First Steps Towards Cumulative Inductive Types in CIC

We discuss our on-going research on making inductive types cumulative in the predicative calculus of inductive constructions (pCIC) – the logic of the Coq proof assistant. Having inductive types be cumulative alleviates some problems that occur while working with large inductive types, e.g., the category of small categories, in pCIC. We present the pCuIC system which adds cumulativity for inductive types to pCIC and briefly discuss some of its properties and possible extensions. We, in addition, give a justification for the introduced cumulativity relation for inductive types. First Steps Towards Cumulative Inductive Types in CIC: Extended Version Amin Timany and Bart Jacobs iMinds-DistriNet, KU Leuven [email protected] Abstract. We discuss our on-going research on making inductive types cumulative in the predicative calculus of inductive constructions (pCIC) – the logic of the Coq proof assistant. Having inductive types be cumulative alleviates some problems that occur while working with large inductive types, e.g., the category of small categories, in pCIC. We present the pCuIC system which adds cumulativity for inductive types to pCIC and briefly discuss some of its properties and possible extensions. We, in addition, give a justification for the introduced cumulativity relation for inductive types. We discuss our on-going research on making inductive types cumulative in the predicative calculus of inductive constructions (pCIC) – the logic of the Coq proof assistant. Having inductive types be cumulative alleviates some problems that occur while working with large inductive types, e.g., the category of small categories, in pCIC. We present the pCuIC system which adds cumulativity for inductive types to pCIC and briefly discuss some of its properties and possible extensions. We, in addition, give a justification for the introduced cumulativity relation for inductive types.