330 research outputs found
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
A Vernacular for Coherent Logic
We propose a simple, yet expressive proof representation from which proofs
for different proof assistants can easily be generated. The representation uses
only a few inference rules and is based on a frag- ment of first-order logic
called coherent logic. Coherent logic has been recognized by a number of
researchers as a suitable logic for many ev- eryday mathematical developments.
The proposed proof representation is accompanied by a corresponding XML format
and by a suite of XSL transformations for generating formal proofs for
Isabelle/Isar and Coq, as well as proofs expressed in a natural language form
(formatted in LATEX or in HTML). Also, our automated theorem prover for
coherent logic exports proofs in the proposed XML format. All tools are
publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014
Towards lightweight front-end for Isabelle/Isar
This work describes an attempt to assemble a lightweight prototype front-end for verifying propositional logic proofs that relies on the Isabelle/Isar proof authoring and verification system. This prototype serves as an opportunity to become familiar with some of Isabelle/Isar's verification capabilities and limitations, and provides a starting point for future work incorporating Isabelle/Isar as one of the underlying component tools in the Aartifact accessible integrated environment for formal modelling and verification
ProofPeer - A Cloud-based Interactive Theorem Proving System
ProofPeer strives to be a system for cloud-based interactive theorem proving.
After illustrating why such a system is needed, the paper presents some of the
design challenges that ProofPeer needs to meet to succeed. Contexts are
presented as a solution to the problem of sharing proof state among the users
of ProofPeer. Chronicles are introduced as a way to organize and version
contexts
User-friendly Support for Common Concepts in a Lightweight Verifier
Machine verification of formal arguments can only increase our confidence in the correctness of those arguments, but the costs of employing machine verification still outweigh the benefits for some common kinds of formal reasoning activities. As a result, usability is becoming increasingly important in the design of formal verification tools. We describe the "aartifact" lightweight verification system, designed for processing formal arguments involving basic, ubiquitous mathematical concepts. The system is a prototype for investigating potential techniques for improving the usability of formal verification systems. It leverages techniques drawn both from existing work and from our own efforts. In addition to a parser for a familiar concrete syntax and a mechanism for automated syntax lookup, the system integrates (1) a basic logical inference algorithm, (2) a database of propositions governing common mathematical concepts, and (3) a data structure that computes congruence closures of expressions involving relations found in this database. Together, these components allow the system to better accommodate the expectations of users interested in verifying formal arguments involving algebraic and logical manipulations of numbers, sets, vectors, and related operators and predicates. We demonstrate the reasonable performance of this system on typical formal arguments and briefly discuss how the system's design contributed to its usability in two case studies
Verifying Safety Properties With the TLA+ Proof System
TLAPS, the TLA+ proof system, is a platform for the development and
mechanical verification of TLA+ proofs written in a declarative style requiring
little background beyond elementary mathematics. The language supports
hierarchical and non-linear proof construction and verification, and it is
independent of any verification tool or strategy. A Proof Manager uses backend
verifiers such as theorem provers, proof assistants, SMT solvers, and decision
procedures to check TLA+ proofs. This paper documents the first public release
of TLAPS, distributed with a BSD-like license. It handles almost all the
non-temporal part of TLA+ as well as the temporal reasoning needed to prove
standard safety properties, in particular invariance and step simulation, but
not liveness properties
Using the isabelle ontology framework: Linking the formal with the informal
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordWhile Isabelle is mostly known as part of Isabelle/HOL (an interactive theorem prover), it actually provides a framework for developing a wide spectrum of applications. A particular strength of the Isabelle framework is the combination of text editing, formal verification, and code generation. Up to now, Isabelle’s document preparation system lacks a mechanism for ensuring the structure of different document types (as, e.g., required in certification processes) in general and, in particular, mechanism for linking informal and formal parts of a document. In this paper, we present Isabelle/DOF, a novel Document Ontology Framework on top of Isabelle. Isabelle/DOF allows for conventional typesetting as well as formal development. We show how to model document ontologies inside Isabelle/DOF, how to use the resulting meta-information for enforcing a certain document structure, and discuss ontology-specific IDE support
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