Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

A Functional Shell that Dynamically Combines Compiled Code

Contains fulltext : 60594.pdf (author's version ) (Open Access)We present a new shell that provides the full basic functionality of a strongly typed lazy functional language, including overloading. The shell can be used for manipulating files, applications, data and processes at the command line. The shell does type checking and only executes well-typed expressions. Files are typed, and applications are simply files with a function type. The shell executes a command line by combining existing code of functions on disk. We use the hybrid static/dynamic type system of Clean to do type checking/inference. Its dynamic linker is used to store and retrieve any expression (both data and code) with its type on disk. Our shell combines the advantages of interpreters (direct response) and compilers (statically typed, fast code). Applications (compiled functions) can be used, in a type safe way, in the shell, and functions defined in the shell can be used by any compiled application.IFL 200

Sharing Resource-Sensitive Knowledge using Combinator Logics

Research on ontologies has been pursued as a solution to the difficult problem of knowledge sharing. Ontologies consist of a domain description which suits the needs of all systems to be integrated. Any agreed ontology, however, is not the end of the problems involved in knowledge sharing since how we represent knowledge is intimately linked to the inferences we expect to perform with it. Knowledge sharing cannot ignore the similarities and differences between the inference engines participating in the information exchange. This paper illustrates this issue via a case study on resource-sensitive knowledge-based systems and we show how these can efficiently share their knowledge using combinator logics. 1 Introduction One of the benefits of formally representing knowledge lies in its potential to be shared. Technologies for computer interconnection, now relatively cheap and widespread, make it possible for knowledge bases and inference engines developed in different locations to..