curryparty 0.4.0

Python playground to learn lambda calculus

Curry party

curryparty is a library created to explore, visualize and teach lambda-calculus concepts.

Install

Run pip install curryparty or uv add curryparty depending on your package manager.

How to use

from curryparty import L, o

# Build classic lambda calculus expressions

# Identity: λx. x
identity = L("x").o("x").build()

# Const (K combinator): λx. λy. x
const = L("x", "y").o("x").build()

# Omega: λx. x x
omega = L("x").o("x", "x").build()
print(omega(omega))  # (λ0 x0(x0))((λ1 x1(x1)))

# Church numerals
zero = L("f", "x").o("x").build()
one = L("f", "x").o("f", "x").build()
two = L("f", "x").o("f", o("f", "x")).build()

succ = L("n", "f", "x").o("f", o("n", "f", "x")).build()

# S combinator: λf. λg. λx. f x (g x)
s_comb = L("f", "g", "x").o("f", "x", o("g", "x")).build()

# Beta reduction
# Nothing happens until you reduce:
app = identity(identity)
print(app)  # (λ0 x0)((λ1 x1))

# Perform one reduction step:
reduced = app.beta()
print(reduced)  # λ0 x0

# Multiple reductions:
term = succ(zero)
print(f"Steps: {len(list(term.reduction_chain()))}")  # Steps: 3

# Print each step:
for step in term.reduction_chain():
    print(step)

# Or get the final result directly:
result = succ(zero).reduce()
print(result)  # λ0 λ1 x0(x1) (i.e, one)

But the main point of this library is the svg-based display system. If you use a notebook such as jupyternotebook or marimo, you will see something like this:

You can also use term.show_reduction to get an animated version.

Tutorial

lambda.py shows a tutorial in marimo format. Click on the button to try it out:

How it works

Under the wood, all the terms are converted into a list of nodes, that can either be a lambda, an application (with 2 arguments) or a variable (with 0 arguments).

For efficiency, they are converted to a polars dataframe in prefix traversal order. If you want to understand how it works, start by looking at the .nodes attribute of any term.