Related papers: Interaction with Formal Mathematical Documents in …
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…
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…
We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…
This EPTCS volume collects the post-proceedings of the 10th International Workshop On User Interfaces for Theorem Provers (UITP 2012), held as part of the Conferences on Intelligent Computer Mathematics (CICM 2012) in Bremen on July 11th…
Reactive systems are composed of a well defined set of input events that the system reacts with by executing an associated handler to each event. In concurrent environments, event handlers can interact with the execution of other programs…
Quick interaction between a human teacher and a learning machine presents numerous benefits and challenges when working with web-scale data. The human teacher guides the machine towards accomplishing the task of interest. The learning…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
In interactive coding, Alice and Bob wish to compute some function $f$ of their individual private inputs $x$ and $y$. They do this by engaging in an interactive protocol to jointly compute $f(x,y)$. The goal is to do this in an…
We present the first verified implementation of a decision procedure for the quantifier-free theory of partial and linear orders. We formalise the procedure in Isabelle/HOL and provide a specification that is made executable using…
Dynamic Epistemic Logic (DEL) provides a framework for epistemic planning that is capable of representing non-deterministic actions, partial observability, higher-order knowledge and both factual and epistemic change. The high expressivity…
We present an ongoing effort to build a framework and a library in Isabelle/HOL for formalising primal-dual arguments for the analysis of algorithms. We discuss a number of example formalisations from the theory of matching algorithms,…
This paper explores how natural-language descriptions of formal languages can be compared to their formal representations and how semantic differences can be explained. This is motivated from educational scenarios where learners describe a…
This volume contains the proceedings of F-IDE 2015, the second international workshop on Formal Integrated Development Environment, which was held as an FM 2015 satellite event, on June 22, 2015, in Oslo (Norway). High levels of safety,…
Modern-day Integrated Development Environments (IDEs) have come a long way from the early text editing utilities to the complex programs encompassing thousands of functions to help developers. However, with the increasing number of…
Systematic reviews provide comprehensive syntheses of research fields. As a result, systematic reviews often emphasize synthesizing across the large bodies of literature rather than just describing the studies from which the conclusions…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Agile software development evolves so rapidly that research struggles to remain timely and transferable - an issue heightened by the swift adoption of generative AI and agentic tools. Earlier discussions highlight theory and time gaps,…