The Implicit Calculus of Constructions

@inproceedings{Miquel2001TheIC,
  title={The Implicit Calculus of Constructions},
  author={Alexandre Miquel},
  booktitle={TLCA},
  year={2001}
}
In this paper, we introduce a new type system, the Implicit Calculus of Constructions, which is a Curry-style variant of the Calculus of Constructions that we extend by adding an intersection type binder-called the implicit dependent product. Unlike the usual approach of Type Assignment Systems, the implicit product can be used at every place in the universe hierarchy. We study syntactical properties of this calculus such as the βη-subject reduction property, and we show that the implicit… Expand
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