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.
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.
Python >= 3.10 is required to use this package.
python3 -m pip install lambda-calculus(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"))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"))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"))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"))
)
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