A framework for defining logics
Journal of the ACM (JACM)
Handbook of logic in computer science (vol. 2)
Using typed lambda calculus to implement formal systems on a machine
Journal of Automated Reasoning
Autarkic Computations in Formal Proofs
Journal of Automated Reasoning
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-Order Abstract Syntax in Coq
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Experience with Embedding Hardware Description Languages in HOL
Proceedings of the IFIP TC10/WG 10.2 International Conference on Theorem Provers in Circuit Design: Theory, Practice and Experience
Five Axioms of Alpha-Conversion
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
Natural Deduction for Intuitionistic Non-communicative Linear Logic
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Consistency of the theory of contexts
Journal of Functional Programming
A Framework for Defining Logical Frameworks
Electronic Notes in Theoretical Computer Science (ENTCS)
Mechanizing metatheory in a logical framework
Journal of Functional Programming
A Conditional Logical Framework
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Embedding pure type systems in the lambda-pi-calculus modulo
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Higher-order representation of substructural logics
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Beluga: a framework for programming and reasoning with deductive systems (system description)
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
LFP: a logical framework with external predicates
Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
Lambda Calculus with Types
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Throughout the history of Mathematics, several different proof cultures have co-existed, and still do co-exist. After 25 years of Logical Frameworks, we can say that even as far as proof metalanguages go, a definitive system is utopian and that we are witnessing the continuous development of a diversity of formal proof cultures, see e.g. [10-12, 17, 19, 21, 23, 24, 28]. In this paper, we propose a contribution towards the clarification of some controversial issues that have arisen in the theory and practice of Logical Frameworks, and have possibly motivated such a manifold speciation. Using as a running example the encoding of the critical features of Non- Commutative Linear Logic (NCLL) [26] in the Logical Framework LFP [20], we discuss the notions of adequacy of an encoding, locality of a side-condition, deep and shallow encodings, and how to embed heterogenous justifications or external evidence in LF. This discussion naturally leads to the question of how to express formally the expressive power of a Logical Framework, a minimal requirement being that of encoding itself within itself. We focus on LFP and we discuss its relations to the original LF [17], and briefly to the Conditional LF [21], and the Pattern LF [19] previously introduced by the authors. We conclude the paper by briefly comparing LFP to λ-calculus modulo [12], the Linear LF [9], and the Concurrent LF[28].