> Please provide the free variable name along with its substitution. e.g. x:=M denotes replacing free occurences of x with lambda term M
> or press ENTER to finish
y:=(\x.x)
Free variable substitution :- [ ( \ v1 . v1 ) ] [ ( \ v2 . v2 ) ]
================
> All free variables have been substituted successfully! (Closed Form)
Exiting...
================
β-reduction :-
Step 1. ( \ v2 . v2 )
No further reduction possible!
================
Final β-reduced form '( \ v2 . v2 )' saved to 'out.txt'
================
```
You may find some of the lambda expression files in `tests/` directory.
## Team Members
Ayush Kumar
Gurbaaz Singh Nandra
![]()
Kritin Sharma
## Star History
[](https://star-history.com/#gurbaaz27/typeless&Date)