scholarly journals TacticToe: Learning to Reason with HOL4 Tactics

10.29007/ntlb ◽  
2018 ◽  
Author(s):  
Thibault Gauthier ◽  
Cezary Kaliszyk ◽  
Josef Urban

Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants. Such “hammer” techniques complement traditional proof assistant automation as implemented by tactics and decision procedures. In this paper we present a unified proof assistant automation approach which attempts to automate the selection of appropriate tactics and tactic-sequences combined with an optimized small-scale hammering approach. We implement the technique as a tactic-level automation for HOL4: TacticToe. It implements a modified A*-algorithm directly in HOL4 that explores different tactic-level proof paths, guiding their selection by learning from a large number of previous tactic-level proofs. Unlike the existing hammer methods, TacticToe avoids translation to FOL, working directly on the HOL level. By combining tactic prediction and premise selection, TacticToe is able to re-prove 39% of 7902 HOL4 theorems in 5 seconds whereas the best single HOL(y)Hammer strategy solves 32% in the same amount of time.

Author(s):  
David Castro ◽  
Francisco Ferreira ◽  
Nobuko Yoshida

Abstract Session types provide a principled programming discipline for structured interactions. They represent a wide spectrum of type-systems for concurrency. Their type safety is thus extremely important. EMTST is a tool to aid in representing and validating theorems about session types in the Coq proof assistant. On paper, these proofs are often tricky, and error prone. In proof assistants, they are typically long and difficult to prove. In this work, we propose a library that helps validate the theory of session types calculi in proof assistants. As a case study, we study two of the most used binary session types systems: we show the impossibility of representing the first system in $$\alpha $$-equivalent representations, and we prove type preservation for the revisited system. We develop our tool in the Coq proof assistant, using locally nameless for binders and small scale reflection to simplify the handling of linear typing environments.


2020 ◽  
Vol 15 ◽  
Author(s):  
Deeksha Saxena ◽  
Mohammed Haris Siddiqui ◽  
Rajnish Kumar

Background: Deep learning (DL) is an Artificial neural network-driven framework with multiple levels of representation for which non-linear modules combined in such a way that the levels of representation can be enhanced from lower to a much abstract level. Though DL is used widely in almost every field, it has largely brought a breakthrough in biological sciences as it is used in disease diagnosis and clinical trials. DL can be clubbed with machine learning, but at times both are used individually as well. DL seems to be a better platform than machine learning as the former does not require an intermediate feature extraction and works well with larger datasets. DL is one of the most discussed fields among the scientists and researchers these days for diagnosing and solving various biological problems. However, deep learning models need some improvisation and experimental validations to be more productive. Objective: To review the available DL models and datasets that are used in disease diagnosis. Methods: Available DL models and their applications in disease diagnosis were reviewed discussed and tabulated. Types of datasets and some of the popular disease related data sources for DL were highlighted. Results: We have analyzed the frequently used DL methods, data types and discussed some of the recent deep learning models used for solving different biological problems. Conclusion: The review presents useful insights about DL methods, data types, selection of DL models for the disease diagnosis.


2021 ◽  
pp. 0887302X2199594
Author(s):  
Ahyoung Han ◽  
Jihoon Kim ◽  
Jaehong Ahn

Fashion color trends are an essential marketing element that directly affect brand sales. Organizations such as Pantone have global authority over professional color standards by annually forecasting color palettes. However, the question remains whether fashion designers apply these colors in fashion shows that guide seasonal fashion trends. This study analyzed image data from fashion collections through machine learning to obtain measurable results by web-scraping catwalk images, separating body and clothing elements via machine learning, defining a selection of color chips using k-means algorithms, and analyzing the similarity between the Pantone color palette (16 colors) and the analysis color chips. The gap between the Pantone trends and the colors used in fashion collections were quantitatively analyzed and found to be significant. This study indicates the potential of machine learning within the fashion industry to guide production and suggests further research expand on other design variables.


2021 ◽  
Vol 23 (4) ◽  
pp. 2742-2752
Author(s):  
Tamar L. Greaves ◽  
Karin S. Schaffarczyk McHale ◽  
Raphael F. Burkart-Radke ◽  
Jason B. Harper ◽  
Tu C. Le

Machine learning models were developed for an organic reaction in ionic liquids and validated on a selection of ionic liquids.


Author(s):  
Zhongyu Wan ◽  
Quan-De Wang ◽  
Dongchang Liu ◽  
Jinhu Liang

Enzyme-catalyzed synthesis reactions are of crucial importance for a wide range of applications. An accurate and rapid selection of optimal synthesis conditions is crucial and challenging for both human knowledge...


