A Sequent Calculus for Type Theory

  title={A Sequent Calculus for Type Theory},
  author={St{\'e}phane Lengrand and Roy Dyckhoff and James McKinna},
Based on natural deduction, Pure Type Systems (PTS) can express a wide range of type theories. In order to express proof-search in such theories, we introduce the Pure Type Sequent Calculi (PTSC) by enriching a sequent calculus due to Herbelin, adapted to proof-search and strongly related to natural deduction. PTSC are equipped with a normalisation procedure, adapted from Herbelin’s and defined by local rewrite rules as in Cut-elimination, using explicit substitutions. It satisfies Subject… CONTINUE READING
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