Programming with proofs and explicit contexts
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
The Abella Interactive Theorem Prover (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Reasoning in Abella about Structural Operational Semantics Specifications
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Role of Names in Reasoning about λ-tree Syntax Specifications
Electronic Notes in Theoretical Computer Science (ENTCS)
Case Analysis of Higher-Order Data
Electronic Notes in Theoretical Computer Science (ENTCS)
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Reasoning with hypothetical judgments and open terms in hybrid
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Relating nominal and higher-order abstract syntax specifications
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
A meta-programming approach to realizing dependently typed logic programming
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Mechanizing the metatheory of LF
ACM Transactions on Computational Logic (TOCL)
Information and Computation
Reasoning about computations using two-levels of logic
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Journal of Automated Reasoning
Programming with binders and indexed data-types
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Permissive-nominal logic: First-order logic over nominal terms and sets
ACM Transactions on Computational Logic (TOCL)
Stratification in logics of definitions
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Proof pearl: abella formalization of λ-calculus cube property
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
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Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that allow direct, logic-based reasoning about such descriptions: the treatment of atomic judgments as fixed points (recursive definitions) and an encoding of binding constructs via generic judgments. However, the logics encompassing these two features have thus far treated them orthogonally: that is, they do not provide the ability to define object-logic properties that themselves depend on an intrinsic treatment of binding. We propose a new and simple integration of these features within an intuitionistic logic enhanced with induction over natural numbers and we show that the resulting logic is consistent. The pivotal benefit of the integration is that it allows recursive definitions to not just encode simple, traditional forms of atomic judgments but also to capture generic properties pertaining to such judgments. The usefulness of this logic is illustrated by showing how it can provide elegant treatments of object-logic contexts that appear in proofs involving typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.