Krivine's notation for lambda-terms Krivine in his book (Lambda-calculus: Types and Models) introduces the grammar of lambda-terms and then abbreviations to denote them. The grammar itself is not ambiguous:  Lambda-terms are
obtained by applying, a finite number of times, the following rules :


any variable x is a λ-term ;
whenever t and u are λ-terms, then so is (t)u ;
whenever t is a λ-term and x is a variable, then λx t is a λ-term.


Then: "the term $(...(((t)u_1)u_2)...)u_k$ will also be written "$(t)u_1 u_2 ...u_k$". But let us consider the two following different $\lambda$-terms:


$v_1 = ((x)\lambda y. (y)z)w$ 
$v_2 = (x)\lambda y. ((y)z)w$


($w, x, y, z$ are variables)
and now it seems that I have two ways to interpret the notation $(x)\lambda y. (y)z w$:


either $t = x$, $k = 2$, $u_1 =\lambda y. (y)z$ and $u_2 = w$
or $t = x$, $k= 1$ and $u_1 = \lambda y. ((y)z)w$


It seems that the notation "$(t)u_1 u_2 ...u_k$" is ambiguous. Which rule am I violating in my interpretation?
Here's a quote from this version which can be found on the author's page (emphasis mine):


  The term $(t)u$ should be thought of as “$t$ applied to $u$” ; it will also be denoted by $t u$ if there is no ambiguity ; the term $(\dots (((t)u_1)u_2)\dots)u_k$ will also be written $(t)u_1u_2\dots u_k$ or $tu_1u_2\dots u_k$. Thus, for example, $(t)uv$, $(tu)v$ and $tuv$ denote the same term.


I'd expect the "if there is no ambiguity" condition to also apply to the second notation (which is just the first notation applied $k-1$ times).