Incomplete logical proofs are the logical counterpart of the incomplete λ-terms that one usually works with in an interactive theorem prover based on type theory. In this paper we extend the formalization of such incomplete proofs given in [5] by introducing unknowns that are allowed to provide temporary bindings for variables that are supposed to be bound, but whose binders are not constructed...

The shortcomings of traditional Information Retrieval are most evident when users require exact information rather than relevant documents. This practical need is pushing the research community towards systems that can exactly pinpoint those parts of documents that contain the information requested. Answer Extraction (AE) systems aim to satisfy this need. This paper presents one such system (Ex...

This paper presents a new proof language for the Coq proof assistant. This language uses the declarative style. It aims at providing a simple, natural and robust alternative to the existing Ltac tactic language. We give the syntax of our language, an informal description of its commands and its operational semantics. We explain how this language can be used to implement formal proof sketches. F...

In this paper, we define new decision procedures for Łukasiewicz logics. They are based on particular integer-labelled hypersequents and of logical proof rules for such hypersequents. These rules being proved strongly invertible our procedures naturally allow one to generate countermodels. From these results we define a “merge”-free calculus for the infinite version of Łukasiewicz logic and pro...

The theorem of Sylow is proved in Isabelle HOL. We follow the proof by Wielandt that is more general than the original and uses a non-trivial combinatorial identity. The mathematical proof is explained in some detail leading on to the mechanization of group theory and the necessary combinatorics in Isabelle. We present the mechanization of the proof in detail giving reference to theorems contai...

Hilbert’s concept of formal proof is an ideal of rigour for mathematics which has important applications in mathematical logic, but seems irrelevant for the practice of mathematics. The advent, in the last twenty years, of proof assistants was followed by an impressive record of deep mathematical theorems formally proved. Formal proof is practically achievable. With formal proof, correctness re...

We present a formalization of Cauchy’s residue theorem and two of its corollaries: the argument principle and Rouché’s theorem. These results have applications to verify algorithms in computer algebra and demonstrate Isabelle/HOL’s complex analysis library.

In this paper we focus on a composition model for services, which are composed from pre-programmed service components represented as Java classes. A common formal basis for representing the semantics of dynamic composition of services from service components is presented. We propose a logic and a specification language that enable us to reason about and deploy service components automatically. ...

The HOL4 proof assistant supports specification and proof in classical higher order logic. It is the latest in a long line of similar systems. In this short overview, we give an outline of the HOL4 system and how it may be applied in formal verification.