Open Proofs and Open Terms: A Basis for Interactive Logic

@inproceedings{Geuvers2002OpenPA,
  title={Open Proofs and Open Terms: A Basis for Interactive Logic},
  author={Herman Geuvers and Gueorgui I. Jojgov},
  booktitle={CSL},
  year={2002}
}
In the process of interactive theorem proving one often works with incomplete higher order proofs. In this paper we address the problem of giving a correctness criterion for these incomplete proofs by presenting open higher order logic o-Predω as a conservative extension of Predω. We define a typing system o-λPredω and show that the CurryHoward embedding extends to embedding into o-λPredω. We show that the contexts of this typing system extended with definitions can represent the notion of… CONTINUE READING
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