Abstract
Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. ion does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems.
Highlights
ObjectivesOur objective is to employ these types as a basis for abstracting more abstract ones
We provide a conceptual and mathematical analysis of “data abstraction” and “representation” and their relationship
We demonstrate that abstraction and representation are related to each other as “congruence” and “homomorphism”
Summary
Our objective is to employ these types as a basis for abstracting more abstract ones. We aim to abstract the following “more abstract” type. Our objective is to abstract the abstract type of finite sets from lists/queues. Our goal is to use this insight to provide a mathematical foundation for data abstraction where kinds are replaced by abstract data types. Our objective is to provide one based upon the above neo-Fregeans Hale and Wright [24] respond by severely restricting the class of acceptable concept concept of of “Fregean
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