This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

http://types10.mimuw.edu.pl/content/slides/day1/HenkBarendregt.pdf

Lambda Calculus with Types

Journal of the ACM

In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.

Term Rewriting Systems

Functional Programming Languages and Computer Architecture

What do you do to start reading automatic sequences theory applications generalizations? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this automatic sequences theory applications generalizations.

Automatic sequences. Theory, applications, generalizations.

We are concerned with demonstrating productivity of specifications of infinite streams of data, based on orthogonal rewrite rules. In general, this property is undecidable, but for restricted formats computable sufficient conditions can be obtained. The usual analysis, also adopted here, disregards the identity of data, thus leading to approaches that we call data-oblivious. We present a method that is provably optimal among all such data-oblivious approaches. This means that in order to improve on our algorithm one has to proceed in a data-aware fashion.

/pdf/data-oblivious-stream-productivity-486kysoegw.pdf

Data-Oblivious Stream Productivity

We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions.
A stream definition is called ‘productive’ if it can be evaluated continually in such a way that a uniquely
determined stream in constructor normal form is obtained as the limit. Whereas productivity is undecidable
for stream definitions in general, we show that it can be decided for ‘pure’ stream definitions. For every pure
stream definition the process of its evaluation can be modelled by the dataflow of abstract stream elements,
called ‘pebbles’, in a finite ‘pebbleflow net(work)’. And the production of a pebbleflow net associated with
a pure stream definition, that is, the amount of pebbles the net is able to produce at its output port, can
be calculated by reducing nets to trivial nets.

Productivity of stream definitions

http://www.phil.uu.nl/~clemens/linkedfiles/psdTCS.pdf

We solve an open question of Milner [1984]. We define a set of so-called well-behaved finite automata that, modulo bisimulation equivalence, corresponds exactly to the set of regular expressions, and we show how to determine whether a given finite automaton is in this set. As an application, we consider the star height problem.

/pdf/a-characterization-of-regular-expressions-under-bisimulation-45yoarrxrb.pdf

Clemens Grabmayer

Papers

Data-Oblivious Stream Productivity

Productivity of stream definitions

Productivity of stream definitions

A characterization of regular expressions under bisimulation

On equal μ-terms