What does identify mean in untyped lambda calculus? In the back of Henk's book "The Lambda Calculus, its Syntax and Semantics" he writes: > The Lambda Calculus, ..., consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. What does identify mean in that sentence? I've seen it used in other places throughout the book but I'm sure he didn't define it or talk about it in the book.

To "identify" terms means to determine whether or not the terms mean the same thing. (Thanks to @amd)

The book talks about "convertibility" being the basic equivalence relation on λ-terms. If M, N are terms and M = N then M and N are called convertible. I think that also means that M and N have been "identified". Furthermore, all terms in the equivalence class containing M (and N) have been "identified", i.e. mean the same thing.