lambda

A Lambda Calculus interpreter. Uses PEG.js, CoffeeScript, and Underscore.

See also A Tutorial Introduction to the Lambda Calculus by Raul Rojas

The story:

• Built a Lambda Calculus interpreter in Haskell for a class (Design of Programming Languages with Professor Fred Martin and TA Nat Tuck at UMass Lowell Spring 2013)
• Thought to myself "Is the JavaScript platform up to the task?"
• Thought of a way to emulate the pattern matching syntax of Haskell in CoffeeScript (see byType in lambda.coffee)
• Learned how to use PEG.js to build a parser.
• Thought to generate an abstract syntax tree using simple object literals with a string type property (one of 'lambda', 'apply', 'name')
• Had to write helper functions for the parser to achieve proper associativity for sequential apply statements and multi-argument lambdas.
• Ported Haskell interpreter to CoffeeScript (using Underscore when needed)
• Started by mixing pure functional (immutable AST nodes) and imperative (mutable AST nodes) styles
  • Using mutable AST nodes led to an error where multiple references to the same node appeared multiple times in the tree (from the substitution step), leading to a stack overflow error when reducing due to circular reference (e.g. applying a node to itself).
• For safety, chose to go with pure functional style by always creating new AST nodes for all reduction steps
• Ideas for future work:
  • Use a procedural style that mutates AST nodes during reduction steps.
  • Instrument the code to count how many new AST objects are created.
  • Visualize a table with the following columns:
    • input - a lambda calculus expression (from unit tests)

    • new AST objects created in functional style

    • new AST objects created in procedural style