Lambda Calculus Visualizer

This application is a Dash-based tool for visualizing and evaluating lambda calculus expressions. It features an interactive tree view rendered with dash-cytoscape, allowing users to perform beta reductions and arithmetic operations step-by-step.

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Installation

• Ensure you have:

  • Python 3.11+

• Clone the repository:

  git clone https://github.com/linnerlek/Lambda-Engine.git
  cd Lambda-Engine/

• Install dependencies:

  pip3 install -r requirements.txt

• Start the application with:

  python app.py --hostname <hostname> --port <port>

  • If you do not specify the hostname and port by default localhost and 8081 will be used

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Usage

1. Enter a lambda expression in the input box
2. Click "Submit" to visualize the expression tree
3. Interact with the tree:
   • Green nodes: click to perform beta reduction
   • Operator nodes: click to evaluate arithmetic
4. Use "Back" to return to previous states
5. Use "Reset" to start over

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Expression Format

Node types

• Lambda abstractions: triangles
• Applications: circles (green when reducible)
• Variables/numbers: rectangles

Grammar

A lambda expression is defined inductively as follows:

• A variable is a lambda expression (e.g. x, y, m, n, etc)
• A number is a lambda expression (e.g. 10, 2, -5, 6.5, etc)
• If M is a lambda expression and x is a variable, then (lambda x M) - is a lambda expression
• If M and N are lambda expressions then (M N) is a lambda expression
• If M and N are lambda expressions then (op M N) is a lambda expression, where op is +, -, *, or /

Examples

(((lambda x (lambda y (+ x y))) 10) 5);

(((lambda f (lambda x (f x))) (lambda y (* y y))) 12);

((((lambda f (lambda x ((f x) f))) (lambda y (lambda g (g (* y y))))) 2) (lambda a a));

(lambda f ((lambda x (f (x x)))(lambda x (f (x x)))));

Note: Terminate all expressions with a semicolon (;).