Categories and Subject Descriptors We show how to efficiently obtain linear a priori bounds on the heap space consumption of first-order functional programs. The analysis takes space reuse by explicit deallocation into account and also furnishes an upper bound on the heap usage in the presence of garbage collection. It covers a wide variety of examples including, for instance, the familiar sorting algorithms for lists, including quicksort. The analysis relies on a type system with resource annotations. Linear programming (LP) is used to automatically infer derivations in this enriched type system. We also show that integral solutions to the linear programs derived correspond to programs that can be evaluated without any operating system support for memory management. The particular integer linear programs arising in this way are shown to be feasibly solvable under mild assumptions.

This article The purpose of this paper is to introduce b, a simply typed -calculus that supports type-based recursive definitions. Although heavily inspired from previous work by Giménez (Giménez 1998) and closely related to recent work by Amadio and Coupet (Amadio and Coupet-Grimal 1998), the technical machinery behind our system puts a slightly different emphasis on the interpretation of types. More precisely, we formalize the notion of type-based termination using a restricted form of type dependency (a.k.a. indexed types), as popularized by (Xi and Pfenning 1998; Xi and Pfenning 1999). This leads to a simple and intuitive system which is robust under several extensions, such as mutually inductive datatypes and mutually recursive function definitions; however, such extensions are not treated in the paper

The paradigm of type-based termination is explored for functional programming with recursive data types. The article introduces , a lambda-calculus with recursion, inductive types, subtyping and bounded quanti cation. Decorated type variables representing approximations of inductive types are used to track the size of function arguments and return values. The system is shown to be type safe and strongly normalizing. The main novelty is a bidirectional type checking algorithm whose soundness is established formally.

Abstract. We study the problem of determining stack boundedness and the exact maximum stack size for three classes of interrupt-driven programs. Interrupt-driven programs are used in many real-time applications that require responsive interrupt handling. In order to ensure responsiveness, programmers often enable interrupt processing in the body of lower-priority interrupt handlers. In such programs a programming error can allow interrupt handlers to be interrupted in cyclic fashion to lead to an unbounded stack, causing the system to crash. For a restricted class of interrupt-driven programs, we show that there is a polynomial-time procedure to check stack boundedness, while determining the exact maximum stack size is PSPACE-complete. For a larger class of programs, the two problems are both PSPACE-complete, and for the largest class of programs we consider, the two problems are PSPACE-hard and can be solved in exponential time. 1

In the simply-typed lambda-calculus, a hereditary substitution replaces a free variable in a normal form r by another normal form s of type a, removing freshly created redexes on the fly. It can be defined by lexicographic induction on a and r, thus, giving rise to a structurally recursive normalizer for the simply-typed lambda-calculus. We generalize this scheme to simultaneous substitutions, preserving its simple termination argument. We further implement hereditary simultaneous substitutions in a functional programming language with sized heterogeneous inductive types, Fωb, arriving at an interpreter whose termination can be tracked by the type system of its host programming language.

Abstract. A type-based approach to termination uses sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls occur just at a smaller size. This approach is only sound if the type of the recursive function is admissible, i.e., depends on the size index in a certain way. To explore the space of admissible functions in the presence of higher-kinded data types and impredicative polymorphism, a semantics is developed where sized types are interpreted as functions from ordinals into sets of strongly normalizing terms. It is shown that upper semi-continuity of such functions is a sufficient semantical criterion for admissibility. To provide a syntactical criterion, a calculus for semi-continuous function is developed. 1

The parallel-functional language Eden extends Haskell by constructs to explicitly dene and communicate processes. These extensions allow the easy denition of skeletons as higher-order functions. However, the programmer can inadvertently introduce busy loops or deadlocks in them. In this paper a sized type system is extended in order to use it for Eden programs, so that those well-typed skeletons are guaranteed either to terminate or to be productive. The problems raised by Eden features and their possible solutions are described in detail, and several skeletons are typed in this modied system such as the parallel map, farm, pipeline, divide and conquer, and replicated workers. 1

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