PIDE as front-end technology for Coq

Isabelle/PIDE is the current Prover IDE technology for Isabelle. It has been developed in ML and Scala in the past 4-5 years for this particular proof assistant, but with an open mind towards other systems. PIDE is based on an asynchronous document model, where the prover receives edits continuously and updates its internal state accordingly. The interpretation of edits and the policies for proof document processing are determined by the prover. The editor front-end merely takes care of visual rendering of formal document content. Here we report on an experiment to connect Coq to the PIDE infrastructure of Isabelle. This requires to re-implement the core PIDE protocol layer of Isabelle/ML in OCaml. The payload for semantic processing of proof document content is restricted to lexical analysis in the sense of existing CoqIde functionality. This is sufficient as proof-of-concept for PIDE connectivity. Actual proof processing is then a matter of improving Coq towards timeless and stateless proof processing, independently of PIDE technicalities. The implementation worked out smoothly and required minimal changes to the refined PIDE architecture of Isabelle2013. This experiment substantiates PIDE as general approach to prover interaction. It illustrates how other provers of the greater ITP family can participate by following similar reforms of the classic TTY loop as was done for Isabelle in the past few years

Isabelle/PIDE as Platform for Educational Tools

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 so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Virtualization of HOL4 in Isabelle

We present a novel approach to combine the HOL4 and Isabelle theorem provers: both are implemented in SML and based on distinctive variants of HOL. The design of HOL4 allows to replace its inference kernel modules, and the system infrastructure of Isabelle allows to embed other applications of SML. That is the starting point to provide a virtual instance of HOL4 in the same run-time environment as Isabelle. Moreover, with an implementation of a virtual HOL4 kernel that operates on Isabelle/HOL terms and theorems, we can load substantial HOL4 libraries to make them Isabelle theories, but still disconnected from existing Isabelle content. Finally, we introduce a methodology based on the transfer package of Isabelle to connect the imported HOL4 material to that of Isabelle/HOL

Isabelle/DOF: Design and Implementation

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record17th International Conference, SEFM 2019 Oslo, Norway, September 18–20, 2019DOF is a novel framework for defining ontologies and enforcing them during document development and evolution. A major goal of DOF is the integrated development of formal certification documents (e. g., for Common Criteria or CENELEC 50128) that require consistency across both formal and informal arguments. To support a consistent development of formal and informal parts of a document, we provide Isabelle/DOF, an implementation of DOF on top of the formal methods framework Isabelle/HOL. A particular emphasis is put on a deep integration into Isabelleâs IDE, which allows for smooth ontology development as well as immediate ontological feedback during the editing of a document. In this paper, we give an in-depth presentation of the design concepts of DOFâs Ontology Definition Language (ODL) and key aspects of the technology of its implementation. Isabelle/DOF is the first ontology language supporting machine-checked links between the formal and informal parts in an LCF-style interactive theorem proving environment. Sufficiently annotated, large documents can easily be developed collabo- ratively, while ensuring their consistency, and the impact of changes (in the formal and the semi-formal content) is tracked automatically.IRT SystemX, Paris-Saclay, Franc

Seventeen Provers under the Hammer

International audienceOne of the main success stories of automatic theorem provers has been their integration into proof assistants. Such integrations, or "hammers," increase proof automation and hence user productivity. In this paper, we use Isabelle/HOL's Sledgehammer tool to find out how useful modern provers are at proving formulas in higher-order logic. Our evaluation follows in the steps of Böhme and Nipkow's Judgment Day study from 2010, but instead of three provers we use 17, including SMT solvers and higher-order provers. Our work offers an alternative yardstick for comparing modern provers, next to the benchmarks and competitions emerging from the TPTP World and SMT-LIB

Automated Generation of User Guidance by Combining Computation and Deduction

Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an emerging generation of educational mathematics assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction, is the most reliable technology used to check user input. However ATP is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck then the system should be able to suggest possible next steps. The key idea of Lucas Interpretation is to compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides the next steps. User guidance is generated by combining deduction and computation: the latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas Interpretation so that open questions can adequately be addressed, and prerequisites for further work are provided.Comment: In Proceedings THedu'11, arXiv:1202.453

Using Ontologies in Formal Developments Targeting Certification

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this recordIFM 2019: 15th International Conference on integrated Formal Methods, 4-6 December 2019, Bergen, NorwayA common problem in the certification of highly safety or security critical systems is the consistency of the certification documentation in general and, in particular, the linking between semi-formal and formal content of the certification documentation. We address this problem by using an existing framework, Isabelle/DOF, that allows writing certification documents with consistency guarantees, in both, the semi-formal and formal parts. Isabelle/DOF supports the modeling of document ontologies using a strongly typed ontology definition language. An ontology is then enforced inside documents including formal parts, e.g., system models, verification proofs, code, tests and validations of corner-cases. The entire set of documents is checked within Isabelle/HOL, which includes the definition of ontologies and the editing of integrated documents based on them. This process is supported by an IDE that provides continuous checking of the document consistency. In this paper, we present how a specific software-engineering certification standard, namely CENELEC 50128, can be modeled inside Isabelle/DOF. Based on an ontology covering a substantial part of this standard, we present how Isabelle/DOF can be applied to a certification case-study in the railway domain.IRT System