lambda-calculus-game-of-life

λ-calculus implementations of Conway's Game of Life

An implementation of Conway's Game of Life written in JavaScript using λ-calculus. The full implementation contains in lambda-calculus.js file.

Rules being used for building terms:

1. Function parameter or alias to previously defined terms:

   x
   

2. Creating alias for term:

   const x = $TERM$;
   

3. Lambda abstraction:

   Lambda is a function taking one argument and returning some value.

   There's two ways to define an lambda abstraction:

   (x) => $TERM$
   

   or

   (x) => {
       const y = $TERM_Y$; 
   
       return $RETURN_TERM$;
   }
   

   Every lambda function should contain only one return statement (inner functions do not count).

4. A function application:

   fun(arg)
   

   It is forbidden to use recursion:

   const fun = (x) => {
       return fun(x); /* FORBIDDEN */
   };
   

These rules mean, that it's forbidden to use any libraries (even stdlib), primitives, classes, ifs, whiles, lambdas with 0, 2 or more arguments, lambdas returning void, arrays and other things. The only building block is lambda function, taking 1 argument and returning value.

Rules above may be ignored only in modules, responsible for unit testing or interaction with "outer world" (console.log). These modules are defined in files lambda-calculus.test.ts, lambda-calculus.frontend.ts, conway-game-of-life.frontend.ts.

This app is created for educational purposes. The performance of this app is extremely low, this is not a way how read-world apps are being written.

Run the app using command:

deno task game-of-life