Theory and Practice of Higher-type Computation (Tutorial)

In higher-type computation, established by Kleene and Kreisel in the late 1950\u27s (independently), one works with the data types obtained from the discrete natural numbers by closing under finite products and function spaces. For the theory of higher-type programming languages, it is natural to work with a corresponding hierarchy, or type structure, of domains, identified by Ershov and Scott in the late 1960\u27s (again independently). The Kleene-Kreisel and Ershov-Scott hierarchies account for total and partial computation respectively. In this tutorial I\u27ll explain the theory and practice of higher-type computation and programming languages, and develop old and new applications. From a theoretical point of view, I\u27ll present Kleene-Kreisel spaces and Ershov-Scott domains, and relate the two. Moreover, I\u27ll discuss common generalizations, chiefly QCB spaces and equilogical spaces, which admit further useful closure properties, and their relationship to TTE (Schroeder, Simpson. Scott, Bauer, Weihrauch and many others). I\u27ll also present a natural higher-type model of computation/programming language, namely PCF (Platek, Scott, Plotkin). From a practical point of view, I\u27ll introduce a fragment of the language Haskell as a faithful implementation of PCF. Moreover, I\u27ll develop and run several examples (and prove theorems about them), pertaining to (i) exhaustive search of infinite sets in finite time in particular Ulrich Berger\u27s algorithm and generalizations), and (ii) computation with real numbers (in particular Alex Simpson\u27s integration algorithm and generalizations)

Computer Verified Exact Analysis (Tutorial)

This tutorial will illustrate how to use the Coq proof assistant to implement effective and provably correct computation for analysis. Coq provides a dependently typed functional programming language that allows users to specify both programs and formal proofs. We will introduce dependent type theory and show how it can be used to develop both mathematics and programming. We will show how to use dependent type theory to implement constructive analysis. Specifically we will cover how to implement effective real numbers and effective integration. This work will be done using the Coq proof assistant. The tutorial will cover how to use the Coq proof assistant. Attendees are encouraged to download and install Coq 8.2 from {tt http://coq.inria.fr/download} and also download and make the full system of C-CoRN from {tt http://c-corn.cs.ru.nl/download.html} beforehand

Contents EURASIP MESSAGES

On the Integration between Digital Watermarking and Cryptography..............

Kolokasi kata ??? dalam Alqur'an (studi terjamah M. Quraish Shihab)

xiv, 88 hlm,; ilus.; 30 cm

Kolokasi kata ??? dalam Alqur'an (studi terjamah M. Quraish Shihab)

xiv, 88 hlm,; ilus.; 30 cm

Kolokasi kata ??? dalam Alqur'an (studi terjamah M. Quraish Shihab)

xiv, 88 hlm,; ilus.; 30 cm