Procedia CIRP ◽  
2021 ◽  
Vol 96 ◽  
pp. 272-277
Author(s):  
Hannah Lickert ◽  
Aleksandra Wewer ◽  
Sören Dittmann ◽  
Pinar Bilge ◽  
Franz Dietrich

2021 ◽  
Vol 11 (2) ◽  
pp. 472
Author(s):  
Hyeongmin Cho ◽  
Sangkyun Lee

Machine learning has been proven to be effective in various application areas, such as object and speech recognition on mobile systems. Since a critical key to machine learning success is the availability of large training data, many datasets are being disclosed and published online. From a data consumer or manager point of view, measuring data quality is an important first step in the learning process. We need to determine which datasets to use, update, and maintain. However, not many practical ways to measure data quality are available today, especially when it comes to large-scale high-dimensional data, such as images and videos. This paper proposes two data quality measures that can compute class separability and in-class variability, the two important aspects of data quality, for a given dataset. Classical data quality measures tend to focus only on class separability; however, we suggest that in-class variability is another important data quality factor. We provide efficient algorithms to compute our quality measures based on random projections and bootstrapping with statistical benefits on large-scale high-dimensional data. In experiments, we show that our measures are compatible with classical measures on small-scale data and can be computed much more efficiently on large-scale high-dimensional datasets.


2011 ◽  
Vol 21 (4) ◽  
pp. 827-859 ◽  
Author(s):  
FRÉDÉRIC BLANQUI ◽  
ADAM KOPROWSKI

Termination is an important property of programs, and is notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting. Over the years, many methods and tools have been developed to address the problem of deciding termination for specific problems (since it is undecidable in general). Ensuring the reliability of those tools is therefore an important issue.In this paper we present a library formalising important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools.The sources are freely available athttp://color.inria.fr/.


2015 ◽  
Vol 47 (1) ◽  
pp. 5-17
Author(s):  
Jolanta Korycka-Skorupa

Abstract The author discuss effectiveness of cartographic presentations. The article includes opinions of cartographers regarding effectiveness, readability and efficiency of a map. It reminds the principles of map graphic design in order to verify them using examples of small-scale thematic maps. The following questions have been asked: Is the map effective? Why is the map effective? How do cartographic presentation methods affect effectiveness of the cartographic message? What else can influence effectiveness of a map? Each graphic presentation should be effective, as its purpose is to complete written word, draw the recipients’ attention, make text more readable, expose the most important information. Such a significant role of graphics results in the fact that graphic presentations (maps, diagrams) require proper preparation. Users need to have a chance to understand the graphics language in order to draw correct conclusions about the presented phenomenon. Graphics should demonstrate the most important elements, some tendencies, and directions of changes. It should generalize and present a given subject from a slightly different perspective. There are numerous examples of well-edited and poorly edited small-scale thematic maps. They include maps, which are impossible to interpret correctly. They are burdened with methodological defects and they cannot fulfill their task. Cartography practice indicates that the principles related to graphic design of cartographic presentation are frequently omitted during the process of developing small-scale thematic maps used – among others – in the press and on the Internet. The purpose of such presentations is to quickly interpret them. On such maps editors’ problems with the selection of an appropriate symbol and graphic variable (fig. 1A, 9B) are visible. Sometimes they use symbols which are not sufficiently distinguishable nor demonstrative (fig. 11), it does not increase their readability. Sometime authors try too hard to reflect presented phenomenon and therefore the map becomes more difficult to interpret (fig. 4A,B). The lack of graphic sense resulting in the lack of graphic balance and aesthetics constitutes a weak point of numerous cartographic presentations (fig. 13). Effectiveness of cartographic presentations consists of knowledge and skills of the map editor, as well as the recipients’ perception capabilities and their readiness to read and interpret maps. The qualifications of the map editor should include methodological qualifications supported by the knowledge of the principles for cartographic symbol design, as well as relevant technical qualifications, which allow to properly use the tools to edit a map. Maps facilitate the understanding of texts they accompany and they present relationships between phenomenon better than texts, appealing to the senses.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Go-Eun Yu ◽  
Younhee Shin ◽  
Sathiyamoorthy Subramaniyam ◽  
Sang-Ho Kang ◽  
Si-Myung Lee ◽  
...  

AbstractBellflower is an edible ornamental gardening plant in Asia. For predicting the flower color in bellflower plants, a transcriptome-wide approach based on machine learning, transcriptome, and genotyping chip analyses was used to identify SNP markers. Six machine learning methods were deployed to explore the classification potential of the selected SNPs as features in two datasets, namely training (60 RNA-Seq samples) and validation (480 Fluidigm chip samples). SNP selection was performed in sequential order. Firstly, 96 SNPs were selected from the transcriptome-wide SNPs using the principal compound analysis (PCA). Then, 9 among 96 SNPs were later identified using the Random forest based feature selection method from the Fluidigm chip dataset. Among six machines, the random forest (RF) model produced higher classification performance than the other models. The 9 SNP marker candidates selected for classifying the flower color classification were verified using the genomic DNA PCR with Sanger sequencing. Our results suggest that this methodology could be used for future selection of breeding traits even though the plant accessions are highly heterogeneous.


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