Post-Doctoral Research Visit F/M Reasoning up to inclusion and isomorphism in type theory

The job is within the framework of the Malinca project (http://malinca.org). It will be located at the IRIF lab in Paris.

Travel expenses are covered within the limits of the scale in force.

It is common in informal mathematical proofs to reason up to implicit inclusion or isomorphism of structure. The objective of the post-doc is to study such inclusions or isomorphisms in the formal context of type theory, with application to proof assistants. This includes questions such as:
- robustness of type-theoretic constructions up to universe cumulativity or subtyping (e.g. what definitional equalities should satisfy type-theoretic constructions so that an implicit inclusion can be equivalently interpreted as an explicit one)
- robustness of type-theoretic constructions up to isomorphism (e.g. how to ensure that a recursive definition of lists of some length transparently behaves the same when replaced by an equivalent indexed inductive definition)
- interaction between eta-rules and reasoning up to inclusion
- type inference in the presence of inclusions or isomorphisms

Strong expertise expected in type theory, in type-theory-based proof assistants, in the formalization of type theory, in elaboration techniques for proof assistants.

Fluency in French or English recommended.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage