Automating recursive type definitions in higher order logic
Current trends in hardware verification and automated theorem proving
From LCF to HOL: a short history
Proof, language, and interaction
Inductive Datatypes in HOL - Lessons Learned in Formal-Logic Engineering
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
A formal treatment of the barendregt variable convention in rule inductions
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Alpha-structural recursion and induction
Journal of the ACM (JACM)
Alpha-structural recursion and induction
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
A design structure for higher order quotients
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Nominal techniques in Isabelle/HOL
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Abstract Syntax: Substitution and Binders
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
A Head-to-Head Comparison of de Bruijn Indices and Names
Electronic Notes in Theoretical Computer Science (ENTCS)
Formalising in Nominal Isabelle Crary's Completeness Proof for Equivalence Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
Barendregt's Variable Convention in Rule Inductions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Revisiting Cut-Elimination: One Difficult Proof Is Really a Proof
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Electronic Notes in Theoretical Computer Science (ENTCS)
Formal SOS-Proofs for the Lambda-Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Formalising FinFuns --- Generating Code for Functions as Data from Isabelle/HOL
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Formalising the π-calculus using nominal logic
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Recursion principles for syntax with bindings and substitution
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Structured induction proofs in isabelle/isar
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Journal of Automated Reasoning
Reasoning about constants in nominal isabelle or how to formalize the second fixed point theorem
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
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The nominal datatype package implements an infrastructure in Isabelle/HOL for defining languages involving binders and for reasoning conveniently about alpha-equivalence classes. Pitts stated some general conditions under which functions over alpha-equivalence classes can be defined by a form of structural recursion and gave a clever proof for the existence of a primitive-recursion combinator. We give a version of this proof that works directly over nominal datatypes and does not rely upon auxiliary constructions. We further introduce proving tools and a heuristic that made the automation of our proof tractable. This automation is an essential prerequisite for the nominal datatype package to become useful.