This course provides a first introduction to the Curry-Howard correspondence between programs and proofs, from a theoretical programmer's perspective: we want to understand the theory behind logic and programming languages, but also to write concrete programs (in OCaml) and proofs (in Agda). After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.
Every serious student of Japanese needs a reliable and user–friendly dictionary in their collection. Tuttle Concise Japanese Dictionary, now with 30% more content, is a thoroughly updated dictionary designed for students and business people who are living in Japan and using the Japanese language on a daily basis. Its most significant advantage is that it contains recent idiomatic expressions and slang which have become popular in the past several years and which are not found in other competing dictionaries. The dictionary has been thoroughly updated through the addition of modern vocabulary relating to computers, mobile phones, social media and the Internet. Other special features that set this dictionary apart include: Over 25,000 words and expressions including idioms and slang. User-friendly layout with main entries in color. Complete Japanese–English, and English–Japanese sections. Romanized forms and the Japanese script are given for all Japanese words. A guide to pronunciation helps the user to pronounce Japanese words correctly. Different senses of each word are distinguished by multiple definitions.
This is a compact and user friendly Japanese to English and English to Japanese dictionary.
Utilizing concepts from algebraic topology, this monograph explores their application to various models, offering a unique perspective on mathematical structures. It delves into the interplay between algebraic methods and topological theories, providing insights that may enhance understanding in both fields. The work is geared towards researchers and students interested in the intersection of topology and algebra, presenting theoretical advancements and practical implications in a clear and accessible manner.