Skip to content

formal proof

Our formalisation of Linear Resources and Process Compositions has been published in the Archive of Formal Proof

    Abstract

    In this entry we formalise a framework for process composition based on actions that are specified by their input and output resources. We verify their correctness by translating compositions of process into deductions of intuitionistic linear logic. As part of the verification we derive simple conditions on the compositions which ensure well-formedness of the corresponding deduction.

    We describe an earlier version of this formalisation in our article Linear Resources in Isabelle/HOL, which also includes a formalisation of manufacturing processes in the simulation game Factorio.

    Our formalisation of Lie Groups and Algebras has been published in the Archive of Formal Proof

      Abstract

      Lie Groups are formalised as locales, building on the AFP theory of Smooth Manifolds. We formalise the diffeomorphism group of a manifold, and the action of a Lie group on a manifold. The general linear group is shown to be a Lie group by proving properties of the determinant, and matrix inverses. We also develop a theory of smooth vector fields on a manifold , defined as smooth maps from the manifold to its tangent bundle . We employ a shortcut that avoids difficulties in defining the tangent bundle as a manifold, but which still leads to vector fields with the properties one would expect. We then construct the Lie algebra of a Lie group as an algebra of left-invariant smooth vector fields.

      Schmoetten R. and Fleuriot J. D. (2024). Lie Groups and Algebras. Archive of Formal Proofs. ISSN: 2150-914x.

      Our paper “Linear Resources in Isabelle/HOL” has just been published in the Journal of Automated Reasoning

        Abstract:

        We present a formal framework for process composition based on actions that are specified by their input and output resources. The correctness of these compositions is verified by translating them into deductions in intuitionistic linear logic. As part of the verification we derive simple conditions on the compositions which ensure well-formedness of the corresponding deduction when satisfied. We mechanise the whole framework, including a deep embedding of ILL, in the proof assistant Isabelle/HOL. Beyond the increased confidence in our proofs, this allows us to automatically generate executable code for our verified definitions. We demonstrate our approach by formalising part of the simulation game Factorio and modelling a manufacturing process in it. Our framework guarantees that this model is free of bottlenecks.

        Smola, F., Fleuriot, J.D. Linear Resources in Isabelle/HOL. J Autom Reasoning 68, 9 (2024). https://doi.org/10.1007/s10817-024-09698-2

        Paper accepted at CICM 2022

          Our paper, “Re-imagining the Isabelle Archive of Formal Proofs” (MacKenzie, Huch, Vaughan and Fleuriot), has been accepted at the 15th Conference on Intelligent Computer Mathematics (CICM 2022).