Jonas Kaiser

Jonas Kaiser

Frankfurt, Hessen, Deutschland
219 Follower:innen 216 Kontakte

Info

I am currently working at ioki GmbH as a Software Engineering Expert in the Mobility…

Aktivitäten

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Berufserfahrung

  • ioki – a DB company Grafik

    ioki – a DB company

    Frankfurt am Main, Hesse, Germany

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    Frankfurt am Main, Hessen, Germany

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    Frankfurt Am Main Area, Germany

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    Saarbrücken Area, Germany

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    Munich Area, Germany

Ausbildung

  • Universität des Saarlandes Grafik

    Universität des Saarlandes

    Development of techniques to formally (i.e. in the proof assistant Coq) reason about correspondence proofs between various type systems and similar syntactic languages with a focus on the binding of local variables and the handling of contextual information. Thesis submission planned for December 2018, with defense in 2019.

  • Saarbrücken Graduate School of Computer Science. Major courses: Introduction to Computational Logic, Semantics, Verification, Machine Learning, Type Systems for Modules, Compiler Verification, Concurrent Program Logics. M.Sc. Thesis: "Formal Construction of a Set Theory in Coq".

  • Activities and Societies: SciSoc

    General undergraduate 3-year course in computer science, with physics as minor subject during first year. BA Thesis: "Reconsidering Lucid – a modern approach" an actor-based concurrent, demand-driven Scala implementation of the dataflow language Lucid.

Bescheinigungen und Zertifikate

Veröffentlichungen

  • Binder Aware Recursion over Well-Scoped de Bruijn Syntax

    Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2018, Los Angeles, CA, USA

    The de Bruijn representation of syntax with binding is commonly used, but flawed when it comes to recursion. As the structural recursion principle associated to an inductive type of expressions is unaware of the binding discipline, each recursive definition requires a separate proof of compatibility with variable instantiation. We solve this problem by extending Allais' notion of syntax traversals to obtain a framework for instantiation-compatible recursion. The framework is general enough to…

    The de Bruijn representation of syntax with binding is commonly used, but flawed when it comes to recursion. As the structural recursion principle associated to an inductive type of expressions is unaware of the binding discipline, each recursive definition requires a separate proof of compatibility with variable instantiation. We solve this problem by extending Allais' notion of syntax traversals to obtain a framework for instantiation-compatible recursion. The framework is general enough to handle multivariate, potentially mutually recursive syntactic systems. With our framework we define variable renaming and instantiation, syntax directed typing and certain unary logical relations for System F. These definitons lead to concise proofs of type preservation, as well as weak and strong normalisation. Our framework is designed to serve as the theoretical foundation of future versions of the Autosubst Coq library. All developments and case studies are formalised in the Coq proof assistant.

    Andere Autor:innen
    • Kathrin Stark
    • Steven Schäfer
    Veröffentlichung anzeigen
  • Autosubst 2: Towards Reasoning with Multi-Sorted de Bruijn Terms and Vector Substitutions

    International Workshop on Logical Frameworks and Meta Languages: Theory and Practice, LFMTP 2017, Oxford, UK

    Formalising metatheory in the Coq proof assistant is tedious as native support for reasoning about languages with binders is marginal at best. The Autosubst framework (Schäfer, Smolka and Tebbi, 2015) automates working with de Brujin terms: for each annotated inductive type, it generates a corresponding substitution operation and a decision procedure for assumption-free substitution lemmas. A key part of the equational theory are parallel substitutions which combine multiple single-variable…

    Formalising metatheory in the Coq proof assistant is tedious as native support for reasoning about languages with binders is marginal at best. The Autosubst framework (Schäfer, Smolka and Tebbi, 2015) automates working with de Brujin terms: for each annotated inductive type, it generates a corresponding substitution operation and a decision procedure for assumption-free substitution lemmas. A key part of the equational theory are parallel substitutions which combine multiple single-variable substitutions. However, due to its separate treatment of sorts Autosubst lacks support for mutual inductive types. This restriction is removed in our prototype implementation of Autosubst 2: second-order HOAS specifications are translated into potentially mutual inductive term sorts. Again, parallelising substitutions is the key: we introduce vector substitutions to combine the application of multiple parallel substitutions into exactly one instantiation operation for each sort. The resulting equational theory is both simpler and more expressive than that of the original Autosubst framework.

    Andere Autor:innen
    • Kathrin Stark
    • Steven Schäfer
    Veröffentlichung anzeigen
  • Relating System F and λ2: A Case Study in Coq, Abella and Belug

    Proceedings of the 2nd International Conference on Formal Structures for Computation and Deduction, FSCD 2017, Oxford, UK

    We give three formalisations of a proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system (PTS) variant λ2. This is established by reducing the typability problem of F to λ2 and vice versa. A key challenge is the treatment of variable binding and contextual information. The formalisations all share the same high level proof structure using relations to connect the type systems. They do, however, differ significantly in their…

    We give three formalisations of a proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system (PTS) variant λ2. This is established by reducing the typability problem of F to λ2 and vice versa. A key challenge is the treatment of variable binding and contextual information. The formalisations all share the same high level proof structure using relations to connect the type systems. They do, however, differ significantly in their representation and manipulation of variables and contextual information. In Coq, we use pure de Bruijn indices and parallel substitutions. In Abella, we use higher-order abstract syntax (HOAS) and nominal constants of the ambient reasoning logic. In Beluga, we also use HOAS but within contextual modal type theory. Our contribution is twofold. First, we present and compare a collection of machine-checked solutions to a non-trivial theoretical result. Second, we propose our proof as a benchmark, complementing the POPLmark and ORBI challenges by testing how well a given proof assistant or framework handles complex contextual information involving multiple type systems.

    Andere Autor:innen
    • Brigitte Pientka
    • Gert Smolka
    Veröffentlichung anzeigen
  • Equivalence of System F and λ2 in Coq Based on Context Morphism Lemmas

    Proceedings of the 6th ACM SIGPLAN Conference on Certified Proofs and Programs, CPP 2017, Paris, France

    We give a machine-checked proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system variant λ2. This is established by reducing the typing problem of F to λ2 and vice versa. The difficulty lies in aligning different binding-structures and different contexts (dependent vs. non-dependent). The use of de Bruijn syntax, parallel substitutions, and context morphism lemmas leads to an elegant proof. We use the Coq proof assistant and the…

    We give a machine-checked proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system variant λ2. This is established by reducing the typing problem of F to λ2 and vice versa. The difficulty lies in aligning different binding-structures and different contexts (dependent vs. non-dependent). The use of de Bruijn syntax, parallel substitutions, and context morphism lemmas leads to an elegant proof. We use the Coq proof assistant and the substitution library Autosubst.

    Andere Autor:innen
    • Gert Smolka
    • Tobias Tebbi
    Veröffentlichung anzeigen

Sprachen

  • German

    Muttersprache oder zweisprachig

  • English

    Verhandlungssicher

  • Spanish

    Grundkenntnisse

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