# Lambda calculus simplification excercise

Below is the lambda expression which I am finding difficult to reduce i.e. I am not able to understand how to go about this problem.

(λx.λy.yx)z (λw.w) I am lost with this.

if anyone could lead me in the right direction that would be much appreciated

• Did you try to find a partition of the problem where you'd been able to solve at least one part? – greybeard Sep 14 at 6:42
• It may help to note that lambda calculus is confluent (Church-Rosser) under the full $\beta$-reduction strategy. – ShyPerson Sep 19 at 19:28

It is better to remind ourselves the Lambda calculus precedence rules first. See https://stackoverflow.com/q/4794330/9939883 for better details about precedence.

Application has higher precedence than Abstraction. Application is left associateive and Abstraction is right associative.

(λx.λy.y x) z (λw.w)


Since application has higher precedence,

(λx.λy.(y x)) z (λw.w)


Since application is left associative

= ((λx.λy.(y x)) z) (λw.w)


Applying repeated abstractions

= (λy.(y z)) (λw.w)

= (λw.w) z

= z

• Thank you, I have made some edits. – silversilva Sep 15 at 2:55
• Thank you! Nice explanation! – D.W. Sep 15 at 5:15