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On the strength of proof-irrelevant type theories
release_uin4mledlzazdia4e76favcgwq
by
Benjamin Werner
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as a article
.
2008
Abstract
We present a type theory with some proof-irrelevance built into the
conversion rule. We argue that this feature is useful when type theory is used
as the logical formalism underlying a theorem prover. We also show a close
relation with the subset types of the theory of PVS. We show that in these
theories, because of the additional extentionality, the axiom of choice implies
the decidability of equality, that is, almost classical logic. Finally we
describe a simple set-theoretic semantics.
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