Setoid type theory - a syntactic translation

Abstract : We introduce setoid type theory, an intensional type theory with a proof-irrelevant universe of propositions and an equality type satisfying function extensionality, propositional extensionality and a def-initional computation rule for transport. We justify the rules of setoid type theory by a syntactic translation into a pure type theory with a universe of propositions. We conjecture that our syntax is complete with regards to this translation.
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https://hal.inria.fr/hal-02281225
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Thorsten Altenkirch, Simon Boulier, Ambrus Kaposi, Nicolas Tabareau. Setoid type theory - a syntactic translation. Mathematics of Program Construction, Oct 2019, Porto, Portugal. ⟨hal-02281225⟩

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