Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Pebble, a kernel language for modules and abstract data types
Information and Computation - Semantics of Data Types
Computational category theory
PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Towards a computation system based on set theory
Theoretical Computer Science
How to make ad-hoc polymorphism less ad hoc
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
LFP '92 Proceedings of the 1992 ACM conference on LISP and functional programming
ESOP'92 Symposium proceedings on 4th European symposium on programming
Theoretical Computer Science
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Closure under alpha-conversion
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Cayenne—a language with dependent types
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Abstract types have existential types
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Specification and proof in membership equational logic
Theoretical Computer Science - Trees in algebra and programming
Proof, language, and interaction
Theoretical Computer Science
Using dependent types to express modular structure
POPL '86 Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
An Operational Approach to Combining Classical Set Theory and Functional Programming Languages
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the 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
A Type Annotation Scheme for Nuprl
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Codifying Guarded Definitions with Recursive Schemes
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
A de Bruijn Notation for Higher-Order Rewriting
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Rewriting Logic as a Unifying Framework for Petri Nets
Unifying Petri Nets, Advances in Petri Nets
Comparing Combinatory Reduction Systems and Higher-order Rewrite Systems
HOA '93 Selected Papers from the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Importing Mathematics from HOL into Nuprl
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
A Simple Model Construction for the Calculus of Constructions
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Relating Strands and Multiset Rewriting for Security Protocol Analysis
CSFW '00 Proceedings of the 13th IEEE workshop on Computer Security Foundations
Revisiting the algebra of Petri net processes under the collective token philosophy
Fundamenta Informaticae - Concurrency specification and programming
A non-type-theoretic semantics for type-theoretic language
A non-type-theoretic semantics for type-theoretic language
Qualified types: theory and practice (ordering relation)
Qualified types: theory and practice (ordering relation)
Higher-Order and Symbolic Computation
All about maude - a high-performance logical framework: how to specify, program and verify systems in rewriting 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.