A framework for defining logics
Journal of the ACM (JACM)
Toward a foundational typed assembly language
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Towards a mechanized metatheory of standard ML
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An executable formalization of the HOL/Nuprl connection in the metalogical framework twelf
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Journal of Automated Reasoning
Proofs you can believe in: proving equivalences between Prolog semantics in Coq
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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Logical framework research is based on the philosophical point of view that it should be possible to capture mathematical concepts such as proofs, logics, and meaning in a formal system -- directly, adequately (in the sense that there are no spurious or exotic witnesses), and without having to commit to a particular logical theory. Instead of working with one general purpose representation language, we design special purpose logical frameworks for capturing reoccurring concepts for special domains, such as, for example, variable renaming, substitution application, and resource management for programming language theory. Most logical frameworks are based on constructive type theories, such as Isabelle (on the simply-typed *** -calculus), LF [HHP93] (on the dependently typed *** -calculus), and LLF (on a linearly typed *** -calculus). The representational strength of the logical framework stems from the choice of definitional equality on terms. For example, *** -conversion models the tacit renaming of variables, β -contraction models substitution application, and *** -expansion guarantees the adequacy of encodings.