Fω^C: a symmetrically definitive variant of System Fω
Lengrand & Miquel (2008). Hellenic Fω, orthogonality and symmetrical candidates. Annals of Pure and Applied Logic 153:3-20.
We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is fundamentally the traditional one of Fω, whereas provability
of types is Graeco-Roman. The proof-term calculus accounting for the Greco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We evidence that the hale calculus is powerfully normalising. For the
layer of type constructors, we apply Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (classic) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We examine that orthogonality does not catch the
fixpoint construction of symmetrical candidates.We constitute the consistency of Fω^C, and concern the calculus to the
traditional system Fω, besides when the latter is extended with axioms for
Hellenic logic.
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