Related papers: Towards Evolutionary Theorem Proving for Isabelle/…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
We present a trustworthy connection between the Leon verification system and the Isabelle proof assistant. Leon is a system for verifying functional Scala programs. It uses a variety of automated theorem provers (ATPs) to check verification…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…
Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
The Isabelle Archive of Formal Proofs has grown to a significant size in the past years. It makes up for an impressive body of research, which enables a number of statistical approaches to various aspects in theorem proving, and has not yet…
Solving an optimization task in any domain is a very challenging problem, especially when dealing with nonlinear problems and non-convex functions. Many meta-heuristic algorithms are very efficient when solving nonlinear functions. A…
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
Elfe is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
In the last few years, the formulation of real-world optimization problems and their efficient solution via metaheuristic algorithms has been a catalyst for a myriad of research studies. In spite of decades of historical advancements on the…
We present a method to estimate the provability of a mathematical formula. We adapt the tactical theorem prover TacticToe to factor in these estimations. Experiments over the HOL4 library show an increase in the number of theorems re-proven…
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…
Currently, many verification algorithms are available to improve the reliability of software systems. Selecting the appropriate verification algorithm typically demands domain expertise and non-trivial manpower. An automated algorithm…