Proofs and types
A framework for defining logics
Journal of the ACM (JACM)
A modal analysis of staged computation
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Dependent types in practical programming
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-Order Abstract Syntax with Induction in Coq
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
On Mints' Reduction for ccc-Calculus
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Higher-Order Abstract Syntax in Coq
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Primitive Recursion for Higher-Order Abstract Syntax
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Automated Theorem Proving in a Simple Meta-Logic for LF
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
A Logic for Reasoning with Higher-Order Abstract Syntax
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Semantical Analysis of Higher-Order Abstract Syntax
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
On the Logical Content of Computational Type Theory: A Solution to Curry's Problem
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Higher-Order Intensional Type Analysis
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Boxes go bananas: encoding higher-order abstract syntax with parametric polymorphism
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Special issue: Modalities in type theory
Mathematical Structures in Computer Science
A definitional approach to primitivexs recursion over higher order abstract syntax
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
Practical Reflection for Sequent Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts
Journal of Automated Reasoning
Boxes go bananas: Encoding higher-order abstract syntax with parametric polymorphism*
Journal of Functional Programming
Programming with proofs and explicit contexts
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
Cut-free Gentzen calculus for multimodal CK
Information and Computation
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This paper presents an extension of the simply typed λ-calculus that allows iteration and case reasoning over terms of functional types that arise when using higher order abstract syntax. This calculus aims at being the kernel for a type theory in which the user will be able to formalize logics or formal systems using the LF methodology, while taking advantage of new induction and recursion principles, extending the principles available in a calculus such as the Calculus of Inductive Constructions. The key idea of our system is the use of modal logic S4. We present here the system, its typing rules and reduction rules. The system enjoys the decidability of typability, soundness of typed reduction with respect to the typing rules, the Church–Rosser and strong normalization properties and it is a conservative extension over the simply typed λ-calculus. These properties entail the preservation of the adequacy of encodings.