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Formalization of Transform Methods using HOL Light [article]

Adnan Rashid, Osman Hasan
2017 arXiv   pre-print
In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover.  ...  In particular, we present the motivation of the formalization, which is followed by the related work.  ...  Acknowledgements This work was supported by the National Research Program for Universities grant (number 1543) of Higher Education Commission (HEC), Pakistan.  ... 
arXiv:1705.10050v1 fatcat:wpigu4et6bgp5m3m7xmtqicuxm

Formalization of Transform Methods Using HOL Light [chapter]

Adnan Rashid, Osman Hasan
2017 Lecture Notes in Computer Science  
In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover.  ...  In particular, we present the motivation of the formalization, which is followed by the related work.  ...  Acknowledgements This work was supported by the National Research Program for Universities grant (number 1543) of Higher Education Commission (HEC), Pakistan.  ... 
doi:10.1007/978-3-319-62075-6_22 fatcat:nh6h44hfkbc5dh6kk7aaz4cf4y

Verifying a Synthesized Implementation of IEEE-754 Floating-Point Exponential Function using HOL

B. Akbarpour, A. T. Abdel-Hamid, S. Tahar, J. Harrison
2009 Computer journal  
In this paper, we have hierarchically formalized and verified a hardware implementation of the IEEE-754 table-driven floating-point exponential function algorithm using the HOL theorem prover.  ...  Deep datapath and algorithm complexity have made the verification of floating-point units a very hard task.  ...  Formal Specification of the Exponential Function The original analysis of the floating-point exponential function in algorithmic level was performed by Harrison [7] using the HOL Light theorem prover  ... 
doi:10.1093/comjnl/bxp023 fatcat:wvf6ehqqefaqtj6yhois52grmy

Design and verification of a frequency domain equalizer

Anis Souari, Amjad Gawanmeh, Sofiène Tahar, Mohamed Lassaad Ammari
2014 Microelectronics Journal  
We conduct both floating-point and fixed-point error estimations for the design in Simulink and System Generator, respectively.  ...  In this work we provide a methodology for the design and verification of a frequency domain equalizer.  ...  Harisson [17] used the HOL-Light theorem prover to approximate floating-point algorithms to their mathematical counterparts.  ... 
doi:10.1016/j.mejo.2013.10.012 fatcat:2mfy7r7efvg55ofqqjivmsikku

Error Analysis and Verification of an IEEE 802.11 OFDM Modem using Theorem Proving

Abu Nasser Mohammed Abdullah, Behzad Akbarpour, Sofiène Tahar
2009 Electronical Notes in Theoretical Computer Science  
The versatile expressive power of HOL helped us model the original design at all abstraction levels starting from a floating-point model to the fixed-point design and then synthesized and implemented in  ...  the OFDM modem in HOL.  ...  Akbarpour's analysis of DSP algorithms follows Harrison's verification [11] of the floating-point algorithm for the exponential function using the HOL Light theorem prover which is a prior example of  ... 
doi:10.1016/j.entcs.2009.06.020 fatcat:zuiavmbnxbcirfeupm5cs76tvi

Floating-Point Verification Using Theorem Proving [chapter]

John Harrison
2006 Lecture Notes in Computer Science  
This chapter describes our work on formal verification of floating-point algorithms using the HOL Light theorem prover. let th6 = REAL_ARITH 'abs(c -a) < e ∧ abs(b) <= d =⇒ abs((a + b) -c) < d + e';;  ...  There are many theorem proving programs, 1 and quite a few have been applied to floating-point verification, including at least ACL2, Coq, HOL Light and PVS.  ...  In particular, two key strengths of HOL Light are 22 In fact, the reduced argument needs to be represented as two floating-point numbers, so there is an additional correction term that we ignore in this  ... 
doi:10.1007/11757283_8 fatcat:kz7ckh7iyrglbm4yw3mv4zzd3a

Error analysis of digital filters using HOL theorem proving

Behzad Akbarpour, Sofiène Tahar
2007 Journal of Applied Logic  
We use valuation functions to find the real values of the floating-point and fixed-point filter outputs and define the error as the difference between these values and the corresponding output of the ideal  ...  We first model the ideal real filter specification and the corresponding floating-point and fixed-point implementations as predicates in higher-order logic.  ...  using the HOL Light theorem prover.  ... 
doi:10.1016/j.jal.2006.11.001 fatcat:gineqyl46nduni7vqjbm4cahmq

