Interpreting descriptions in intensional type theory

@article{Carlstrm2005InterpretingDI,
  title={Interpreting descriptions in intensional type theory},
  author={Jesper Carlstr{\"o}m},
  journal={Journal of Symbolic Logic},
  year={2005},
  volume={70},
  pages={488 - 514}
}
  • J. Carlström
  • Published 1 June 2005
  • Mathematics
  • Journal of Symbolic Logic
Abstract Natural deduction systems with indefinite and definite descriptions (ε-terms and ι-terms) are presented, and interpreted in Martin-LÖf's intensional type theory. The interpretations are formalizations of ideas which are implicit in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of ‘the element such that the property holds’ and refer by that phrase to the element constructed in the existence proof. In particular, we… 
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