The system F of variable types, fifteen years later
Theoretical Computer Science
Handbook of logic in computer science (vol. 2)
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Intersection type assignment systems with higher-order algebraic rewriting
Theoretical Computer Science
Normalization results for typeable rewrite systems
Information and Computation
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
The Java Language Specification
The Java Language Specification
Principal type-schemes for functional programs
POPL '82 Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
FreshML: programming with binders made simple
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
PPDP '04 Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming
Theoretical Computer Science
Nominal rewriting with name generation: abstraction vs. locality
PPDP '05 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
Information and Computation
Information and Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Curry-Howard for incomplete first-order logic derivations using one-and-a-half level terms
Information and Computation
Principal types for nominal theories
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
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We define a rank 1 polymorphic type system for nominal terms, where typing environments type atoms, variables and function symbols. The interaction between type assumptions for atoms and substitution for variables is subtle: substitution does not avoid capture and so can move an atom into multiple different typing contexts. We give typing rules such that principal types exist and are decidable for a fixed typing environment. a-equivalent nominal terms have the same types; a non-trivial result because nominal terms include explicit constructs for renaming atoms. We investigate rule formats to guarantee subject reduction. Our system is in a convenient Curry-style, so the user has no need to explicitly type abstracted atoms.