A Formal System for the Universal Quantification of Schematic Variables

We advocate the use of de Bruijn’s universal abstraction \lambda {\mathord \infty }{}{}{} for quantification schematic variables in predicative setting, and we present a typed {}{}{}{} -calculus featuring quantifier accompanied by other practically useful constructions like explicit substitutions expected type annotations. Our calculus stands just on two notions, i.e., bound rt-reduction parametric validity, has expressive power \mathord \rightarrow . Thus, while not aiming at being logical framework itself, it does enjoy many desired invariants frameworks including confluence reduction, strong normalization, preservation decidability, correctness types uniqueness up to conversion. This belongs \delta family formal systems, which borrow some features from pure systems languages Automath tradition, but stand outside both families. In particular, our includes evolves earlier this family. Moreover, machine-checked specification its theory is available.