We extend Pure Type Systems with a function turning each term M of type A into a dummy |M| of the same type (|.| is not an identity, in that M ≠ |M|). Intuitively, a dummy represents an unknown, canonical object of the given type: dummies are opaque (cannot be internally inspected), and irrelevant in the sense that dummies of a same type are convertible to each other. This latter condition makes convertibility in PTS with dummies (DPTS) stronger than usual, hence raising not trivial consistency issues. DPTS offer an alternative approach to (proof) irrelevance, tagging irrelevant information at the level of terms and not of types, and avoiding the annoying syntactical duplication of products, abstractions and applications into an explicit and an implicit version, typical of systems like ICC*.
Type systems for dummies
ASPERTI, ANDREA;
2012
Abstract
We extend Pure Type Systems with a function turning each term M of type A into a dummy |M| of the same type (|.| is not an identity, in that M ≠ |M|). Intuitively, a dummy represents an unknown, canonical object of the given type: dummies are opaque (cannot be internally inspected), and irrelevant in the sense that dummies of a same type are convertible to each other. This latter condition makes convertibility in PTS with dummies (DPTS) stronger than usual, hence raising not trivial consistency issues. DPTS offer an alternative approach to (proof) irrelevance, tagging irrelevant information at the level of terms and not of types, and avoiding the annoying syntactical duplication of products, abstractions and applications into an explicit and an implicit version, typical of systems like ICC*.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
