This book constitutes the thoroughly refereed post-conference proceedings of the 11th International Symposium on Trends in Functional Programming, TFP 2010, held in Norman, OK, USA, in May 2010. The 13 revised full papers presented were carefully reviewed and selected from 26 submissions during two rounds of reviewing and improvement. The papers cover new ideas for refactoring, managing source-code complexity, functional language implementation, graphical languages, applications of functional programming in pure mathematics, type theory, multitasking and parallel processing, distributed systems, scientific modeling, domain specific languages, hardware design, education, and testing.

This book constitutes the thoroughly refereed post-conference proceedings of the 12th International Symposium on Trends in Functional Programming, TFP 2011, held in Madrid, Spain, in May 2011. The 12 papers presented were carefully reviewed and selected from 21 submissions. They deal with all aspects of functional programming, taking a broad view of current and future trends in this area. The topical sections the papers are organized in are named as follows: types, compiling, paralelelism and distribution, data structures, and miscellaneous.

Discrete Mathematics Using a Computer offers a new, "hands-on" approach to teaching Discrete Mathematics. Using software that is freely available on Mac, PC and Unix platforms, the functional language Haskell allows students to experiment with mathematical notations and concepts -- a practical approach that provides students with instant feedback and allows lecturers to monitor progress easily.

This second edition of the successful textbook contains significant additional material on the applications of formal methods to practical programming problems. There are more examples of induction proofs on small programs, as well as a new chapter showing how a mathematical approach can be used to motivate AVL trees, an important and complex data structure.

Designed for 1st and 2nd year undergraduate students, the book is also well suited for self-study. No prior knowledge of functional programming is required; everything the student needs is either provided or can be picked up easily as they go along.

Key features include:

• Numerous exercises and examples
• A web page with software tools and additional practice problems, solutions, and explanations, as well as course slides
• Suggestions for further reading

Complete with an accompanying instructor's guide, available via the web, this volume is intended as the primary teaching text for Discrete Mathematics courses, but will also provide useful reading for Conversion Masters and Formal Methods courses.

Visit the booka (TM)s Web page at: http: //www.dcs.gla.ac.uk/~jtod/discrete-mathematics/

An introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory. Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism. For readers who want to see formalization in action, the text presents examples using Proof Pad, a lightweight ACL2 environment. Readers will not become ALC2 experts, but will learn how mechanized logic can benefit software and hardware engineers. In addition, 180 exercises, some of them extremely challenging, offer opportunities for problem solving. There are no prerequisites beyond high school algebra. Programming experience is not required to understand the book's equation-based approach. The book can be used in undergraduate courses in logic for computer science and introduction to computer science and in math courses for computer science students.