Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Information and Computation - Semantics of Data Types
Towards a computation system based on set theory
Theoretical Computer Science
Relating models of polymorphism
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
COLOG-88 Proceedings of the international conference on Computer logic
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
A higher-order calculus and theory abstraction
Information and Computation
Conditional rewriting logic as a unified model of concurrency
Selected papers of the Second Workshop on Concurrency and compositionality
Theoretical Computer Science
Order-sorted algebra solves the constructor-selector, multiple representation, and coercion problems
Information and Computation
A logical theory of concurrent objects and its realization in the Maude language
Research directions in concurrent object-oriented programming
Notes on set theory
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
General logics and logical frameworks
What is a logical system?
Theoretical Computer Science - Special issue: algebraic development techniques
Specification and proof in membership equational logic
Theoretical Computer Science - Trees in algebra and programming
Theoretical Computer Science - Special issue on theories of types and proofs
On Equivalents of Well-Foundedness
Journal of Automated Reasoning
A Unifying Theory of Dependent Types: The Schematic Approach
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
A Finite Axiomatization of Inductive-Recursive Definitions
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Membership algebra as a logical framework for equational specification
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
From Abstract Data Types to Logical Frameworks
Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification
The HOL/NuPRL Proof Translator (A Practical Approach to Formal Interoperability)
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Constructions: A Higher Order Proof System for Mechanizing Mathematics
EUROCAL '85 Invited Lectures from the European Conference on Computer Algebra-Volume I - Volume I
Rewriting Logic as a Semantic Framework for Concurrency: a Progress Report
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
The Calculus of algebraic Constructions
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Polymorphism is Set Theoretic, Constructively
Category Theory and Computer Science
A non-type-theoretic semantics for type-theoretic language
A non-type-theoretic semantics for type-theoretic language
Inductive types in the calculus of algebraic constructions
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Building decision procedures in the calculus of inductive constructions
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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The open calculus of constructions integrates key features of Martin-Löf's type theory, the calculus of constructions, membership equational logic, and rewriting logic into a single uniform language. The two key ingredients are dependent function types and conditional rewriting modulo equational theories. We explore the open calculus of constructions as a uniform framework for programming, specification and interactive verification in an equational higher-order style. By having equational logic and rewriting logic as executable sublogics we preserve the advantages of a first-order semantic and logical framework and we provide a foundation for a broad spectrum of applications ranging from what could be called executable mathematics, involving symbolic computations and logical proofs, to software and system engineering applications, involving symbolic execution and analysis of nondeterministic and concurrent systems.