Related papers: Reconstructing veriT Proofs in Isabelle/HOL
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…
We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…
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…
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
Consensus protocols are crucial for a blockchain system as they are what allow agreement between the system's nodes in a potentially adversarial environment. For this reason, it is paramount to ensure their correct design and implementation…
We present an executable formally verified SAT encoding of classical AI planning. We use the theorem prover Isabelle/HOL to perform the verification. We experimentally test the verified encoding and show that it can be used for reasonably…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
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…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…
Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…