Essay Scoring with LLM Agent
Fernando Polanco Espino, A. Dolganov
This study presents an AI-based agent designed to automate the grading of student essays in the Ecology course at Ural Federal University. The agent leverages the capabilities of Large Language Models (LLMs), particularly from the Llama family, to evaluate various aspects of student writing, including grammar, structure, and content relevance. The system integrates advanced natural language processing techniques, Python libraries for data handling and analysis, and prompt engineering strategies to ensure accurate interpretation of student input. In addition to scoring, the model generates detailed feedback aimed at helping students understand their strengths and areas for improvement.Preliminary results from experiments using different versions of Llama models show a tendency to assign mid-range scores across most submissions. This indicates a challenge in clearly distinguishing between low- and high-quality responses, particularly for essays lacking strong arguments or cohesive structure. Despite occasional inconsistencies in scoring, the implementation of AI in the grading process has the potential to significantly streamline assessment workflows, reduce instructor workload, and enhance the consistency and depth of feedback. These findings suggest promising directions for improving both the accuracy and transparency of automated grading systems in educational contexts.
Bulgaristan Türk Şiirinde “Rodoplar”
Nurcihan Güneş
Rodoplar, Bulgaristan’ın güneyinde yer alan ve bir kısmı Yunanistan’a uzanan, Balkanlar’da önemli bir dağ silsilesidir. Balkanlar’daki Türk kültürünün önemli temsilcileri arasında yer alan ve ağırlıklı olarak Bulgaristan’ın Kırcali, Hasköy (Haskovo) ve Filibe (Plovdiv) illerinde yaşayan Rodop Türkleri, bölgenin sosyal ve kültürel yapısına kayda değer katkılarda bulunmuş; aynı zamanda tarihî ve kültürel kimliğin şekillenmesinde de belirleyici bir rol üstlenmiştir. Bu çalışmada, Bulgaristan Türk şiirinde tematik açıdan öne çıkan unsurlardan biri olan “Rodoplar” temasının farklı boyutlarıyla incelenmesi amaçlanmaktadır. Çalışmanın temel amacı, Türk nüfusunun yoğun olarak yaşadığı, siyasi ve sosyal açıdan stratejik bir öneme sahip olan Rodoplar’ın, Bulgaristan Türk şiirindeki yansımalarını ortaya koymaktır. Bu bağlamda, Recep Küpçü, Niyazi Bahtiyar, Muharrem Zeynel Yumuk, Gülay Rafet Ahmet, Fahriye Mustafa Güney, Nazmi Türker Adalı, Mümün Bekir Mehmet, Osman Aziz, Nefise Habib Adıgüzel, Şahin Mustafa Altan, Mehmet Ali Macar, Ahmet Hasan Cebeci ve Mümin Mustafa Atakan gibi şairlerin şiirleri ele alınmıştır. Rodop Türklerinin ruh dünyasını, sosyal, kültürel ve siyasî deneyimlerini, yaşadıkları coğrafyaya duydukları aidiyet ve bağlılığı yansıtan şiirler üzerinden “Rodoplar” temasının Bulgaristan Türk şiirindeki yeri belirlenmiştir.
Ning-ist ja-ni ja edasi
Külli Habicht, Külli Prillop
From ning to ja and beyond
This article examines the occurrence and functional distribution of the linguistic units ja and ning (‘and’) in early written Estonian texts. In modern Estonian, ja and ning are high-frequency synonymous coordinating conjunctions, whose functions have been described in previous linguistic studies and subjected to prescriptive language regulation. The corpus-based study reveals that while the conjunction ning appears in the oldest preserved texts, evidence of the reinterpretation of the affirmative response particle ja(a) as a conjunction can already be found in early 17th-century texts. Based on the preserved sources of written Estonian, it is evident that the contact-induced particle ja occurs in (inter)subjective contexts, not only in an affirmative function but also in a connective one (jaa > ja). This represents a rare developmental pathway for conjunctions: a contact-induced particle (ja) evolving into a conjunction. This process demonstrates a transition from pragmatics to grammar.
Previous studies suggest that the more common developmental path involves the opposite direction: a conjunction evolving into a particle. However, such an exceptional pathway becomes possible when the contact-induced linguistic unit possesses a suitable phonological structure and meaning. Although the particle functions of ja – affirmative, emphatic, and concordant – also exist in German, the conjunction function develops only in Estonian. The entrenchment of the conjunction ja was further supported by deliberate decisions made during the ecclesiastical reforms of written language in the late 17th century, as well as by the authority of the 1739 Estonian Bible.
