Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Formal Aspects of Computing
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Type theory and functional programming
Type theory and functional programming
Building reliable, high-performance communication systems from components
Proceedings of the seventeenth ACM symposium on Operating systems principles
A Simple Model for Quotient Types
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Semantic Foundations for Embedding HOL in Nuprl
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
Sequent Schema for Derived Rules
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Markov's Principle for Propositional Type Theory
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Proceedings of the Carnegie Mellon Workshop on Logic of Programs
Nuprl-Light: An Implementation Framework for Higher-Order Logics
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
A non-type-theoretic semantics for type-theoretic language
A non-type-theoretic semantics for type-theoretic language
The metaprl logical programming environment
The metaprl logical programming environment
A judgmental reconstruction of modal logic
Mathematical Structures in Computer Science
Formalizing Type Operations Using the “Image” Type Constructor
Electronic Notes in Theoretical Computer Science (ENTCS)
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
A design structure for higher order quotients
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
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In this paper we introduce a new approach to axiomatizing quotient types in type theory. We suggest replacing the existing monolithic rule set by a modular set of rules for a specially chosen set of primitive operations. This modular formalization of quotient types turns out to be much easier to use and free of many limitations of the traditional monolithic formalization. To illustrate the advantages of the new approach, we show how the type of collections (that is known to be very hard to formalize using traditional quotient types) can be naturally formalized using the new primitives. We also show how modularity allows us to reuse one of the new primitives to simplify and enhance the rules for the set types.