Weak reduction and garbage collection in interaction nets

This paper presents an implementation device for the weak reduction of interaction nets to interface normal form. The results produced by running several benchmarks are given, suggesting that weak reduction greatly improves the performance of the interaction combinators-based implementation of the λ-calculus.(undefined

Distilling Abstract Machines (Long Version)

It is well-known that many environment-based abstract machines can be seen as strategies in lambda calculi with explicit substitutions (ES). Recently, graphical syntaxes and linear logic led to the linear substitution calculus (LSC), a new approach to ES that is halfway between big-step calculi and traditional calculi with ES. This paper studies the relationship between the LSC and environment-based abstract machines. While traditional calculi with ES simulate abstract machines, the LSC rather distills them: some transitions are simulated while others vanish, as they map to a notion of structural congruence. The distillation process unveils that abstract machines in fact implement weak linear head reduction, a notion of evaluation having a central role in the theory of linear logic. We show that such a pattern applies uniformly in call-by-name, call-by-value, and call-by-need, catching many machines in the literature. We start by distilling the KAM, the CEK, and the ZINC, and then provide simplified versions of the SECD, the lazy KAM, and Sestoft's machine. Along the way we also introduce some new machines with global environments. Moreover, we show that distillation preserves the time complexity of the executions, i.e. the LSC is a complexity-preserving abstraction of abstract machines.Comment: 63 page

Lambda Calculus with Explicit Recursion

AbstractThis paper is concerned with the study ofλ-calculus with explicit recursion, namely of cyclicλ-graphs. The starting point is to treat aλ-graph as a system of recursion equations involvingλ-terms and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for first-order term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the substitution operation. This leads to a family ofλ-graph calculi, which can be seen as an extension of the family ofλσ-calculi (λ-calculi with explicit substitution). While theλσ-calculi treat the let-construct as a first-class citizen, our calculi support the letrec, a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of program

Simple Parsimonious Types and Logarithmic Space

We present a functional characterization of deterministic logspace-computable predicates based on a variant (although not a subsystem) of propositional linear logic, which we call parsimonious logic. The resulting calculus is simply-typed and contains no primitive besides those provided by the underlying logical system, which makes it one of the simplest higher-order languages capturing logspace currently known. Completeness of the calculus uses the descriptive complexity characterization of logspace (we encode first-order logic with deterministic closure), whereas soundness is established by executing terms on a token machine (using the geometry of interaction)

An Abstract Factorization Theorem for Explicit Substitutions

We study a simple form of standardization, here called factorization, for explicit substitutions calculi, i.e. lambda-calculi where beta-reduction is decomposed in various rules. These calculi, despite being non-terminating and non-orthogonal, have a key feature: each rule terminates when considered separately. It is well-known that the study of rewriting properties simplifies in presence of termination (e.g. confluence reduces to local confluence). This remark is exploited to develop an abstract theorem deducing factorization from some axioms on local diagrams. The axioms are simple and easy to check, in particular they do not mention residuals. The abstract theorem is then applied to some explicit substitution calculi related to Proof-Nets. We show how to recover standardization by levels, we model both call-by-name and call-by-value calculi and we characterize linear head reduction via a factorization theorem for a linear calculus of substitutions

The Dynamic Geometry of Interaction Machine: A Call-by-Need Graph Rewriter

Girard's Geometry of Interaction (GoI), a semantics designed for linear logic proofs, has been also successfully applied to programming language semantics. One way is to use abstract machines that pass a token on a fixed graph along a path indicated by the GoI. These token-passing abstract machines are space efficient, because they handle duplicated computation by repeating the same moves of a token on the fixed graph. Although they can be adapted to obtain sound models with regard to the equational theories of various evaluation strategies for the lambda calculus, it can be at the expense of significant time costs. In this paper we show a token-passing abstract machine that can implement evaluation strategies for the lambda calculus, with certified time efficiency. Our abstract machine, called the Dynamic GoI Machine (DGoIM), rewrites the graph to avoid replicating computation, using the token to find the redexes. The flexibility of interleaving token transitions and graph rewriting allows the DGoIM to balance the trade-off of space and time costs. This paper shows that the DGoIM can implement call-by-need evaluation for the lambda calculus by using a strategy of interleaving token passing with as much graph rewriting as possible. Our quantitative analysis confirms that the DGoIM with this strategy of interleaving the two kinds of possible operations on graphs can be classified as "efficient" following Accattoli's taxonomy of abstract machines

Some urban facts of life

This review of recent literature explores the challenges to urban food and nutrition security in the rapidly urbanizing developing world. The premise of the manuscript is that the causes of malnutrition and food insecurity in urban and rural areas are different due primarily to a number of phenomena that are unique to or exacerbated by urban living. These areas include (1) a greater dependence on cash income; (2) weaker informal safety nets; (3) greater labor force participation of women and its consequences for child care; (4) lifestyle changes, particularly diet and exercise patterns; (5) greater availability of public services, but questionable access by the poor; (6) greater exposure to environmental contamination; and (7) governance by a new, possibly nonexistent, set of property rights. The main focus is on identifying what is different about urban areas, so as to better frame the program and policy responses.Urbanization. ,employment ,Child care ,Malnutrition. ,Labor ,Food security. ,Nutrition ,Property rights ,