Almost Literate Syntax Trees

Suppose you're translating a lambda calculus expression like:

λx.λy.λz.xyz

into a Lisp-like syntax tree:

  (fun 'x
    (fun 'y
      (fun 'z
        (apply
          (apply (sym 'x) (sym 'y))
          (sym 'z)
        )
      )
    )
  )

where sym expresses a reference to a symbol that is (or should be) bound in the current context.

If you replace fun with givenA and sym with the, the result looks like:

  (givenA 'x
    (givenA 'y
      (givenA 'z
        (apply
          (apply (the 'x) (the 'y))
          (the 'z)
        )
      )
    )
  )

This exploits an English speaker's understanding that “a” introduces a term, and “the” refers to an occurrence of that term in the same context.

The second example reads better to me, but I haven't been able to come up with an everyday-English equivalent for apply. Maybe it's just not an everyday concept.