Approaches to Polymorphism in Classical Sequent Calculus

  • Alexander J. Summers
  • Steffen van Bakel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3924)


\(\mathcal X\) is a relatively new calculus, invented to give a Curry-Howard correspondence with Classical Implicative Sequent Calculus. It is already known to provide a very expressive language; embeddings have been defined of the λ-calculus, Bloo and Rose’s λ x, Parigot’s λμ and Curien and Herbelin’s \({\overline{\lambda}\mu\tilde{\mu}}\). We investigate various notions of polymorphism in the context of the \(\mathcal X\)-calculus. In particular, we examine the first class polymorphism of System F, and the shallow polymorphism of ML. We define analogous systems based on the \(\mathcal X\)-calculus, and show that these are suitable for embedding the original calculi.

In the case of shallow polymorphism we obtain a more general calculus than ML, while retaining its useful properties. A type-assignment algorithm is defined for this system, which generalises Milner’s \({\cal W}\).


Classical Logic Atomic Type Reduction Rule Natural Deduction Sequent Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alexander J. Summers
    • 1
  • Steffen van Bakel
    • 1
  1. 1.Department of ComputingImperial College LondonLondonU.K.

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