How do interpret $x \lambda y . \lambda z . x$?

Question

I am not sure how to interpret this term. My first thought is that it is this an application of $x$ to $\lambda y.\lambda z.x$ Is that the correct interpretation or is it not reducible?

Answer 1

Indeed, the only possible parsing of this expression is “$x$ applied to $λy.λz.x$”. In general, standard conventions for writing λ-terms are the usual “Barendregt” one, or the Krivine notation. One should make clear the notation they use when writing λ-terms.

By the way, be careful with the words you are using:

• to interpret a λ-term is something else, it usually refers to giving it a semantics in a model;
• this term is not reducible, at least for the standard notion of reduction (aka. β-reduction), since it does not contain any β-redex.