Concrete Abstractions
Schreiner, Wolfgang.
Concrete Abstractions [electronic resource] : by Wolfgang Schreiner. - 1st ed. 2023. - Cham Springer International Publishing 2023 - XII, 271 p. 79 illus., 53 illus. in color. online resource.
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.
9783031249341
Computational Mathematics and Numerical Analysis.
Computer science
Mathematical Logic and Foundations.
Mathematical logic.
Mathematics
Mathematics of Computing.
4.0151
Concrete Abstractions [electronic resource] : by Wolfgang Schreiner. - 1st ed. 2023. - Cham Springer International Publishing 2023 - XII, 271 p. 79 illus., 53 illus. in color. online resource.
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.
9783031249341
Computational Mathematics and Numerical Analysis.
Computer science
Mathematical Logic and Foundations.
Mathematical logic.
Mathematics
Mathematics of Computing.
4.0151