Reviews for Theorem Proving in Higher Order Logics

The average rating for Theorem Proving in Higher Order Logics based on 2 reviews is 4 stars.

Review # 1 was written on 2021-03-21 00:00:00 Steven Riedlinger This book is suitable for undergraduates in computer-science or mathematics for course-material requiring the use of a computer to explore geometric ideas, or equally the use of geometric knowledge to solve a programming problem. The book contains a fairly typical (and basic) selection of material on the various forms of coordinate geometry (2D,3D,projective) and explores the use of homogeneous coordinates in Euclidean as well as projective geometry. Circles and spheres, polygons and polyhedra are all covered to some extent. There is a fair amount on the pitfalls of using float and double data types to store coordinates, and some discussion of rasterisation. All the example code is in C++. Apart from some use of STL and templates the code in the book is independent of any libraries or platform. Example programs can be downloaded from the publisher's website, but I have not looked at these yet, though they are probably OpenGL based,given that there is an appendix outlining this API, and another outlining the GLOW library that is built on top of it. There is also an appendix outlining how to write programs in PostScript. (These appendices are useful and one of the better things in the book) In places the book shows signs of careless editing - several times there are references expecting us to be familiar with topics that have not yet been, and sometimes never are, introduced. At least once the author makes a statement that is wrong. (He counsels against designing a Tuple base class "because using inheritance means incurring a virtual function table". This is untrue - if there are no virtual methods there is no virtual function table.) There are also unaccountable omissions. For example in a discussion on how to represent a 2D line the author discusses representing it as a triple (a,b,c) and discusses normalising it to make c=1, which he points out is no good for lines through the origin. But there is no mention of the far more useful (and usual) normalisation in which a^2+b^2=1, nor that in this case for points off the line the quantity ax+by+c is the signed distance from the line. The author's heart is in the right place: he wants to encourage good programming habits and the development of code that is reliable and maintainable, and he suggests that it would be a good plan to develop libraries that are geometry neutral (for example libraries usable in both Euclidean and Projective geometries). However, I feel he is overly concerned with type safety: he regards adding two points as an abomination, even though there are many perfectly valid reasons for doing this (as the author himself admits a few pages later on). He is convinced that the use of coordinates (or rather direct access to them) is a major source of bugs. I can't recall this ever causing me a serious problem in my own programs, and I have developed a lot of geometric code including 2D code that goes considerably beyond anything in this book (i.e. common code that can compute with and draw figures using any of S2,E2 and H2 geometry in various models) There is nothing terribly wrong with this book but nothing terribly right either. Too much of the material is either obvious or easily available elsewhere to make this book good value for money. Although they are less systematic in what they cover, I think there is more to be learned from "Graphics Gems II: No. 2 (Graphics Gems - IBM)" and other books in that series.

Review # 2 was written on 2011-03-28 00:00:00 Peter Stockbauer a good book to learn