The emphatic function of the particle ja – conveying meanings ‘indeed, surely’ and derived from German – also appears in 17th-century texts, albeit rarely. This represents a secondary branch of functional development influenced by language contact. However, the development of the conjunction ja is primarily linked to the reinterpretation of the affirmative particle jaa, as evidenced by numerous bridging constructions in texts from the early 17th century onward. The emphatic and affirmative functions connect ja as both an affirmative response particle (jaa) and as an emphatic particle (‘ju’). The decline of emphatic usage and the increased positioning of ja in sentence-internal connective roles led to its preference as a neutral coordinative conjunction from the 18th century onward.
A distinction between Northern and Southern Estonian usage lies in the fact that Southern Estonian texts overwhelmingly favour the conjunction ning until the late 18th century. The affirmative response particle jaa emerges in Southern Estonian texts only in the second half of the 18th century. The emphatic use of ja in the sense of ‘indeed, surely’ is also rare in written Southern Estonian. Consequently, the development of ja into a conjunction occurs earlier and more rapidly in Northern Estonian texts compared to Southern Estonian ones.
Other Finnic languages and dialects
A Multilingual Python Programming Language
Saad Ahmed Bazaz, Mirza Omer Beg
All widely used and useful programming languages have a common problem. They restrict entry on the basis of knowledge of the English language. The lack of knowledge of English poses a major hurdle to many newcomers who do not have the resources, in terms of time and money, to learn the English language. Studies show that people learn better in their own language. Therefore, we propose a language transpiler built on top of the Python programming language, called UniversalPython, which allows one to write Python in their own human language. We demonstrate the ability to create an "Urdu Python" with this transpiler. In the future, we aim to scale the language to encapsulate more human languages to increase the availability of programming. The source code for this transpiler is open-source, and available at https://github.com/universalpython/universalpython
Names of Belemnites and Fulgurites in the Russian Language: Scientific and Old Russian Nomenclature
Arina S. Akhrameeva
This article studies the names of belemnites and fulgurites, functioning in contemporary scientific nomenclature, as well as recorded in the history of the Russian language. For the material of the article, the author refers to mineralogical literature, as well as historical dictionaries of the Russian language. Lexemes in question are considered in historical, lexicological, and motivational-etymological aspects in accordance with the methodology developed by the Ural School of Onomastics, Etymology, and Ethnolinguistics. When analysing the material, special attention is paid to the origin of the nominations: loan translation (громовые трубки, камень светящийся, рысий камень, морская желудь, etc.), borrowings (лешательерит, ливианит, etc.), while some words can be considered foreign inclusions (астрапиалит, керавний, идейские камни), Russian names (перун, перунка). A hypothesis is made about the typologically independent origin of the громовая стрела idiom. Names that have appeared recently and exist only within the framework of scientific nomenclature use set nominative models for mineral names: naming after a scientist (лешательерит), the place of extraction (ливит), the composition of the mineral (стекло кварцевое, стекло кремниевое, трубка песчаная). Several designations (астрапиалит, церавний, перун, фульгурит, белемнит, громовая стрела, etc.) reflect ideas about the connection of the minerals analysed with lightning and about lightning being the reason for the appearance of such a stone; in these representations, the real (фульгурит) and mythopoeic motivation are fused together. Some names employ somatic (водяная кость, чертов палец), faunal (гельмитолит, рысий камень), and floral images (морская желудь). The collection and description of dialectal and foreign language material will determine the further direction of research.
Medical Topic in Nominative Models of Mineralogical Vocabulary
V. Kuchko
This article continues the motivational study of the Russian and foreign-language mineralogical names, initiated in recent years by the Ural School of Onomastics, Etymology, and Ethnolinguistics. The article focuses on a separate group of mineralogical vocabulary that functions in the Russian language, i.e. names that are motivationally related to the vocabulary of the medical thematic field. The purpose of the article is to trace the nomination motives characteristic of this group and identify the naming patterns used within it. The group is formed by means of both official and unofficial terminology (namely, terminology belonging to the professional jargon of those who mine, process, and sell minerals). There are original names, loanwords, and calques. The sociolinguistic heterogeneity of the linguistic facts considered in the work shows the difference in the embodiment of the medical topic by means of different linguistic strata. The author demonstrates that the medical topic is represented by various nominative features. The name can be based on a general motive, such as “a stone has medicinal properties” (камень медика, камень здоровья, etc.) / “medical functions” (аптекарский камень); a motive for providing medical care to a specific organ (нефрит, почечный камень, жад) or getting rid of a certain condition (аметист); “the stone is sick / healing” motive. The medical topic is also implemented in a naming pattern, according to which the name of a mineral or rock includes, for various reasons, the name of a disease (оспенная руда). The article traces the history of certain mineralogical names (in particular, аптекарский камень ‘serpentine,’ нефрит, почечный камень ‘jade’, жадеит) in the Russian language tradition against the background of a foreign language.
