Fred: An approach to generating real, correct, reusable programs from proofs

In this paper we describe our system for automatically extracting "correct" programs from proofs using a development of the Curry-Howard process. Although program extraction has been developed by many authors, our system has a number of novel features designed to make it very easy to use and as close as possible to ordinary mathematical terminology and practice. These features include 1. the use of Henkin's technique to reduce higher-order logic to many-sorted (first-order) logic; 2. the free use of new rules for induction subject to certain conditions; 3. the extensive use of previously programmed (total, recursive) functions; 4. the use of templates to make the reasoning much closer to normal mathematical proofs and 5. a conceptual distinction between the computational type theory (for representing programs)and the logical type theory (for reasoning about programs). As an example of our system we give a constructive proof of the well known theorem that every graph of even parity, which is non-trivial in the sense that it does not consist of isolated vertices, has a cycle. Given such a graph as input, the extracted program produces a cycle as promised.

Um estudante cego no curso de licenciatura em musica da ufrn: questões de acessibilidade curricular e física

This work aims to discuss and analyze the process of school inclusion of a blind person in the Bachelor's Degree in Music, at the School of Music at the Federal University of Rio Grande do Norte, as well as reflect on the importance of establishing systems of support and to ensure university inclusive process of people with visual impairments. In pursuit to achieve these objectives, this research chose a qualitative methodological approach, the case study, using as procedures for data construction an interview, observation, analysis of documents and photographs. Joined the group of participants in this study, a blind student in the class of 2009.1of the EMUFRN Bachelor's Degree in Music, teachers from two disciplines complied by the student, two classmates, a monitor support in music theory, the course coordinator and school principal, and two other individuals who contributed to the inclusion process in actions not formalized institutionally. The results indicate UFRN proposed initiatives that contribute to inclusion of students with disabilities in this institution, the main one is the creation of the Standing Committee of Support for Students with Special Educational Needs (CAENE), a group that guides administrative sectors, teachers, principals, coordinators and students on the measures needed to enter and remain in quality education for all. Physical accessibility is still under construction at UFRN, and many access and sectors see it being adapted for students with physical or visual disabilities, and those with mobility impairments, have access to various parts of the university, however, as shown in this study, some points need to be reconsidered, as there are several places where the installation of tactile floor does not fully follow the guidelines proposed in the legislation. The proposals for access to the curriculum, mediated by EMUFRN, are actions that propose the inclusion of the blind student, as the existence of an educational monitor to help in the study of music theory, however, we need to rethink these proposals to not became actions of reactive intervention. Assuming a more proactive posture, the EMUFRN will be prepared to receive the diversity of students that expects. The study also points out that the blind student is part of a group of students that are practical musicians, who must work in events and evening shows, and who have little knowledge in music theory, leading, respectively, in low frequency classes and learning difficulties in certain curricular components, which may cause the closing of such components. In this case, the challenge of EMUFRN, considering the inclusive perspective, it is not specifically fit for the academic host a blind student, but to develop an accessibility project curriculum to consider effectively the diversity of all its students, taking into account mainly the economic and cultural conditions. This implies a process of resizing academic practices that be guided for collaborative and coordinated actions involving the various educational actors at EMUFRN and UFRN

Aptidão musical : inata ou adquirida?

Relatório de Estágio apresentado à Escola Superior de Artes Aplicadas do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Ensino de Música – Formação Musical e Música de Conjunto.

Die Grundsätze der musikalischen Komposition.

Each vol. has special t.p.

Melodie und Skala /

Offprint: Jahrbuch der Musikbibliothek Peters, 19. Jahrgang (Leipzig: C.F. Peters, 1913).

Handbüchlein der Harmonie-, Melodie- und Formenlehre /

Mode of access: Internet.

Grammatica ragionata della musica considerata sotto l'aspetto di lingua /

Mode of access: Internet.

Principj elementari di musica e metodo per l'insegnamento del Meloplasto /

Mode of access: Internet.

Sull'arte musicale : pensiere /

Mode of access: Internet.

Katechismus der musikalischen Formenlehre, oder die Lehre von den Vokalformen der Kirchenmusik, dramatischen Musik, Kammermusik und des Volks- und Naturegesanges, sowie die instrumental Musikformen der Concert, Salon, Tanz, und Militairmusik mit Bezugnahme auf ihre historische Entwickelung /

Includes index.

Nozioni di musica.

Title from cover.

Principj elementari di musica : adottati dall'I.R. Conservatorio di Milano per le ripetizioni giornaliere degli alunni /

Mode of access: Internet.

Lezioni d'armonia /

Preceded by: Principi elementari di Musica, esposti con nuovo ordine da Domenico Quadri Vicentino per servire d'introduzione alla terza ristampa delle Lezioni d'armonia dello stesso, già pubblicate in Napoli ed in Roma.

Von dem Hervortreten der in den Körpern schlummernden Töne : eine wissenschaftliche Grundlage für die moderne Tonlehre /

Mode of access: Internet.

Nuova gramatica della musica : per uso de' giovanetti romani /

Mode of access: Internet.