Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Constructing the real numbers in HOL
Formal Methods in System Design - Special issue on higher order logic theorem proving and its applications, II
Discrete Mathematical Structures
Discrete Mathematical Structures
A constructive algebraic hierarchy in Coq
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Higher Order Quotients and their Implementation in Isabelle HOL
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Mechanising λ-calculus using a classical first order theory of terms with permutations
Higher-Order and Symbolic Computation
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
Let's Get Physical: Models and Methods for Real-World Security Protocols
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Packaging Mathematical Structures
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Structured formal development with quotient types in Isabelle/HOL
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Quotients revisited for Isabelle/HOL
Proceedings of the 2011 ACM Symposium on Applied Computing
Partizan games in Isabelle/HOLZF
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
A design structure for higher order quotients
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proving bounds for real linear programs in Isabelle/HOL
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proof pearl: defining functions over finite sets
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Nominal techniques in Isabelle/HOL
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
| Hi-index | 0.00 |
A quotient construction defines an abstract type from a concrete type, using an equivalence relation to identify elements of the concrete type that are to be regarded as indistinguishable. The elements of a quotient type are equivalence classes: sets of equivalent concrete values. Simple techniques are presented for defining and reasoning about quotient constructions, based on a general lemma library concerning functions that operate on equivalence classes. The techniques are applied to a definition of the integers from the natural numbers, and then to the definition of a recursive datatype satisfying equational constraints.