A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations

Érik Martin-Dorel, Pierre Roux
2017 Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017  
A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations.  ...  Nevertheless, overapproximations with floating-point arithmetic can be enough to obtain proofs at a much lower cost.  ...  Light/Taylor" corresponds to (Solovyev and Hales 2013) . ( ) Remark: it should be noted that each running time in the last column includes the time (around 11s) for loading the image of the HOL Light  ... 
doi:10.1145/3018610.3018622 dblp:conf/cpp/Martin-DorelR17 fatcat:tuauz6kkzjdihbanfk4t2hrzse

Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq

Érik Martin-Dorel, Guillaume Melquiond
2015 Journal of automated reasoning  
The verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors.  ...  It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions.  ...  Acknowledgements We would like to thank the people from the ANR TaMaDi project for initiating and greatly contributing to the CoqApprox project.  ... 
doi:10.1007/s10817-015-9350-4 fatcat:4ges4bruovhqbphmqstyfhqkz4

A Machine-Checked Theory of Floating Point Arithmetic [chapter]

John Harrison
1999 Lecture Notes in Computer Science  
We also briefly describe how this has been used in the verification effort so far.  ...  This paper discusses the development of a generic floating point library giving definitions of the fundamental terms and containing formal proofs of important lemmas.  ...  The formal verification is being performed in HOL Light, a version of the HOL theorem prover [6] .  ... 
doi:10.1007/3-540-48256-3_9 fatcat:lmwkzws7zbaerhov7cybu34baq

Michael John Caldwell Gordon. 28 February 1948—22 August 2017

Lawrence C. Paulson
2018 Biographical Memoirs of Fellows of the Royal Society  
His students extended the work to such diverse areas as the verification of floating-point algorithms, the verification of probabilistic algorithms and the verified translation of source code to correct  ...  Michael Gordon was a pioneer in the field of interactive theorem proving and hardware verification.  ...  Harrison tackled this [15] ; he went on to accomplish great things in formalised mathematics, including verifying a floating-point exponential function [17] and (much later) playing a major role in  ... 
doi:10.1098/rsbm.2018.0019 fatcat:lionn75yjnddfeupt7dpwmvdcu

Formalization of real analysis: a survey of proof assistants and libraries

SYLVIE BOLDO, CATHERINE LELAY, GUILLAUME MELQUIOND
2015 Mathematical Structures in Computer Science  
We have chosen to look into the formalizations provided in standard by the following systems: Coq, HOL4, HOL Light, Isabelle/HOL, Mizar, ProofPower-HOL, and PVS.  ...  In the recent years, numerous proof systems have improved enough to be used for formally verifying non-trivial mathematical results.  ...  We are also grateful to the anonymous reviewers for their constructive remarks.  ... 
doi:10.1017/s0960129514000437 fatcat:qjnpetpbcbb4rbvm26geem3jai

An approach for the formal verification of DSP designs using Theorem proving

B. Akbarpour, S. Tahar
2006 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
To this end, a shallow embedding of DSP descriptions in HOL at the floatingpoint (FP), fixed-point (FXP), behavioral, register transfer level (RTL), and netlist gate levels is provided.  ...  The high ability of abstraction in HOL allows a seamless hierarchical verification encompassing the whole DSP design path, starting from top-level FP and FXP algorithmic descriptions down to RTL, and gate  ...  mathematical counterparts using the HOL light theorem prover.  ... 
doi:10.1109/tcad.2005.857314 fatcat:os73cqrturglnis2jv2gcub6mi

Deciding Univariate Polynomial Problems Using Untrusted Certificates in Isabelle/HOL

Wenda Li, Grant Olney Passmore, Lawrence C. Paulson
2017 Journal of automated reasoning  
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition.  ...  We present experiments demonstrating the efficacy of this approach, in many cases yielding orders of magnitude improvements over previous methods.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10817-017-9424-6 fatcat:hmwbpdzomvf4vgctwnerib4tp4

Multi-Prover Verification of Floating-Point Programs [chapter]

Ali Ayad, Claude Marché
2010 Lecture Notes in Computer Science  
We give a first-order axiomatization of floating-point operations which allows to reduce verification to checking the validity of logic formulas, in a suitable form for a large class of provers including  ...  In the context of deductive program verification, supporting floatingpoint computations is tricky. We propose an expressive language to formally specify behavioral properties of such programs.  ...  Melquiond for his help in the use of the Gappa tool, the FP-specific Coq tactics, and more generally for his suggestions about the approach presented here.  ... 
doi:10.1007/978-3-642-14203-1_11 fatcat:lje6cjsdvfg47iutx575bq2zh4
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