λ Lambda Toolkit

A toolkit for lambda calculus evaluation, combinator logic, and CLI-powered expression tracing.

Supports pretty-printing, lazy/eager reduction, trace generation, and built-in easter eggs.

Lambda Toolkit Documentation

Version: 1.1.0

Overview

Lambda Toolkit is a symbolic lambda calculus engine built with introspective evaluation, Church encodings, lazy reduction, and educational traceability. This toolkit supports recursive function modeling (via the Y combinator), semantic validation, and customizable expression registries for symbolic reasoning systems.

Features

• Lazy beta-reduction
• Full De Bruijn indexing
• Step-by-step evaluation traces
• Expression registry (define/lookup)
• Church encodings (booleans, numerals, arithmetic, recursion)
• Validation (is_closed, is_normal_form, etc.)
• Mermaid architecture diagram

Getting Started

Install locally:

pip install .

Explore Church encodings:

from lambda_toolkit.core import lookup
print(lookup("TWO"))

Run validation:

from lambda_toolkit.validator import is_normal_form
print(is_normal_form(lookup("TWO")))

See example workflows in examples/.

License

Apache 2.0

Example: Lazy Evaluation of IF

IF TRUE (λx.x) (λx. x x)

Should evaluate to λx.x without touching the diverging branch (λx. x x).

Reduction Trace:

Step 0:
(  (    (      λx0.
        λx1.
          λx2.
            (              (x0
               x1)
             x2)
           λx0.
        λx1.
x0)
       λx0.
x0)
   λx0.
    (x0
     x0))

Step 1:
(  (    λx0.
      λx1.
        (          (            λx2.
              λx3.
x2
           x0)
         x1)
       λx0.
x0)
   λx0.
    (x0
     x0))

Step 2:
(  λx0.
    (      (        λx1.
          λx2.
x1
               λx1.
x1)
     x0)
   λx0.
    (x0
     x0))

Step 3:
(  (    λx0.
      λx1.
x0
       λx0.
x0)
   λx0.
    (x0
     x0))

Step 4:
(  λx0.
    λx1.
x1
   λx0.
    (x0
     x0))

Final:
λx0.
x0

This shows that our evaluation strategy correctly short-circuits evaluation of unnecessary branches. Only TRUE and the identity were evaluated.

CLI Extras

• --trace: Show reduction steps (see example_generation.md)
• monday: Garfield's eternal return. See easter_egg.md.
• crowbar: A nod to Half-Life. See easter_egg.md.

For implementation details, check core.md and nodes.md.