Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Information and Computation - Semantics of Data Types
Handbook of logic in computer science (vol. 2)
LISP 1.5 Programmer's Manual
Proof by computation in the Coq system
Theoretical Computer Science - Special issue on theories of types and proofs
External Rewriting for Skeptical Proof Assistants
Journal of Automated Reasoning
Journal of Automated Reasoning
Proof Synthesis and Reflection for Linear Arithmetic
Journal of Automated Reasoning
Cut Elimination in Deduction Modulo by Abstract Completion
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Dealing with algebraic expressions over a field in Coq using Maple
Journal of Symbolic Computation
Zenon: an extensible automated theorem prover producing checkable proofs
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Theorem proving modulo based on Boolean equational procedures
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Inductive type schemas as functors
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
A computational approach to pocklington certificates in type theory
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Proof-producing program analysis
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Verifying mixed real-integer quantifier elimination
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A proposal for broad spectrum proof certificates
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
A modular integration of SAT/SMT solvers to coq through proof witnesses
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
LFP: a logical framework with external predicates
Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
Dependently typed programming based on automated theorem proving
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
25 years of formal proof cultures: some problems, some philosophy, bright future
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
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Formal proofs in mathematics and computer science are being studied because these objects can be verified by a very simple computer program. An important open problem is whether these formal proofs can be generated with an effort not much greater than writing a mathematical paper in, say, LATEX. Modern systems for proof development make the formalization of reasoning relatively easy. However, formalizing computations in such a manner that the results can be used in formal proofs is not immediate. In this paper we show how to obtain formal proofs of statements such as iPrime$(\underline{61})$ in the context of Peano arithmetic or (ix+1)(ix+1)=ix2+2ix+1 in the context of rings. We hope that the method will help bridge the gap between the efficient systems of computer algebra and the reliable systems of proof development.