Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Information and Computation - Semantics of Data Types
Mathematica: a system for doing mathematics by computer
Mathematica: a system for doing mathematics by computer
First-order logic and automated theorem proving
First-order logic and automated theorem proving
Ontic: a knowledge representation system for mathematics
Ontic: a knowledge representation system for mathematics
Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
Program specification and data refinement in type theory
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
AXIOM: the scientific computation system
AXIOM: the scientific computation system
Elements of interaction: Turing award lecture
Communications of the ACM
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
On the SUP-INF Method for Proving Presburger Formulas
Journal of the ACM (JACM)
A Practical Decision Procedure for Arithmetic with Function Symbols
Journal of the ACM (JACM)
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
A formulation of the simple theory of types (for Isabelle)
COLOG '88 Proceedings of the International Conference on Computer Logic
HUG '93 Proceedings of the 6th International Workshop on Higher Order Logic Theorem Proving and its Applications
On Extensibility of Proof Checkers
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
Verifying a Logic Synthesis Tool in Nuprl: A Case Study in Software Verification
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Nuprl-Light: An Implementation Framework for Higher-Order Logics
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Studying the ML Module System in Hol
Proceedings of the 7th International Workshop on Higher Order Logic Theorem Proving and Its Applications
The complexity of elementary algebra and geometry
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
The Weyl Computer Algebra Substrate
The Weyl Computer Algebra Substrate
Complexity of finitely presented algebras.
Complexity of finitely presented algebras.
A Certified Polynomial-Based Decision Procedure for Propositional Logic
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Reflective metalogical frameworks
ACM Transactions on Computational Logic (TOCL)
A computational approach to reflective meta-reasoning about languages with bindings
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Mechanized meta-reasoning using a hybrid HOAS/de bruijn representation and reflection
Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming
Practical Reflection for Sequent Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
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Proving theorems is a creative act demanding new combinations of ideas and on occasion new methods of argument. For this reason, theorem proving systems need to be extensible. The provers should also remain correct under extension, so there must be a secure mechanism for doing this. The tactic-style provers pioneered by Edinburgh LCF provide a very effective way to achieve secure extensions, but in such systems, all new methods must be reduced to tactics. This is a drawback because there are other useful proof generating tools such as decision procedures; these include, for example, algorithms which reduce a deduction problem, such as arithmetic provability, to a computation on graphs.The Nuprl system pioneered the combination of fixed decision procedures with tactics, but the issue of securely adding new ones was not solved. In this paper we show how to safely include user-defined decision procedures in theorem provers. The idea is to prove properties of the procedure inside the prover’s logic and then invoke a reflection rule to connect the procedure to the system. We also show that using a rich underlying logic permits an abstract account of the approach so that the results carry over to different implementations and other logics.