Learning to Prove Theorems via Interacting with Proof Assistants

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.Comment: Accepted to ICML 201

Speech is My Hammer, It\u27s Time to Build: Hip Hop, Cultural Semiosis and the Africana Intellectual Heritage

The article examines Hip Hop music\u27s relationship with African cultural symbolism and the discipline of Africana Studies. The author maintains that Africana Studies must reclaim the study of cultural semiosis, which may be used to contextualize Hip Hop praxis. Examining semeiotic traces within African and Afrodiasporic primary sources, including Hip Hop lyrics, the article posits that Hip Hop is the latest development in a long tradition of Afro-Kemetic oral artistry, semeiotic systems and the uses of these dual literacies as modes of resistance and affirmations of Black historical and cultural agency. The article adapts Harryette Mullen\u27s literary model of African Spirit Writing and Elaine Richardson\u27s Hip Hop Literacy studies to discuss specific constructs that affirm an African Diasporic worldview and foster resistance to the dominant political-economy that frames Black agency

Expressing the GIVE event in Papuan languages: A preliminary survey

The linguistic expression of the GIVE event is investigated in a sample of 72 Papuan languages, 33 belonging to the Trans New Guinea family, 39 of various non-TNG lineages. Irrespective of the verbal template (prefix, suffix, or no indexation of undergoer), in the majority of languages the recipient is marked as the direct object of a monotransitive verb, which sometimes involves stem suppletion for the recipient. While a few languages allow verbal affixation for all three arguments, a number of languages challenge the universal claim that the `give' verb always has three arguments

Where the eye takes you: the processing of gender in codeswitching

Producción CientíficaLa alternancia de códigos posee gran potencial para explorar cómo interactúan dos sistemas lingüísticos en la mente del bilingüe. Exploramos esta situación de lenguas en contacto a través de datos de seguimiento ocular de bilingües de español L1 e inglés L2. Dado que las comunidades bilingües inglés-español muestran una clara tendencia a producir alternancia entre determinante y nombre (la window / the ventana), desde un punto de vista formal analizamos la direccionalidad de la alternancia y el tipo de mecanismo de concordancia de género implícita que se produce en el caso del determinante español (la/el window // el/la book). Los resultados muestran que se tardan más en procesar tanto la alternancia con determinante español como la del determinante español sin género analógico. Interpretamos estos resultados a la luz de propuestas formales de representación del género y argumentamos que la gramaticalidad del género en la L1 de los participantes determina los costes de procesamiento en este tipo de alternancia.Junta de Castilla y León - FEDER (project VA009P17)Ministerio de Ciencia, Innovación y Universidades - FEDER (project PGC2018-097693-B-I00

The Cowl - v.78 - n.9 - Nov 7, 2013

The Cowl - student newspaper of Providence College. Volume 78 - No. 9 - November 7, 2013. 24 pages

Agency drives category structure in instrumental events

Thematic roles such as Agent and Instrument have a long-standing place in theories of event representation. Nonetheless, the structure of these categories has been difficult to determine. We investigated how instrumental events, such as someone slicing bread with a knife, are categorized in English. Speakers described a variety of typical and atypical instrumental events, and we determined the similarity structure of their descriptions using correspondence analysis. We found that events where the instrument is an extension of an intentional agent were most likely to elicit similar language, highlighting the importance of agency in structuring instrumental categories

Name structures and name survival

No abstract available