A Semi-Syntactic Soundness Proof for HM(X)
Résumé
This document gives a soundness proof for the generic constraint-based type inference framework HM(X). Our proof is semi-syntactic. It consists in two steps. The first step is to define a ground type system, where polymorphism is extensional, and prove its correctness in a syntactic way. The second step is to interpret HM(X) judgements as (sets of) judgements in the underlying system, which gives a logical view of polymorphism and constraints. Overall, the approach may be seen as more modular than a purely syntactic approach: because polymorphism and constraints are dealt with separately, they do not clutter the subject reduction proof. However, it yields a slightly weaker result: it only establishes type soundness, rather than subject reduction, for HM(X).