Related papers: Generic Automatic Proof Tools
We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as…
This paper presents a formalized framework for defining corecursive functions safely in a total setting, based on corecursion up-to and relational parametricity. The end product is a general corecursor that allows corecursive (and even…
G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
We present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL. It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
To address the increasing size and complexity of modern software systems, compositional verification separates the verification of single components from the verification of their composition. In architecture-based verification, the former…
Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
We show how to extract a monotonic learning algorithm from a classical proof of a geometric statement by interpreting the proof by means of interactive realizability, a realizability sematics for classical logic. The statement is about the…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
In the paper I discuss a tool for helping students in their symbolizations of natural language sentences using the formal language of classical first order logic (CFOL). The tool is an extension of Hintikka's concept of (Inquirer's) range…
The formalisation of mathematics is starting to become routine, but the value of this technology to the work of mathematicians remains to be shown. There are few examples of using proof assistants to verify brand-new work. This paper…
In this paper, we present a proof theory for attack trees. Attack trees are a well established and useful model for the construction of attacks on systems since they allow a stepwise exploration of high level attacks in application…
This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state…
We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all…
This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE…