Wikipedia:Reference desk/Archives/Mathematics/2021 August 13

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August 13

Lambda expressions

This paper from Cornell (http://www.cs.cornell.edu/courses/cs312/2008sp/recitations/rec26.html) states that the following two lambda expressions are equivalent:

λx. λy. y

λx.(x (λy.y))

I'm not sure why they are equivalent. The first lambda expression takes an arbitrary variable as a parameter and returns the identity function. The second one takes a variable and applies it to the identity function. How are those the same thing? --Puzzledvegetable^{Is it teatime already?} 02:32, 13 August 2021 (UTC)

It is clearly a (very confusing) typo. The first expression is meant to read λx. x λy. y. The expressions are then not merely equivalent, but the same, just like in high-school algebra a + b × c is "the same" as a + (b × c).  --Lambiam 07:32, 13 August 2021 (UTC)