(Leftmost-Outermost) Beta Reduction is Invariant, Indeed

Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is lambda-calculus a reasonable machine? Is there a way to measure the computational complexity of a lambda-term? This paper presents the first complete positive answer to this long-standing problem. Moreover, our answer is completely machine-independent and based over a standard notion in the theory of lambda-calculus: the length of a leftmost-outermost derivation to normal form is an invariant cost model. Such a theorem cannot be proved by directly relating lambda-calculus with Turing machines or random access machines, because of the size explosion problem: there are terms that in a linear number of steps produce an exponentially long output. The first step towards the solution is to shift to a notion of evaluation for which the length and the size of the output are linearly related. This is done by adopting the linear substitution calculus (LSC), a calculus of explicit substitutions modeled after linear logic proof nets and admitting a decomposition of leftmost-outermost derivations with the desired property. Thus, the LSC is invariant with respect to, say, random access machines. The second step is to show that LSC is invariant with respect to the lambda-calculus. The size explosion problem seems to imply that this is not possible: having the same notions of normal form, evaluation in the LSC is exponentially longer than in the lambda-calculus. We solve such an impasse by introducing a new form of shared normal form and shared reduction, deemed useful. Useful evaluation avoids those steps that only unshare the output without contributing to beta-redexes, i.e. the steps that cause the blow-up in size. The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties.Comment: arXiv admin note: substantial text overlap with arXiv:1405.331

A parallel functional language compiler for message-passing multicomputers

The research presented in this thesis is about the design and implementation of Naira, a parallel, parallelising compiler for a rich, purely functional programming language. The source language of the compiler is a subset of Haskell 1.2. The front end of Naira is written entirely in the Haskell subset being compiled. Naira has been successfully parallelised and it is the largest successfully parallelised Haskell program having achieved good absolute speedups on a network of SUN workstations. Having the same basic structure as other production compilers of functional languages, Naira's parallelisation technology should carry forward to other functional language compilers. The back end of Naira is written in C and generates parallel code in the C language which is envisioned to be run on distributed-memory machines. The code generator is based on a novel compilation scheme specified using a restricted form of Milner's 7r-calculus which achieves asynchronous communication. We present the first working implementation of this scheme on distributed-memory message-passing multicomputers with split-phase transactions. Simulated assessment of the generated parallel code indicates good parallel behaviour. Parallelism is introduced using explicit, advisory user annotations in the source' program and there are two major aspects of the use of annotations in the compiler. First, the front end of the compiler is parallelised so as to improve its efficiency at compilation time when it is compiling input programs. Secondly, the input programs to the compiler can themselves contain annotations based on which the compiler generates the multi-threaded parallel code. These, therefore, make Naira, unusually and uniquely, both a parallel and a parallelising compiler. We adopt a medium-grained approach to granularity where function applications form the unit of parallelism and load distribution. We have experimented with two different task distribution strategies, deterministic and random, and have also experimented with thread-based and quantum- based scheduling policies. Our experiments show that there is little efficiency difference for regular programs but the quantum-based scheduler is the best in programs with irregular parallelism. The compiler has been successfully built, parallelised and assessed using both idealised and realistic measurement tools: we obtained significant compilation speed-ups on a variety of simulated parallel architectures. The simulated results are supported by the best results obtained on real hardware for such a large program: we measured an absolute speedup of 2.5 on a network of 5 SUN workstations. The compiler has also been shown to have good parallelising potential, based on popular test programs. Results of assessing Naira's generated unoptimised parallel code are comparable to those produced by other successful parallel implementation projects

Extending Implicit Computational Complexity and Abstract Machines to Languages with Control

The Curry-Howard isomorphism is the idea that proofs in natural deduction can be put in correspondence with lambda terms in such a way that this correspondence is preserved by normalization. The concept can be extended from Intuitionistic Logic to other systems, such as Linear Logic. One of the nice conseguences of this isomorphism is that we can reason about functional programs with formal tools which are typical of proof systems: such analysis can also include quantitative qualities of programs, such as the number of steps it takes to terminate. Another is the possiblity to describe the execution of these programs in terms of abstract machines. In 1990 Griffin proved that the correspondence can be extended to Classical Logic and control operators. That is, Classical Logic adds the possiblity to manipulate continuations. In this thesis we see how the things we described above work in this larger context

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019

Adaptive object management for distributed systems

This thesis describes an architecture supporting the management of pluggable software components and evaluates it against the requirement for an enterprise integration platform for the manufacturing and petrochemical industries. In a distributed environment, we need mechanisms to manage objects and their interactions. At the least, we must be able to create objects in different processes on different nodes; we must be able to link them together so that they can pass messages to each other across the network; and we must deliver their messages in a timely and reliable manner. Object based environments which support these services already exist, for example ANSAware(ANSA, 1989), DEC's Objectbroker(ACA,1992), Iona's Orbix(Orbix,1994)Yet such environments provide limited support for composing applications from pluggable components. Pluggability is the ability to install and configure a component into an environment dynamically when the component is used, without specifying static dependencies between components when they are produced. Pluggability is supported to a degree by dynamic binding. Components may be programmed to import references to other components and to explore their interfaces at runtime, without using static type dependencies. Yet thus overloads the component with the responsibility to explore bindings. What is still generally missing is an efficient general-purpose binding model for managing bindings between independently produced components. In addition, existing environments provide no clear strategy for dealing with fine grained objects. The overhead of runtime binding and remote messaging will severely reduce performance where there are a lot of objects with complex patterns of interaction. We need an adaptive approach to managing configurations of pluggable components according to the needs and constraints of the environment. Management is made difficult by embedding bindings in component implementations and by relying on strong typing as the only means of verifying and validating bindings. To solve these problems we have built a set of configuration tools on top of an existing distributed support environment. Specification tools facilitate the construction of independent pluggable components. Visual composition tools facilitate the configuration of components into applications and the verification of composite behaviours. A configuration model is constructed which maintains the environmental state. Adaptive management is made possible by changing the management policy according to this state. Such policy changes affect the location of objects, their bindings, and the choice of messaging system