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Lambda calculus engine Gem Version

Ever wanted to evaluate lambda expressions from the command line? Well now you can!

  1. Download this gem; gem install lambda-calculus.
  2. Open up pry or irb and type require 'lambda-calculus'.
  3. Declare a lambda expression; my_exp = LambdaExpression.new('(\x.xy)(\a.a)')
  4. Evaluate or beta reduce!
> my_exp.beta_reduce
=> (\a.a)y
> my_exp.evaluate
=> y

Lambda expressions are a class. Their attributes depend on which kind they are, as defined by the following code snippet from lambda-calculus.rb;

case args.length
when 1
  @kind = :variable
  @value = node_value
when 2
  @kind = :abstraction
  @bound_var = node_value
  @body = child1
when 3
  @kind = :application
  @function = child1
  @argument = child2

Arguments

LambdaExpression.new() has two modes for taking arguments; natively or naturally. I tried to make it as flexible as possible while matching expectations.

Natively it can take one, two or three arguments where one makes it a variable, two makes it an abstraction, and three makes it an application. In each case the first argument must be a symbol or string of the correct form; anything but * for variables and abstractions, and only * for applications. The other arguments can be LambdaExpressions, strings of the natural form, or symbols.

Naturally, one can just give the lambda expression written as a string, the way you might write an expression to someone over text.

Some valid examples are shown below;

This will become a variable;

LambdaExpression.new(:x)
LambdaExpression.new('x')

These will become abstractions;

LambdaExpression.new(:x, :x)
LambdaExpression.new('x', 'x')
LambdaExpression.new(:x, 'xy')

These will become applications;

LambdaExpression.new(:*, :x, :y)
LambdaExpression.new('*', 'x', 'y')
LambdaExpression.new(:*, :x, '\a.bb')

These will be parsed as strings

LambdaExpression.new('x')
LambdaExpression.new('xy')
LambdaExpression.new('(\x.xy)(\a.bb)')
LambdaExpression.new('\x.xy')

Being able to accept arbitrary strings means that a string parser is included. The method beta_reduce will perform beta reduction, but only on the top-level application. Methods for printing facts about lambda expressions are also included; lambda_string_tester for strings, and lambda_tester for native LambdaExpression objects.