The method of differentiating under the integral sign
Journal of Symbolic Computation
Integrated software components: a paradigm for control integration
Proceedings of the European symposium on Software development environments and CASE technology
Experiments with proof plans for induction
Journal of Automated Reasoning
AXIOM: the scientific computation system
AXIOM: the scientific computation system
Well … it isn't quite that simple
ACM SIGSAM Bulletin
CAS/PI: a portable and extensible interface for computer algebra systems
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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
Theorems and algorithms: an interface between Isabelle and Maple
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Checking geometric programs or verification of geometric structures
Proceedings of the twelfth annual symposium on Computational geometry
HOL'92 Proceedings of the IFIP TC10/WG10.2 Workshop on Higher Order Logic Theorem Proving and its Applications
Mathpert: Computer Support for Learning Algebra, Trig, and Calculus
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Floating Point Verification in HOL Light: The Exponential Function
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
DISCO '93 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Program Result Checking: A New Approach to Making Programs More Reliable
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Linking Other Theorem Provers to HOL Using PM: Proof Manager
HOL'92 Proceedings of the IFIP TC10/WG10.2 Workshop on Higher Order Logic Theorem Proving and its Applications
A Lazy Approach to Fully-Expansive Theorem Proving
HOL'92 Proceedings of the IFIP TC10/WG10.2 Workshop on Higher Order Logic Theorem Proving and its Applications
Analytica - A Theorem Prover for Mathematica
Analytica - A Theorem Prover for Mathematica
Maple's evaluation process as constraint contextual rewriting
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
The control layer in open mechanized reasoning systems: annotations and tactics
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
MBase: representing knowledge and context for the intergration of mathematical software systems
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
A Machine-Checked Implementation of Buchberger's Algorithm
Journal of Automated Reasoning
Algorithms and Proofs Inheritance in the FOC Language
Journal of Automated Reasoning
Controlling Control Systems: An Application of Evolving Retrenchment
ZB '02 Proceedings of the 2nd International Conference of B and Z Users on Formal Specification and Development in Z and B
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
Providing a formal linkage between MDG and HOL
Formal Methods in System Design
Context Aware Calculation and Deduction
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Certified Computer Algebra on Top of an Interactive Theorem Prover
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Theorem Proving for Verification (Invited Tutorial)
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Combining Isabelle and QEPCAD-B in the Prover's Palette
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Cooperating Theorem Provers: A Case Study Combining HOL-Light and CVC Lite
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Connecting Logical Representations and Efficient Computations
Electronic Notes in Theoretical Computer Science (ENTCS)
A reconstruction and extension of Maple's assume facility via constraint contextual rewriting
Journal of Symbolic Computation
Dealing with algebraic expressions over a field in Coq using Maple
Journal of Symbolic Computation
A short survey of automated reasoning
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Fast reflexive arithmetic tactics the linear case and beyond
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Verifying nonlinear real formulas via sums of squares
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
A foundational view on integration problems
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Proving valid quantified Boolean formulas in HOL light
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
A computational approach to pocklington certificates in type theory
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving formally the implementation of an efficient gcd algorithm for polynomials
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving equalities in a commutative ring done right in coq
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Interfacing Coq + SSReflect with GAP
Electronic Notes in Theoretical Computer Science (ENTCS)
A universal machine for biform theory graphs
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Communications of the ACM
| Hi-index | 0.02 |
We contrast theorem provers and computer algebra systems, pointing outthe advantages and disadvantages of each, and suggest a simple way toachieve a synthesis of some of the best features of both. Our method isbased on the systematic separation of search for a solution and checking thesolution, using a physical connection between systems. We describe theseparation of proof search and checking in some detail, relating it to proofplanning and to the complexity class NP, and discuss different ways ofexploiting a physical link between systems. Finally, the method isillustrated by some concrete examples of computer algebra results provedformally in the HOL theorem prover with the aid of Maple.