Related papers: SeCaV: A Sequent Calculus Verifier in Isabelle/HOL
Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…
This paper presents a formally verified quantifier elimination (QE) algorithm for first-order real arithmetic by linear and quadratic virtual substitution (VS) in Isabelle/HOL. The Tarski-Seidenberg theorem established that the first-order…
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…
User simulators are increasingly central to interactive information retrieval, yet the community lacks standardized evaluation tools. Simulators serve two objectives, behavioral realism (matching real user behavior) and tester reliability…
We present a tool called HHLPar for verifying hybrid systems modelled in Hybrid Communicating Sequential Processes (HCSP). HHLPar is built upon a Hybrid Hoare Logic for HCSP, which is able to reason about continuous-time properties of…
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…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
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…
We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…
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…
Studying unified model averaging estimation for situations with complicated data structures, we propose a novel model averaging method based on cross-validation (MACV). MACV unifies a large class of new and existing model averaging…
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…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…
Church's Higher Order Logic is a basis for influential proof assistants -- HOL and PVS. Church's logic has a simple set-theoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of…
Cuv\'ee is a program verification tool that reads SMT-LIB-like input files where terms may additionally contain weakest precondition operators over abstract programs. Cuv\'ee translates such inputs into first-order SMT-LIB by symbolically…
OCaml is particularly well-fitted for formal verification. On one hand, it is a multi-paradigm language with a well-defined semantics, allowing one to write clean, concise, type-safe, and efficient code. On the other hand, it is a language…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…