We review the development of the class so far, now considering quantifiers and negation. This requires the notion of a parametric judgment, that is, a judgment with a free parameter for which we can substitute arbitrary objects from the right syntactic class.
We then discuss the annotation of sequent derivations with proof terms, and a first simple search strategies which is shown to be sound and complete. This is the restriction to atomic initial sequents.
The material on parametric judgments, quantification, and negation is distributed throughout the notes handed out so far (collected in the file atp.ps). Parametric judgment are introduction on page 3, negation on page 10, the quantifiers on pages 12-14. Material on proof term assignment for the sequent calculus is in the handout below.