LambdaCat

🐾 LambdaCat

A practical functional programming library grounded in category theory.

Features

**Core Category Theory**: Complete implementation of categories with objects, morphisms, composition, and identities. Includes functors and natural transformations.

**Law Checking**: Built-in test suites that verify mathematical laws for categories, functors, applicatives, and monads at runtime.

**Functional Programming**: Standard typeclasses (Functor, Applicative, Monad) with implementations for Option, Result, Reader, Writer, and State.

**Agent Framework**: Plan execution system with composable operations like `sequence`, `parallel`, `choose`, and `focus`.

**Diagram Rendering**: Export categories and computation plans to Mermaid and Graphviz formats.

**Advanced Features**: Limits, colimits, adjunctions, and Kleisli category construction.

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Why LambdaCat?

Category theory provides a rigorous foundation for functional programming. LambdaCat makes these concepts accessible and practical:

• Composable: Build complex behavior from simple, well-tested components
• Verifiable: Mathematical laws are checked automatically

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Setup

python -m venv .venv
source ./.venv/bin/activate  # On Windows: .venv\Scripts\activate
pip install -U pip
pip install -e .

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Quick Start

Basic Categories

from LambdaCat.core import obj, arrow, build_presentation, Cat

# Create a category with objects and morphisms
A = obj("A")
B = obj("B")
f = arrow("f", "A", "B")

presentation = build_presentation([A, B], [f])
C = Cat.from_presentation(presentation)

# Composition works as expected
result = C.compose("f", "id:A")  # Returns "f"

Standard Categories

from LambdaCat.core.standard import discrete, simplex, walking_isomorphism

# Discrete category - only identity arrows
D = discrete(["A", "B", "C"])

# Simplex category - linear or