Syntactic Type Soundness for the Region Calculus

Abstract The region calculus of Tofte and Talpin is an annotated polymorphically typed lambda calculus which makes memory allocation and deallocation explicit. It is intended as an intermediate language in a compiler for ML-like languages. The region annotations are obtained by static region and effect inference, which makes it an attractive alternative for garbage collection. Soundness of the region and effect system is crucial to guarantee safe deallocation of regions, i.e. deallocation should only take place for objects which are provable dead. Tofte and Talpin have proved type soundness of the region calculus using rule-based co-induction. This proof is quite complicated and not very intuitive. Much of the problem lies in the low-level big-step operational semantics which involves manipulations of an explicit store and which has a co-inductive definition. In this paper, we present a small-step operational semantics for the region calculus, based on syntactic rewriting. We prove type soundness following the approach of Wright and Felleisen, leading to very simple inductive proofs.

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