A Formulae-as-Types Interpretation of Subtractive Logic

@article{Crolard2004AFI,
  title={A Formulae-as-Types Interpretation of Subtractive Logic},
  author={Tristan Crolard},
  journal={J. Log. Comput.},
  year={2004},
  volume={14},
  pages={529-570}
}
  • T. Crolard
  • Published 1 August 2004
  • Mathematics
  • J. Log. Comput.
We present a formulae-as-types interpretation of Subtractive Logic (i.e. bi-intuitionistic logic). This presentation is two-fold: we first define a very natural restriction of the λμ-calculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a computational standpoint, the resulting calculus provides a type system for first-class coroutines (a… 

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