Formal Foundations of Computer Science 1

Wolfgang Schreiner
Research Institute for Symbolic Computation (RISC-Linz)
Johannes Kepler University, Linz, Austria

Abstract

We introduce basic mathematical domains and techniques as a foundation for the formal treatment of various concepts in computer science and engineering. Mathematical domains like numbers, functions, and relations are constructed on the basis of the fundamental notions of set theory thus exhibiting their inner structure and properties. As for mathematical techniques, we present the language of logic for the precise description of mathematical objects and facts and give rules for correct reasoning and arguing. The constructions are partially implemented with the help of an interpreter that executes a simple subset of logic and set theory.