Related papers: Isabelle: The Next 700 Theorem Provers
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
This article presents a pattern-based language designed to select (a set of) subterms of a given term in a concise and robust way. Building on this language, we implement a single-step rewriting tactic in the Isabelle theorem prover, which…
As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena…
This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…
Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent…
Formal verification of cyber-physical and robotic systems requires that we can accurately model physical quantities that exist in the real-world. The use of explicit units in such quantities can allow a higher degree of rigour, since we can…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
We introduce a theorem proving approach to the specification and generation of temporal logical constraints for training neural networks. We formalise a deep embedding of linear temporal logic over finite traces (LTL$_f$) and an associated…
Deciding which sub-tool to use for a given proof state requires expertise specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR recommends proof…
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…
A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…
An Isabelle/HOL formalisation of G\"odel's two incompleteness theorems is presented. The work follows \'Swierczkowski's detailed proof of the theorems using hereditarily finite (HF) set theory. Avoiding the usual arithmetical encodings of…
The Isabelle Archive of Formal Proofs (AFP) has grown to over 500 articles in late 2019. Meanwhile, finding formalizations in it has not exactly become easier. At the time of writing, the site-specific AFP google search and the Isabelle…
Model execution allows us to prototype and analyse software engineering models by stepping through their possible behaviours, using techniques like animation and simulation. On the other hand, deductive verification allows us to construct…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…
Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical…
Assurance cases are often required as a means to certify a critical system. Use of formal methods in assurance can improve automation, and overcome problems with ambiguity, faulty reasoning, and inadequate evidentiary support. However,…
We describe our Natural Deduction Assistant (NaDeA) and the interfaces between the Isabelle proof assistant and NaDeA. In particular, we explain how NaDeA, using a generated prover that has been verified in Isabelle, provides feedback to…
We describe an extension to the TLA+ specification language with constructs for writing proofs and a proof environment, called the Proof Manager (PM), to checks those proofs. The language and the PM support the incremental development and…