Related papers: Translating Scala Programs to Isabelle/HOL
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
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…
We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
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…
In Isabelle/HOL, declarative proofs written in the Isar language are widely appreciated for their readability and robustness. However, some users may prefer writing procedural "apply-style" proof scripts since they enable rapid exploration…
Abella is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and…
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.…
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…
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…
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…
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 assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…
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…
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…
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…
We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…
Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules,…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…