On the stability by union of reducibility candidates

Authors:
Colin Riba
Affiliations:
INPL & LORIA, Nancy, France
Venue:
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Year:
2007

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Abstract

We investigate some aspects of proof methods for the termination of (extensions of) the second-order λ-calculus in presence of union and existential types. We prove that Girard's reducibility candidates are stable by union iff they are exactly the non-empty sets of terminating terms which are downward-closed w.r.t. a weak observational preorder. We show that this is the case for the Curry-style second-order λ-calculus. As a corollary, we obtain that reducibility candidates are exactly the Tait's saturated sets that are stable by reduction. We then extend the proof to a system with product, co-product and positive iso-recursive types.