Related papers: The Elfe System - Verifying mathematical proofs of…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…
The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have…
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…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
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…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Equational reasoning is one of the key features of pure functional languages such as Haskell. To date, however, such reasoning always took place externally to Haskell, either manually on paper, or mechanised in a theorem prover. This…
HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…
The Edinburgh Logical Framework (LF) is a dependently type lambda calculus that can be used to encode formal systems. The versatility of LF allows specifications to be constructed also about the encoded systems. The Twelf system exploits…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
A number of introductory textbooks for Haskell use calculations right from the start to give the reader insight into the evaluation of expressions and the behavior of functional programs. Many programming concepts that are important in the…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
This paper presents Holbert: a work-in-progress pedagogical proof assistant and online textbook platform, aimed at the educational use-case, specifically for the teaching of programming language theory. Holbert allows proof exercises and…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
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…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
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,…
Proof competence, i.e. the ability to write and check (mathematical) proofs, is an important skill in Computer Science, but for many students it represents a difficult challenge. The main issues are the correct use of formal language and…