lambda_calculus

The lambda_calculus package contains classes which implement basic operations of the lambda calculus.

To use it, simply import the classes Variable, Abstraction and Application from this package and nest them to create more complex lambda terms.

You can also use the visitors subpackage to define your own operations on terms or use predefined ones from the terms subpackage.

More information is available on Read the Docs.

Notice

This package is intended to be used for educational purposes and is not optimized for speed.

Furthermore, it expects all terms to be finite, which means the absence of cycles.

RecursionError may be raised if the visitors get passed an infinite term or the evaluation is too complex.

Requirements

Python >= 3.10 is required to use this package.

Installation

python3 -m pip install lambda-calculus

Examples

(λy.(λx.(λy. + x y)) y 3) 4

Nesting

from lambda_calculus import Variable, Abstraction, Application

term = Application(Variable("+"), Variable("x"))
term = Application(term, Variable("y"))
term = Abstraction("y", term)
term = Abstraction("x", term)
term = Application(term, Variable("y"))
term = Application(term, Variable("3"))
term = Abstraction("y", term)
term = Application(term, Variable("4"))

Utility Methods

from lambda_calculus import Variable, Abstraction, Application

x = Variable.with_valid_name("x")
y = Variable.with_valid_name("y")

term = Application.with_arguments(Variable.with_valid_name("+"), (x, y))
term = Abstraction.curried(("x", "y"), term)
term = Application.with_arguments(term, (y, Variable.with_valid_name("3")))
term = Abstraction("y", term)
term = Application(term, Variable.with_valid_name("4"))

Method Chaining

from lambda_calculus import Variable, Abstraction, Application

x = Variable.with_valid_name("x")
y = Variable.with_valid_name("y")

term = Variable("+") \
    .apply_to(x, y) \
    .abstract("x", "y") \
    .apply_to(y, Variable("3")) \
    .abstract("y") \
    .apply_to(Variable("4"))

Evaluation

from lambda_calculus import Variable, Application
from lambda_calculus.visitors.normalisation import BetaNormalisingVisitor

assert BetaNormalisingVisitor().skip_intermediate(term) == Application.with_arguments(
    Variable("+"),
    (Variable("4"), Variable("3"))
)