Abstract
\(\mathcal X\) 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 \({\cal W}\).
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Summers, A.J., van Bakel, S. (2006). Approaches to Polymorphism in Classical Sequent Calculus. In: Sestoft, P. (eds) Programming Languages and Systems. ESOP 2006. Lecture Notes in Computer Science, vol 3924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11693024_7
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DOI: https://doi.org/10.1007/11693024_7
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