2019/06/24 by Siek, Jeremy G.
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Programming Languages (cs.PL)
paper · doi:10.48550/arxiv.1906.09709
The subtyping rules for intersection types traditionally employ a transitivity rule (Barendregt et al. 1983), which means that subtyping does not satisfy the subformula property, making it more difficult to use in filter models for compiler verification. Laurent develops a sequent-style subtyping system, without transitivity, and proves transitivity via a sequence of six lemmas that culminate in cut-elimination (2018). This article develops a subtyping system in regular style that omits transitivity and provides a direct proof of transitivity, significantly reducing the length of the proof, exchanging the six lemmas for just one. Inspired by Laurent's system, the rule for function types is essentially the β-soundness property. The new system satisfies the "subformula conjunction property": every type occurring in the derivation of A