An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Unification under a mixed prefix
Journal of Symbolic Computation
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Primitive recursion for higher-order abstract syntax
Theoretical Computer Science
Higher-Order Abstract Syntax with Induction in Coq
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
A Proof Theory for Generic Judgments: An extended abstract
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Semantics of Name and Value Passing
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Theoretical Computer Science
Proceedings of the 8th ACM SIGPLAN international conference on Principles and practice of declarative programming
About permutation algebras, (pre)sheaves and named sets
Higher-Order and Symbolic Computation
A general mathematics of names
Information and Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Lambda-Calculus and Combinators: An Introduction
Lambda-Calculus and Combinators: An Introduction
Capture-avoiding substitution as a nominal algebra
Formal Aspects of Computing
Journal of Logic and Computation
Nominal Unification from a Higher-Order Perspective
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A study of substitution, using nominal techniques and Fraenkel-Mostowksi sets
Theoretical Computer Science
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
The lambda-context calculus (extended version)
Information and Computation
Journal of Logic and Computation
A formal calculus for informal equality with binding
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
A Nominal Axiomatization of the Lambda Calculus
Journal of Logic and Computation
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Capture-avoiding substitution as a nominal algebra
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Nominal Unification from a Higher-Order Perspective
ACM Transactions on Computational Logic (TOCL)
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Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the @?-quantifier or @l-binder are just term-formers satisfying axioms, and their denotation is functions on nominal atoms-abstraction. Then we have higher-order logic (HOL) and its models in ordinary (i.e. Zermelo-Fraenkel) sets; the denotation of @? or @l is functions on full or partial function spaces. This raises the following question: how are these two models of binding connected? What translation is possible between PNL and HOL, and between nominal sets and functions? We exhibit a translation of PNL into HOL, and from models of PNL to certain models of HOL. It is natural, but also partial: we translate a restricted subsystem of full PNL to HOL. The extra part which does not translate is the symmetry properties of nominal sets with respect to permutations. To use a little nominal jargon: we can translate names and binding, but not their nominal equivariance properties. This seems reasonable since HOL-and ordinary sets-are not equivariant. Thus viewed through this translation, PNL and HOL and their models do different things, but they enjoy non-trivial and rich subsystems which are isomorphic.