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Description:

lambdacalculus 3.1.0

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"))
)