Notions of computation and monads
Information and Computation
Compiling standard ML to Java bytecodes
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Primitive recursion for higher-order abstract syntax
Theoretical Computer Science
Some Lambda Calculus and Type Theory Formalized
Journal of Automated Reasoning
Higher-Order Abstract Syntax with Induction in Coq
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
Higher-Order Abstract Syntax in Coq
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Combining Higher Order Abstract Syntax with Tactical Theorem Proving and (Co)Induction
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Two-Level Meta-reasoning in Coq
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Semantical Analysis of Higher-Order Abstract Syntax
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Proof Theory for Generic Judgments: An extended abstract
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Reasoning in a logic with definitions and induction
Reasoning in a logic with definitions and induction
Recursion over objects of functional type
Mathematical Structures in Computer Science
Multi-level meta-reasoning with higher-order abstract syntax
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
A formalization of an Ordered Logical Framework in Hybrid with applications to continuation machines
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
A computational approach to reflective meta-reasoning about languages with bindings
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Combining higher-order abstract syntax with first-order abstract syntax in ATS
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Abstract Syntax: Substitution and Binders
Electronic Notes in Theoretical Computer Science (ENTCS)
Two-Level Hybrid: A System for Reasoning Using Higher-Order Abstract Syntax
Electronic Notes in Theoretical Computer Science (ENTCS)
Category Theoretic Semantics for Typed Binding Signatures with Recursion
Fundamenta Informaticae - Logic for Pragmatics
Recursion principles for syntax with bindings and substitution
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Journal of Automated Reasoning
The ∇-calculus. functional programming with higher-order encodings
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
A Canonical Locally Named Representation of Binding
Journal of Automated Reasoning
Category Theoretic Semantics for Typed Binding Signatures with Recursion
Fundamenta Informaticae - Logic for Pragmatics
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It is well known that there are problems associated with formal systems which attempt to combine higher order abstract syntax (HOAS) with principles of induction and recursion. We describe a formal system, called Bsyntax, which we have implemented in Isabelle HOL. Our contribution is to prove the existence of a combinator for primitive recursion with parameters over HOAS. The definition of the combinator is facilitated by the use of terms with infinite contexts. In particular, our work is purely definitional, and is thus consistent with classical logic and choice. An immediate payoff is that we obtain a primitive recursive definition of higher order substitution. We give a presheaf model of Bsyntax, providing additional semantic validation of Bsyntax's principles of recursion. We outline an application of our work to mechanized reasoning about the compiler intermediate language MIL-lite [2].