Drawing together two lines of research (that done in type-safe region-based memory management and that done in monadic encapsuation of effects), we give a type-preserving translation from a variation of the region calculus of Tofte and Talpin into an extension of System F augmented with monadic types and operations. Our source language is a novel region calculus, dubbed the Single Effect Calculus, in which sets of effects are specified by a single region representing an upper bound on the set. Our target language is F RGN, which provides an encapsulation operator whose parametric type ensures that regions (and values allocated therein) are neither accessible nor visible outside the appropriate scope. 1

Abstract. We consider a type system capable of tracking reading, writing and allocation in a higher-order language with dynamically allocated references. We give a denotational semantics to this type system which allows us to validate a number of effect-dependent program equivalences in the sense of observational equivalence. An example is the following: x = e; y = e; e ′ (x, y) is equivalent to x = e; e ′ (x, x) provided that e does not read from memory regions that it writes to and moreover does not allocate memory that is encapsulated in the values of x and y. Here x can be a higher-order function or a reference or a combination of both. The two sides of the above equivalence turn out to be related in the denotational semantics which implies that they are observationally equivalent, ie can be replaced by one another in any (well-typed) program. On the way we learn popular techniques such as parametrised logical relations, regions, admissible relations, etc., which belong to the toolbox of researchers in principles of programming languages.

Region-based memory management is a scheme for managing dynamically allocated data. A defining characteristic of region-based memory management is the bulk deallocation of data, which avoids both the tedium of malloc/free and the overheads of a garbage collector. Type systems for region-based memory manag-ment enhance the utility of this scheme by statically determining when a program is guaranteed to not perform any erroneous region operations. We describe three type systems for region-based memory management: • a type-and-effect system (à la the Tofte-Talpin region calculus); • a novel monadic type system; • a novel substructural type system. We demonstrate how to successively encode the type-and-effect system into the monadic type system and the monadic type system into the substructural type system. These type systems and encodings support the argument that the type-and-effect systems that have traditionally been used to ensure the safety of region-based memory management are neither the simplest nor the most expressive type

Abstract. A region calculus is a programming language calculus with explicit instrumentation for memory management. Every value is annotated with a region in which it is stored and regions are allocated and deallocated in a stack-like fashion. The annotations can be statically inferred by a type and effect system, making a region calculus suitable as an intermediate language for a compiler of statically typed programming languages. Although a lot of attention has been paid to type soundness properties of different flavors of region calculi, it seems that little effort has been made to develop a semantic framework. In this paper, we present a theory based on bisimulation, which serves as a coinductive proof principle for showing equivalences of polymorphically region-annotated terms. Our notion of bisimilarity is reminiscent of open bisimilarity for the π-calculus and we prove it sound and complete with respect to Morris-style contextual equivalence. As an application, we formulate a syntactic equational theory, which is used elsewhere to prove the soundness of a specializer based on region inference. We use our bisimulation framework to show that the equational theory is sound with respect to contextual equivalence.

A region calculus is a polymorphically typed lambda calculus with explicit memory management primitives. Every value is annotated with a region in which it is stored. Regions are allocated and deallocated in a stack-like fashion. The annotations can be statically inferred by a type and eect system, making a region calculus suitable as an intermediate language for a compiler of statically typed programming languages.

. A tension in language design has been between simple semantics

There are a number of applied lambda-calculi in which terms and types are annotated with parameters denoting either locations or locations in machine memory. Such calculi have been designed with safe memory-management operations in mind. It is difficult to construct directly denotational models for existing calculi of this kind. We approach the problem differently, by starting from a class of mathematical models that describe some of the essential semantic properties intended in these calculi. In particular, disjointness conditions between regions (or locations) are implicit in many of the memory-management operations. Bunched polymorphism provides natural type-theoretic mechanisms for capturing the disjointness conditions in such models. We illustrate this by adding regions to the basic disjointness model of αλ, the lambda-calculus associated to the logic of bunched implications. We show how both additive and multiplicative polymorphic quantifiers arise naturally in our models. A locations model is a special case. In order to relate this enterprise back to previous work on memory-management, we provide an example in which the model is refined and used to provide a denotational semantics for a language with explicit allocation and disposal of regions.

We give a denotational semantics to a region-based effect system tracking reading, writing and allocation in a higher-order language with dynamically allocated integer references. Effects are interpreted in terms of the preservation of certain binary relations on the store, parameterized by region-indexed partial bijections on locations. The semantics validates a number of effect-dependent program equivalences and can thus serve as a foundation for effect-based compiler transformations.

There are a number of applied lambda-calculi in which terms and types are annotated with parameters denoting either locations or locations in machine memory. Such calculi have been designed with safe memory-management operations in mind. It is difficult to construct directly denotational models for existing calculi of this kind. We approach the problem differently, by starting from a class of mathematical models that describe some of the essential semantic properties intended in these calculi. In particular, disjointness conditions between regions (or locations) are implicit in many of the memory-management operations. Bunched polymorphism provides natural type-theoretic mechanisms for capturing the disjointness conditions in such models. We illustrate this by adding regions to the basic disjointness model of αλ, the lambda-calculus associated to the logic of bunched implications. We show how both additive and multiplicative polymorphic quantifiers arise naturally in our models. A locations model is a special case. In order to relate this enterprise back to previous work on memory-management, we provide an example in which the model is refined and used to provide a denotational semantics for a language with explicit allocation and disposal of regions.