Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory

@inproceedings{Pfenning2001IntensionalityEA,
  title={Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory},
  author={Frank Pfenning},
  booktitle={LICS},
  year={2001}
}
We develop a uniform type theory that integrates intensionality, extensionality, and proof irrelevance as judgmental concepts. Any object may be treated intensionally (subject only toα-conversion), extensionally (subject also to βη-conversion), or as irrelevant (equal to any other object at the same type), depending on where it occurs. Modal restrictions developed in prior work for simple types are generalized and employed to guarantee consistency between these views of objects. Potential… CONTINUE READING
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