Concrete Abstractions

CONCRETE ABSTRACTIONS offers students a hands-on, abstraction-based experience of thinking like a computer scientist. This text covers the basics of programming and data structures, and gives first-time computer science students the opportunity to not only write programs, but to prove theorems and analyze algorithms as well. Students learn a variety of programming styles, including functional programming, assembly-language programming, and object-oriented programming (OOP). While most of the book uses the Scheme programming language, Java is introduced at the end as a second example of an OOP system and to demonstrate concepts of concurrent programming.

This book demonstrates how to formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software.The presented domains are typically investigated in discrete mathematics, logic, algebra, and computer science; they are modeled in a formal language based on first-order logic which is sufficiently rich to express the core entities in whose correctness we are interested: mathematical theorems and algorithmic specifications. This formal language is the language of RISCAL, a “mathematical model checker” by which the validity of all formulas and the correctness of all algorithms can be automatically decided. The RISCAL software is freely available; all formal contents presented in the book are given in the form of specification files by which the reader may interact with the software while studying the corresponding book material.

An approach to software design that introduces a fully automated analysis giving designers immediate feedback, now featuring the latest version of the Alloy language. In Software Abstractions Daniel Jackson introduces an approach to software design that draws on traditional formal methods but exploits automated tools to find flaws as early as possible. This approach—which Jackson calls “lightweight formal methods” or “agile modeling”—takes from formal specification the idea of a precise and expressive notation based on a tiny core of simple and robust concepts but replaces conventional analysis based on theorem proving with a fully automated analysis that gives designers immediate feedback. Jackson has developed Alloy, a language that captures the essence of software abstractions simply and succinctly, using a minimal toolkit of mathematical notions. This revised edition updates the text, examples, and appendixes to be fully compatible with Alloy 4.

Art produced outside hegemonic centers is often seen as a form of derivation or relegated to a provisional status. Forming Abstraction turns this narrative on its head. In the first book-length study of postwar Brazilian art and culture, Adele Nelson highlights the importance of exhibitionary and pedagogical institutions in the development of abstract art in Brazil. By focusing on the formation of the São Paulo Biennial in 1951; the early activities of artists Geraldo de Barros, Lygia Clark, Waldemar Cordeiro, Hélio Oiticica, Lygia Pape, and Ivan Serpa; and the ideas of critics like Mário Pedrosa, Nelson illuminates the complex, strategic processes of citation and adaption of both local and international forms. The book ultimately demonstrates that Brazilian art institutions and abstract artistic groups—and their exhibitions of abstract art in particular—served as crucial loci for the articulation of societal identities in a newly democratic nation at the onset of the Cold War.

A landmark study of abstraction in architectural history, theory, and practice that challenges our assumptions about the meaning of abstract forms. In this theoretical study of abstraction in architecture—the first of its kind—Pier Vittorio Aureli argues for a reconsideration of abstraction, its meanings, and its sources. Although architects have typically interpreted abstraction in formal terms—the purposeful reduction of the complexities of design to its essentials—Aureli shows that abstraction instead arises from the material conditions of building production. In a lively study informed by Walter Benjamin, Karl Marx, Alfred Sohn-Rethel, and other social theorists, this book presents abstraction in architecture not as an aesthetic tendency but as a movement that arises from modern divisions of labor and consequent social asymmetries. These divisions were anticipated by the architecture of antiquity, which established a distinction between manual and intellectual labor, and placed the former in service to the latter. Further abstractions arose as geometry, used for measuring territories, became the intermediary between land and money and eventually produced the logic of the grid. In our own time, architectural abstraction serves the logic of capitalism and embraces the premise that all things can be exchanged—even experience itself is a commodity. To resist this turn, Aureli seeks a critique of architecture that begins not by scaling philosophical heights, but by standing at the ground level of material practice.

This book is a collection of critical engagements with Andrew Sayer, one of the foremost postdisciplinary thinkers of our times, with responses from Sayer himself. Sayer’s ground-breaking contributions to the fields of geography, political economy and social theory have reshaped the terms of engagement with issues and debates running from the methodology of social science through to the environment, and industrial development to the ethical dimensions of everyday life. Transatlantic scholars across a wide range of fields explore his work across four main areas: critical realism; moral economy; political economy; and relations between social theory, normativity and class. This is the first full-length critical assessment of Sayer’s work. It will be of interest to readers in sociology, economics, political economy, social and political philosophy, ethics, social policy, geography and urban studies, from upper-undergraduate levels upwards.

Colburn (computer science, U. of Minnesota-Duluth) has a doctorate in philosophy and an advanced degree in computer science; he's worked as a philosophy professor, a computer programmer, and a research scientist in artificial intelligence. Here he discusses the philosophical foundations of artificial intelligence; the new encounter of science and philosophy (logic, models of the mind and of reasoning, epistemology); and the philosophy of computer science (touching on math, abstraction, software, and ontology).

Shows how Lefebvre's theory of space developed out of direct engagement with architecture, urbanism, and urban sociology.