Abstract
We define rank 1 polymorphic types for nominal rewrite rules and equations. Typing environments type atoms, variables, and function symbols, and since we follow a Curry-style approach there is no need to fully annotate terms with types. Our system has principal types, and we give rule and axiom formats to guarantee preservation of types under both rewriting and equality reasoning. This is non-trivial because substitution does not avoid capture, so a substituted symbol can—if we are not careful—appear in inconsistent typing contexts.
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Fairweather, E., Fernández, M., Gabbay, M.J. (2011). Principal Types for Nominal Theories. In: Owe, O., Steffen, M., Telle, J.A. (eds) Fundamentals of Computation Theory. FCT 2011. Lecture Notes in Computer Science, vol 6914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22953-4_14
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DOI: https://doi.org/10.1007/978-3-642-22953-4_14
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