Industrial Culture in the Mirror of Ekaterinburg Urbanonymy
M. Golomidova, S. Goryaev
This article is devoted to a linguocultural study of urbanonyms of Ekaterinburg in the context of representation of industrial culture. Factories have played a pivotal role in the development of the sociocultural environment of the Ural city and in the exploration of its physical space. As proper names of topographic objects are closely related to the particularities of the spiritual and material culture of a society, the urbanonyms of Ekaterinburg can be regarded as a transmitter of value-based perceptions connected to the dynamics of the city’s industrial life. The article describes semantic variants of objectification of the “industrial” nomination theme in urban toponyms of Ekaterinburg (Sverdlovsk) and attempts to reveal the topicality of industrial culture for the modern urbanonymic nomination. The language material of the research involves urbanonyms from several types of proper names (horonyms, hodonyms, agoronyms, monumentonyms, and partially oikodomonyms) collected from written sources — formal, scholarly, and journalistic texts. The main method of interpreting the empiric material is the onomasiological analysis of the inner form of toponyms followed by linguocultural comments on the motivational meanings. The chosen research technique makes it possible to determine the implementation of a wide range of nomination variants in the framework of the large “industrial” theme. Urbanonyms emphasize the spatial proximity of the named topographic items to factories and plants, express respect for the working people in general and representatives of different professions in particular, verbalize the relation with manufacturing processes and production, posit the semantic reference to industrial towns and settlements. The analysis carried out proves that the toponymic implementation of the “industrial” theme dating back to the eighteenth century is still going on at present, albeit moving to new spheres of designation (art-clusters), yet maintaining its role in preserving the Ural identity.
Kuningamäe(d)
Tiina Laansalu, Peeter Päll
The name(s) Kuningamäe
This article examines Estonian place names containing the term kuningas ‘king’. The earliest records of Kuninga-names date back to the 16th century. The Place Names Archive of the Institute of the Estonian Language lists more than 200 place names beginning with Kuning(a)-. By comparison, terms denoting other noble ranks are significantly less common: there are 86 names starting with krahv ‘count’, 43 with parun ‘baron’, 29 each with keiser ‘emperor’ and prints ‘prince’, four with vürst ‘prince’ (from the German Würst), and one with hertsog ‘duke’.
Kuningamäe is a typical Estonian compound place name, composed of kuningas : kuninga ‘king’ + mägi : mäe ‘hill, mountain’. One instance of Kuningamäe is a translation of the German Königsberg, referring to a village near Põltsamaa. Notably, the renowned Königsberg of East Prussia was not translated into Estonian; the German name was retained instead. When Poland reverted the name Kaliningrad to its historical Polish equivalent Królewiec, a parallel debate arose in Estonia. However, Estonia lacks a formal mechanism for standardizing foreign names. Instead, the writing of foreign place names in Estonian is largely guided by the dictionary of standard Estonian.
The act of naming is often more than linguistic; it can reflect political, cultural, historical, and societal considerations. This interplay makes it a rich area of study within socio-onomastics.
Other Finnic languages and dialects
Phrases constructed with turkish organ names in the hamdullah hamdî's yusuf u züleyhâ
Züleyha
Masnavi is a form of verse in which short forms of aruz are used and each couplet is
rhymed among itself. Masnavis are important in that they convey the messages the poet wants
to say to the society in a detailed and comfortable way. Yusuf u Züleyha Masnavi, one of the
oldest religious masnavis, which is about the love of Prophet Yusuf and Zuleyha, has an
important place both religiously and literaryly in terms of the messages it contains.
In the study, the idioms formed with Turkish organ names in the last 4235 couplets of
the Yusuf u Züleyha masnavi written by the Hamdullah Hamdî, one of the 15th century poets,
were discussed. Examining the simile motifs in the idioms formed with the names of organs and
elucidating the hidden bond between the literal meaning and the figurative meaning has an
important place for linguistics research.
