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This paper describes a memory management discipline for programs that perform dynamic memory allocation and de-allocation. At runtime, all values are put into regions. The store consists of a stack of regions. All points of region allocation and de-allocation are inferred automatically, using a type and effect based program analysis. The scheme does not assume the presence of a garbage collector. The scheme was first presented in 1994 (M. Tofte and J.-P. Talpin, in``Proceedings of the 21st ACM SIGPLAN SIGACT Symposium on Principles of Programming Languages,'' pp. 188 201); subsequently, it has been tested in The ML Kit with Regions, a region-based, garbage-collection free implementation of the Standard ML Core language, which includes recursive datatypes, higher-order functions and updatable references L. Birkedal, M. Tofte, and M. Vejlstrup, (1996), in``Proceedings of the 23 rd ACM SIGPLAN SIGACT Symposium on Principles of Programming Languages,'' pp. 171 183. This paper defines a region-based dynamic semantics for a skeletal programming language extracted from Standard ML. We present the inference system which specifies where regions can be allocated and de-allocated and a detailed proof that the system is sound with respect to a standard semantics. We conclude by giving some advice on how to write programs that run well on a stack of regions, based on practical experience with the ML Kit. ] 1997 Academic Press

We present a translation scheme for the polymorphically typed call-by-value λ-calculus. All runtime values, including function closures, are put into regions. The store consists of a stack of regions. Region inference and effect inference are used to infer where regions can be allocated and de-allocated. Recursive functions are handled using a limited form of polymorphic recursion. The translation is proved correct with respect to a store semantics, which models a regionbased run-time system. Experimental results suggest that regions tend to be small, that region allocation is frequent and that overall memory demands are usually modest, even without garbage collection.

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Milner, R. and M. Tofte, Co-induction in relational semantics, Theoretical Computer Science 87 (1991) 209-220.An application of the mathematical theory of maximum fixed points of monotonic set operators to relational semantics is presented. It is shown how an important proof method which we call co-induction, a variant of Park's (1969) principle of fixpoint induction, can be used to prove the consistency of the static and the dynamic relational semantics of a small functional programming language with recursive functions.

Region Inference is a program analysis which infers lifetimes of values. It is targeted at a runtime model in which the store consists of a stack of regions and memory management predominantly consists of pushing and popping regions, rather than performing garbage collection. Region Inference has previously been specified by a set of inference rules which formalize when regions may be allocated and deallocated. This article presents an algorithm which implements the specification. We prove that the algorithm is sound with respect to the region inference rules and that it always terminates even though the region inference rules permit polymorphic recursion in regions. The algorithm is the result of several years of experiments with region inference algorithms in the ML Kit, a compiler from Standard ML to assembly language. We report on practical experience with the algorithm and give hints on how to implement it.

Abstract. We report on our experience with designing, implementing, proving correct, and evaluating a regionbased memory management system.