Classical F_omega, orthogonality and symmetric candidates

Stéphane Lengrand (1, 2) , Alexandre Miquel (1)

1 PPS - Preuves, Programmes et Systèmes
2 School of Computer Science [University of St Andrews]

We present a version of system F_omega in which the layer of type constructors is essentially the traditional one of F_omega, whereas provability of types is classical. The proof-term calculus accounting for the classical reasoning is a variant of Barbanera and Berardi's symmetric Lambda-calculus. We prove that the whole calculus is strongly normalising. For the layer of type constructors, we use Tait and Girard's reducibility method combined with orthogonality techniques. For the (classical) layer of terms, we use Barbanera and Berardi's method based on a symmetric notion of reducibility candidate. We prove that orthogonality does not capture the fixpoint construction of symmetric candidates. We establish the consistency of the classical F_omega, and relate the calculus to the traditional system F_omega, also when the latter is extended with axioms for classical logic.

Mots clés: Classical logic; F_omega; orthogonality; reducibility

Domaines: Logique en informatique [cs.LO]

Stéphane Lengrand, Alexandre Miquel. Classical F_omega, orthogonality and symmetric candidates. 2007. ⟨hal-00150283⟩