Many studies have been carried out on organ names from past to present. Based on
these studies, among the idioms formed with the names of organs, the most numerous idioms
formed with the names of head, tongue, hand, heart, eye and facial organs are numerically more
numerous. In this study, the idioms established with the names of these basic organs of the body
and other organs will be identified and classified according to the organs, and the idiom will be
shown in bold form at the beginning, and on the right side, the transfer of the idiom to today's
Turkish, followed by the example couplet it is in, the transfer of the example couplet to today's
Turkish and in parentheses. The number of couplets of the couplet will be specified. Afterwards,
these idioms will be given in alphabetical order and the total number of idioms formed by organ
names in the work will be determined. Thus, it will be stated whether these idioms identified in
the 15th century period work continue to be used in today's Turkish.
Language and Literature, Ural-Altaic languages
Unsafe Impedance: Safe Languages and Safe by Design Software
Lee Barney, Adolfo Neto
In December 2023, security agencies from five countries in North America, Europe, and the south Pacific produced a document encouraging senior executives in all software producing organizations to take responsibility for and oversight of the security of the software their organizations produce. In February 2024, the White House released a cybersecurity outline, highlighting the December document. In this work we review the safe languages listed in these documents, and compare the safety of those languages with Erlang and Elixir, two BEAM languages. These security agencies' declaration of some languages as safe is necessary but insufficient to make wise decisions regarding what language to use when creating code. We propose an additional way of looking at languages and the ease with which unsafe code can be written and used. We call this new perspective \em{unsafe impedance}. We then go on to use unsafe impedance to examine nine languages that are considered to be safe. Finally, we suggest that business processes include what we refer to as an Unsafe Acceptance Process. This Unsafe Acceptance Process can be used as part of the memory safe roadmaps suggested by these agencies. Unsafe Acceptance Processes can aid organizations in their production of safe by design software.
Scheduling Languages: A Past, Present, and Future Taxonomy
Mary Hall, Cosmin Oancea, Anne C. Elster
et al.
Scheduling languages express to a compiler a sequence of optimizations to apply. Compilers that support a scheduling language interface allow exploration of compiler optimizations, i.e., exploratory compilers. While scheduling languages have become a common feature of tools for expert users, the proliferation of these languages without unifying common features may be confusing to users. Moreover, we recognize a need to organize the compiler developer community around common exploratory compiler infrastructure, and future advances to address, for example, data layout and data movement. To support a broader set of users may require raising the level of abstraction. This paper provides a taxonomy of scheduling languages, first discussing their origins in iterative compilation and autotuning, noting the common features and how they are used in existing frameworks, and then calling for changes to increase their utility and portability.
Deep Learning-Based Decision Prediction in Turkish Legal Texts
Seher Solmaz, M. Dursun
Since text recognition studies in the literature are generally carried out in English, tokenization processes of Turkish legal texts in the Ural-Altaic language family cannot be used much. In this study, we tokenize Turkish legal texts and perform decision prediction using a deep learning Convolutional Neural Network (CNN) model. Artificial intelligence (AI), which is developing at a rapid pace, has become applicable to almost all fields of study and has started to be used effectively. Developments in AI have affected the field of law as well as other fields of study. The use and spread of AI in the field of law has increased significantly in recent years. One of the most important factors in this increase is that there is a huge amount of data in the field of law. It has become a need to analyze this data and transform it into meaningful and usable information. This paper aims to make decision prediction using artificial intelligence in judicial applications. In the study, using CNN, a neural network-based deep learning model, decision prediction was made with the data published by the Ombudsman's Office on the institution's website, which is free from publicly accessible personal data. The model was trained on the applicant information and the type of decision in the decision text. An F1 score of 0.63 was achieved for decision prediction.
