Higher Order Quotients and their Implementation in Isabelle HOL
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Quotient Types: A Modular Approach
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Theory Interpretations in PVS
Defining functions on equivalence classes
ACM Transactions on Computational Logic (TOCL)
The design and implementation of typed scheme
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Mechanizing the Metatheory of LF
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Revisiting Cut-Elimination: One Difficult Proof Is Really a Proof
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Mathematical quotients and quotient types in Coq
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
A design structure for higher order quotients
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
General bindings and alpha-equivalence in nominal Isabelle
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Verified synthesis of knowledge-based programs in finite synchronous environments
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Reasoning about constants in nominal isabelle or how to formalize the second fixed point theorem
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Data refinement in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Program analysis and verification based on kleene algebra in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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Higher-Order Logic (HOL) is based on a small logic kernel, whose only mechanism for extension is the introduction of safe definitions and of non-empty types. Both extensions are often performed in quotient constructions. To ease the work involved with such quotient constructions, we re-implemented in the Isabelle/HOL theorem prover the quotient package by Homeier. In doing so we extended his work in order to deal with compositions of quotients and also specified completely the procedure of lifting theorems from the raw level to the quotient level. The importance for theorem proving is that many formal verifications, in order to be feasible, require a convenient reasoning infrastructure for quotient constructions.