lambda-calculus 1.10.1

Implementation of the Lambda calculus

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.

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

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"))

using 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"))

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"))
)