PhD in mathematics and fondamental computer science
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Organisation/Company CNRS Department Institut de Recherche en Informatique Fondamentale Research Field Computer science Mathematics » Algorithms Researcher Profile First Stage Researcher (R1) Application Deadline 14 Oct 2026 - 23:59 (UTC) Country France Type of Contract Temporary Job Status Full-time Hours Per Week 35 Offer Starting Date 1 Nov 2026 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Is the Job related to staff position within a Research Infrastructure? No
Offer Description
The aim of the project is to participate in the development of a new generation of proof assistants that integrate both a linguistic layer and automated assistance tools to guide scientists and facilitate the construction of certified mathematical documents, from the choice of concepts and definitions to the elaboration of theorems and proofs.
Linear duality and higher algebraic effects in homotopy type theory
The goal of this PhD thesis will be to define a unified, syntactic, and functorial framework that integrates linear logic, algebraic effects, and homotopic type theory. To this end, we will start with the semantic interpretation of a system of dependent types with universe Type : Type as defined in the language of domain theory. The first step will be to axiomatize the structures of this semantic interpretation and to establish a connection with the relational model of linear logic. We will then formulate extensions of the theory of dependent types with intersection types, drawing on the correspondence between intersection types and finite elements of the relational semantics. In parallel, we will study the connections between linear continuations, duality in dialogue games, and higher algebraic effects, within the framework of a homotopic and multimodal type theory.
Skills
- Good knowledge of the syntax and semantics of dependent type theory with equality
- Good knowledge of a proof assistant such as Agda, Isabelle, Lean or Rocq in terms of formalisation and implementation
- Good knowledge of one programming language such as Haskell, OCaml or Rust
- English: B2 (European Framework of Reference)
- Ability to conceptualise
- Critical thinking skills
- Organisational skills
- Ability to work in a team
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