Generating functionology
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
Type Classes and Overloading in Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Combinatorial Enumeration
Context Aware Calculation and Deduction
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Automating Elementary Number-Theoretic Proofs Using Gröbner Bases
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Constructive type classes in Isabelle
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Proof pearl: defining functions over finite sets
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
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We present a formalization of the topological ring of formal power series in Isabelle/HOL. We also formalize formal derivatives, division, radicals, composition and reverses. As an application, we show how formal elementary and hyper-geometric series yield elegant proofs for some combinatorial identities. We easily derive a basic theory of polynomials. Then, using a generic formalization of the fraction field of an integral domain, we obtain formal Laurent series and rational functions for free.