Korean language attitude in the Altai language system
N. Nikolaeva, M. Song
The relevance of the study is determined by the growing interest of the scientific community in constructing typologies of linguistic features of the Korean language in its relation to the Altai language system. A review of research shows that to date, discussions regarding the place of the Korean language in the Altai language system continue, since there are no uniform criteria by which to describe the relationship of these two languages. The purpose of the article is to systematize the features that allow us to determine the place of the Korean language in the Altai language system. Objectives: provide an overview of studies of the Altai language system; consider arguments about the relationship between the Korean and Altai languages; consider criticism of the theory of kinship between the Korean and Altaic languages. Research methods: systematization, generalization, description, comparison, critical analysis. It has been established that even if we completely deny the family connection between the theory of the Altaic language family and the Korean language, it is still possible to establish a friendly connection between them, which can be taken as a research hypothesis. This is made possible by the fact that the common elements that have been clearly outlined so far exist, albeit in meager quantities. If these elements were not borrowed, it would be difficult to conclude that this is a coincidence. However, it does not seem convincing that the scant data is sufficient to prove the kinship of Koreans and Altai. In this situation, just as it is impossible to draw an unambiguous conclusion that the Korean language has a related relationship with the Altai language or the Altai language family, it is also impossible to conclude that there are no such relationships at all. It is true that the origins of the Korean language are still unclear. Since the existing theory of the Altaic language family and the theory of kinship with Korean were accepted almost without criticism, the counter-arguments against them can be equally strong. However, there are significant differences between these views. Some say this completely refutes conventional wisdom, while others say it is a hypothesis that has not yet been proven. The prospects for the study are seen in the systematization of linguistic typological features of the Korean language in its relation to the Altai language system.
An Archaic Compound Suffix in Old Uyghur: +DXrtI
Kenan Azılı
As many world languages, Turkic also has simple suffixes in terms of structure, as well as complex suffixes with controversial origins. Although some of these suffixes have been systematized and bound to certain rules, the emergence of some suffixes still remains a mystery. Old Uyghur, which is one of the historical periods of the Turkic language, has such an undeciphered suffix. The compound suffix of +DXrtI has been evaluated by some researchers to date; however, no definite conclusion has been reached regarding its origin and function. For this purpose, various structures in Altaic languages will be examined and a connection will be made between this suffix and the ‘extraordinary’ examples seen in Old Uyghur.
The The comparative study of concepts related to religion on the Mongŏ-yuhae (蒙語類解) and Panŏn-čibsog (方言集釋)
Erdenetuya Purevdorj
This paper will compared the words and concepts related to religion in Mongolian and Korean languages, which have branched from the ancestral Altaic language, in the sources of Mongŏyuhae(蒙語類解) and (Panŏnčibsog) (方言集釋). One of the sources known as The Three Books for the Study of Mongolian (蒙語類解) and the similar 5 language dictionary (Panŏnčibsog) (方言集釋) were used as source materials. It is important to bring these sources belonging to the XVII-XVIII centuries into the research circulation, to compare the words and concepts related to religion in Mongolian and Korean languages, which have branched out from the ancestral Altaic language, in the sources of Chosŏn Dynasty (Korean Empire in 1392-1897). Mongŏ-yuhae (蒙語類解) and Panŏn-čibsog (方言集釋) сурвалж дахь шашны холбоотой үг хэллэгийн харьцуулсан судалгаа Хураангуй: Тухайн үндэстний соёл, сэтгэлгээний гол илэрхийлэл, үгийн утгын баялаг уурхай бол толь бичиг байдаг. Тийм ч учраас эрдэмтэд “Толь бичиг нь үгсийн цомог, тайлбар төдий зүйл бус, үндэстний соёл сэтгэлгээний нэг хэсэг юм. Дорно дахины толь бичгийн уламжлалыг хадгалан бичсэн Солонгос улсын Чусон үеийн монгол хэлний зүйл хуваасан 3 ба 5 хэлний толь бичигт буй шашны холбоотой үг хэллэгийн гарал хийгээд Монгол, Солонгос хэлэнд илэрхийлж буй утга, стэгэлгээний онцлогийг харьцуулан авч үзлээ. Түлхүүр үг: концепц, шашны холбоотой үг хэллэг, Mongŏ-yuhae 3 хэлний толь, Panŏn-čibsog 5 хэлний толь
ChatGPT: Beginning of an End of Manual Annotation? Use Case of Automatic Genre Identification
Taja Kuzman, Igor Mozetiˇc, Nikola Ljubeši´c
Eesti vaatamisverbide sihilisusest
Natalia Vaiss
Artiklis vaadeldakse verbi vaatama sünonüümide transitiivseid ja intransitiivseid kasutusi. Eesmärk on selgitada, kas eri tähendusnüanssidega vaatamisverbid erinevad oma transitiivsete kasutuste regulaarsuse poolest.Vaatluse all on 12 vaatama-verbi sünonüümi: kaema, vahtima, piiluma, kiikama, silmama, silmitsema, põrnitsema, jõllitama, kõõritama, jälgima, vaatlema ja uudistama. Korpuspõhine uuring näitas, et ühte leksikaalsemantilisse rühma kuuluvad verbid võivad oma transitiivsete ja intransitiivsete kasutuste rohkuse poolest oluliselt erineda. Peaaegu kõik uuritud vaatamisverbid võimaldavad nii sihitise kui ka suunamääruse lisamist ning võivad esineda ka ilma sõltlaienditeta. Spetsiifilise vaatamisviisi komponent verbi semantikas võib sõltlaiendita esinemist soodustada või ka hoopis piirata.
