A Complete Decision Procedure for Univariate Polynomial Problems in Isabelle/HOL
نویسندگان
چکیده
We present a complete, certificate-based decision procedure for first-order univariate polynomial problems in Isabelle [17]. It is built around an executable function to decide the sign of a univariate polynomial at a real algebraic point. The procedure relies on no trusted code except for Isabelle’s kernel and code generation. This work is the first step towards integrating the MetiTarski theorem prover [1] into Isabelle.
منابع مشابه
Combining WS1S and HOL
We investigate the combination of the weak second-order monadic logic of one successor (WS1S) with higher-order logic (HOL). We show how these two logics can be combined, how theorem provers based on them can be safely integrated, and how the result can be used. In particular, we present an embedding of the semantics of WS1S in HOL that provides a basis for coupling the MONA system, a decision ...
متن کاملUsing a SAT Solver as a Fast Decision Procedure for Propositional Logic in an LCF-style Theorem Prover
This paper describes the integration of a leading SAT solver with Isabelle/HOL, a popular interactive theorem prover. The SAT solver generates resolution-style proofs for (instances of) propositional tautologies. These proofs are verified by the theorem prover. The presented approach significantly improves Isabelle’s performance on propositional problems, and furthermore exhibits counterexample...
متن کاملThe Factorization Algorithm of Berlekamp and Zassenhaus
We formalize the Berlekamp-Zassenhaus algorithm for factoring square-free integer polynomials in Isabelle/HOL. We further adapt an existing formalization of Yun’s square-free factorization algorithm to integer polynomials, and thus provide an efficient and certified factorization algorithm for arbitrary univariate polynomials. The algorithm first performs a factorization in the prime field GF(p...
متن کاملAutomated Provers doing (Higher-Order) Proof search: A Case Study in the Verification of Pointer Programs
We would like to present results obtained after doing a case study on the possibilities of doing proof search in a higher-order logic using existing automated proof tools. A commonly occurring type of proof obligation necessary to prove the correctness of the Schorr-Waite algorithm in the interactive prover Isabelle/HOL is given as a problem to the automated prover haRVey. Preliminary experimen...
متن کاملParametric Linear Arithmetic over Ordered Fields in Isabelle/HOL
We use higher-order logic to verify a quantifier elimination procedure for linear arithmetic over ordered fields, where the coefficients of variables are multivariate polynomials over another set of variables, we call parameters. The procedure generalizes Ferrante and Rackoff’s algorithm for the non-parametric case. The formalization is based on axiomatic type classes and automatically carries ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1506.08238 شماره
صفحات -
تاریخ انتشار 2015