On the Strength of Proof-Irrelevant Type Theories

  • Benjamin Werner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)


We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is particularly 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. Finally 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.


Type Theory Dependent Type Reduction Rule Strong Normalization Conversion Rule 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Benjamin Werner
    • 1
  1. 1.INRIA-Futurs and LIX, Ecole PolytechniqueFrance

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