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On the transitivity of Estonian watching-looking verbs
The article studies the differences in the transitivity of Estonian watching-looking verbs. The aim is to determine their lexical semantic features that are related to the degree of transitivity, using the same corpus method. The analysis based on the Estonian National Corpus 2019 shows that Estonian watching-looking verbs vary in their degree of transitivity (i.e. the regularity of transitive and intransitive uses). According to the percentage of the transitive uses among 200 corpus sentences, the analyzed verbs can be divided into three categories (under 40%, 75–85%, and more than 90%). Most Estonian watching-looking verbs can be used with directional postpositions or other direction adverbials (e.g. to the left, down, into the future, etc.), but can also function without an object or a direction. The manner component reflected in the semantics of some Estonian watching-looking verbs can both promote and restrict the occurrence of the verb without an object or a direction. For all the verbs analysed, the occurrence without an object or a direction was syntactically favoured by the association of two or more actions, infinitive verb forms, the imperative, separative and sometimes also locative place adverbials, manner adverbials, and comparisons.
Philology. Linguistics, Finnic. Baltic-Finnic
Language counselling: Bridging the gap between codification and language use
Urška Vranjek Ošlak
In Slovenia, language counselling activities, especially the online Language Counselling Service, help linguists fill in the gaps in codification caused by the inadequacy of current language manuals for the Slovenian standard language. In this sense, the Language Counselling Service acts as an interpreter of the linguistic information available in the language manuals and as a bridge over the codification gaps. The Service is further one of the main tools used to identify language users’ dilemmas; it automatically creates a provisional online language compendium. The knowledge gained in this way is then used by linguists to create the new normative guide for the Slovenian language.
Kokkuvõte. Urška Vranjek Ošlak: Keelenõuanne kui sild normingute ja keelekasutuse vahel. Sloveenias aitavad keelenõuande teenused, eriti veebipõhine keelenõuandla, keeleteadlastel täita lünki normingutes, mille on põhjustanud praeguste keelekäsiraamatute puudused sloveeni standardkeele kirjeldamisel. Keelenõuandla on mõnes mõttes nagu keelekäsiraamatutes oleva keelelise teabe tõlgendaja ja sild normingulünkade ületamisel. Nõuandla on ka üks peamisi viise, kuidas keelekasutajate dilemmasid tuvastada; see loob veebis automaatselt esialgse kokkuvõtte keelemuredest. Niiviisi saadud teadmisi kasutavad keeleteadlased seejärel uue normatiivse sloveeni keele käsiraamatu loomiseks.
Philology. Linguistics, Finnic. Baltic-Finnic
Positive Data Languages
Florian Frank, Stefan Milius, Henning Urbat
Positive data languages are languages over an infinite alphabet closed under possibly non-injective renamings of data values. Informally, they model properties of data words expressible by assertions about equality, but not inequality, of data values occurring in the word. We investigate the class of positive data languages recognizable by nondeterministic orbit-finite nominal automata, an abstract form of register automata introduced by Bojańczyk, Klin, and Lasota. As our main contribution we provide a number of equivalent characterizations of that class in terms of positive register automata, monadic second-order logic with positive equality tests, and finitely presentable nondeterministic automata in the categories of nominal renaming sets and of presheaves over finite sets.
VyZX: Formal Verification of a Graphical Quantum Language
Adrian Lehmann, Ben Caldwell, Bhakti Shah
et al.
Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded languages. This creates obstacles to formally reasoning about graphical languages, since imposing an inductive structure obfuscates the diagrammatic nature of graphical languages, along with their corresponding equational theories. To address this gap, we present VyZX, a verified library for reasoning about inductively defined graphical languages. These inductive constructs arise naturally from category-theoretic definitions. We developed VyZX to Verify the ZX-calculus, a graphical langauge for reasoning about quantum computation. The ZX-calculus comes with a collection of diagrammatic rewrite rules that preserve the graph's semantic interpretation. We show how inductive graphs in VyZX are used to prove the soundness of the ZX-calculus rewrite rules and apply them in practice using standard proof assistant techniques. We also provide an IDE-integrated visualizer for proof engineers to directly reason about diagrams in graphical form.