Abstract. The number of products and services available over the Internet increases dramatically during the last years and it is already beyond the human ability to analyze and combine them efficiently. At the same time if we consider works in software engineering (and, in particular, in component-based system development) then we can find quite strong similarity in problem description. The web services can be treated in a way similar to software components and service composition can be considered as problem of software synthesis and composition. Basic idea of our approach is applying the software synthesis and composition methods to value added web services composition. We also describe some technical details within the approach, in particular, a web service description language and a program synthesis method. 1

In this paper, we take an abstract view of search by describing search procedures via particular kinds of proofs in type theory. We rely on the proofs-as-programs interpretation to extract programs from our proofs. Using these techniques we explore, in depth, a large family of search problems by parameterizing the speci cation of the problem. A constructive proof is presented which has as its computational content a correct search procedure for these problems. We show how a classical extension to an otherwise constructive system can be used to describe a typical use of the nonlocal control operator call/cc. Using the classical typing of nonlocal control we extend our purely constructive proof to incorporate a sophisticated backtracking technique known as ‘con ict-directed backjumping’ (CBJ). A variant of this proof is formalized in Nuprl yielding a correct-by-construction implementation of CBJ. The extracted program has been translated into Scheme and serves as the basis for an implementation of a new solution to the Hamiltonian circuit problem. This paper demonstrates a nontrivial application of the proofs-as-programs paradigm by applying the technique to the derivation of a sophisticated search algorithm; also, it shows the generality of the resulting implementation by demonstrating its application in a new problem

Abstract. The quest for designing secure and trusted software has led to refined Software Engineering methodologies that rely on tools to support the design process. Automated reasoning mechanisms for requirements and software verification are by now a well-accepted part of the design process, and model driven architectures support the automation of the refinement process. We claim that we can further push the envelope towards the automatic exploration and selection among design alternatives and show that this is concretely possible for Secure Tropos, a requirements engineering methodology that addresses security and trust concerns. In Secure Tropos, a design consists of a network of actors (agents, positions or roles) with delegation/permission dependencies among them. Accordingly, the generation of design alternatives can be accomplished by a planner which is given as input a set of actors and goals and generates alternative multiagent plans to fulfill all given goals. We validate our claim with a case study using a state-of-the-art planner. 1

This paper highlights a methodology of Nuprl proof that results in efficient programs that are more readable than those produced by other established methods for extracting programs from proofs. We describe a formal constructive proof of the decidability of a sequent calculus for classical propositional logic. The proof is implemented in the Nuprl system and the resulting proof object yields a "correct-by-construction" program for deciding propositional sequents. If the sequent is valid, the program reports that fact; otherwise, the program returns a counterexample in the form of a falsifying assignment. We employ Kleene's strong three-valued logic to give more informativecounter-examples, it is also shown how this semantics agrees with the standard two-valued presentation.

We describe the development of a Java bytecode optimisation algorithm by the methodology of program extraction. We develop the algorithm as a collection of proofs and definitions in the Coq proof assistant, and then use Coq's extraction mechanism to automatically generate a program in OCaml. The extraction methodology guarantees that this program is correct. We discuss the feasibility of the methodology and suggest some improvements that could be made.

The basic concepts of type theory are fundamental to computer science, logic and mathematics. Indeed, the language of type theory connects these regions of science. It plays a role in computing and information science akin to that of set theory in pure mathematics. There are many excellent accounts of the basic ideas of type theory, especially at the interface of computer science and logic — specifically, in the literature of programming languages, semantics, formal methods and automated reasoning. Most of these are very technical, dense with formulas, inference rules, and computation rules. Here we follow the example of the mathematician Paul Halmos, who in 1960 wrote a 104-page book called Naïve Set Theory intended to make the subject accessible to practicing mathematicians. His book served many generations well. This article follows the spirit of Halmos ’ book and introduces type theory without recourse to precise axioms and inference rules, and with a minimum of formalism. I start by paraphrasing the preface to Halmos ’ book. The sections of this article follow his chapters closely. Every computer scientist agrees that every computer scientist must know some type theory; the disagreement begins in trying to decide how much is some. This article contains my partial answer to that question. The purpose of the article is to tell the beginning student of advanced computer science the basic type theoretic facts of life, and to do so with a minimum of philosophical discourse and logical formalism. The point throughout is that of a prospective computer scientist eager to study programming languages, or database systems, or computational complexity theory, or distributed systems or information discovery. In type theory, “naïve ” and “formal ” are contrasting words. The present treatment might best be described as informal type theory from a naïve point of view. The concepts are very general and very abstract; therefore they may

Abstract. We present a machine-checked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups. Then we can tell whether a given set with a binary operation is a group or not, and derive all properties of groups constructively from these inference rules as well as the axioms of the set theory. The formalization of all other concepts in abstract algebra is based on that of the group. We give an example of a formalization of a concrete group, the Klein 4-group. 1

The topic of this thesis is the extraction of efficient and readable programs from formal constructive proofs of decidability. The proof methods employed to generate the efficient code are new and result in clean and readable Nuprl extracts for two non-trivial programs. They are based on the use of Nuprl's set type and techniques for extracting efficient programs from induction principles. The constructive formal theories required to express the decidability theorems are of independent interest. They formally circumscribe the mathematical knowledge needed to understand the derived algorithms. The formal theories express concepts that are taught at the senior college level. The decidability proofs themselves, depending on this material, are of interest and are presented in some detail. The proof of decidability of classical propositional logic is relative to a semantics based on Kleene's strong three-valued logic. The constructive proof of intuitionistic decidability presented here is the first machine formalization of this proof. The exposition reveals aspects of the Nuprl tactic collection relevant to the creation of readable proofs; clear extracts and efficient code are illustrated in the discussion of the proofs.

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TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research category, each of which was refereed by at least 3 reviewers selected by the program committee. Of these submissions, 21 were accepted for presentation at the conference and publication in volume 3223 of Springer’s Lecture Notes in Computer Science series. In keeping with longstanding tradition, TPHOLs 2004 also offered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief introductory talk and then discuss their work at a poster