linyxus / extended-pdot-calculus

pDOT calculus extended with inversion rules.

Soundness Proof for Extended pDOT Calculus

This repository contains type safety proof for the extended pDOT system, mechanized in Coq.

The calculus is extended with the following record subtyping inversion rules, which will facilitate the formalization of GADT reasoning in pDOT.

G ⊢ U1 <: U2
U1 ↘ {A: S1..T1}
U2 ↘ {A: S2..T2}
_________________
G ⊢ S2 <: S1

G ⊢ U1 <: U2
U1 ↘ {A: S1..T1}
U2 ↘ {A: S2..T2}
_________________
G ⊢ T1 <: T2

The relation U ↘ {A: S..T} states that U is an intersection type with all components being fields, type members or recursive types, the type labels are unique, and it has the type member {A: S..T}.

The proof is modified from pDOT soundness proof.