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Context-sensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. Termination is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of context-sensitive rewriting strategies, i.e., particular, fixed sequences of context-sensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that context-sensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for root-normalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing ...

Distributed implementations of programming languages with implicit parallelism hold out the prospect that the parallel programs are immediately scalable. This paper presents some of the results of our part of Esprit 415, in which we considered the implementation of lazy functional programming languages on distributed architectures. A compiler and abstract machine were designed to achieve this goal. The abstract parallel machine was formally specified, using Miranda 1 . Each instruction of the abstract machine was then implemented as a macro in the Transputer Assembler. Although macro expansion of the code results in non-optimal code generation, use of the Miranda specification makes it possible to validate the compiler before the Transputer code is generated. The hardware currently available consists of five T800--25's, each board having 16M bytes of memory. Benchmark timings using this hardware are given. In spite of the straight forward code-generation, the resulting system compar...

Functional logic programming languages have a functional syntax and use narrowing as operational semantics. Here we consider the efficient implementation of lazy narrowing, a strategy which only evaluates the arguments of a function application, if their evaluation is really demanded. For an efficient implementation of lazy narrowing it is crucial to evaluate the arguments as early as possible. Otherwise the arguments are frequently reevaluated. A demandedness analysis is used to detect which parts of the arguments can safely be evaluated before the call to the function. Several approaches (e.g. [HLW92, JMM92]) also use this idea, but they sacrify laziness in order to avoid inefficiency. Our approach is more lazy than the previous approaches, and it uses a more powerful notion of demandedness, which allows to express infinite demand patterns like e.g. spine normal form. Moreover, in contrast to the previous approaches, we take into account dependencies between the arguments o...

syntax, and syntactic and semantic domains of a flow graph Figure 9. Semantic equations Def and Exp of a flow graph The first argument to the functions Def and Exp specifies a set of nodes that represent a flow graph, from which the element(s) of current interest are selected by pattern matching.

Projection analysis is a technique for finding out information about lazy functional programs. We show how the information obtained from this analysis can be used to speed up sequential implementations, and introduce parallelism into parallel implementations. The underlying evaluation model is evaluation transformers, where the amount of evaluation that is allowed of an argument in a function application depends on the amount of evaluation allowed of the application. We prove that the transformed programs preserve the semantics of the original programs. Compilation rules, which encode the information from the analysis, are given for sequential and parallel machines. 1 Introduction A number of analyses have been developed which find out information about programs. The methods that have been developed fall broadly into two classes, forwards analyses such as those based on the ideas of abstract interpretation (e.g. [9, 18, 19, 7, 17, 12, 4, 20]), and backward analyses such as those based...

Lazy evaluation of functional programs incurs time and memory overheads, and restricts parallelism compared with programs that are evaluated strictly. A number of analysis techniques, such as abstract interpretation and projection analysis, have been developed to find out information that can alleviate these overheads. This paper formalises an evaluation model, the evaluation transformer model of reduction, which can use information from these analysis techniques, and proves that the resulting reduction strategies produce the same answers as those obtained using lazy evaluation.

This thesis concerns fully automatic termination analysis for higher-order purely functional programs, both strict and lazy. We build on existing work on size-change termination, in which a program is deemed to terminate if any potential infinite sequence of calls would result in infinite descent in a well-founded data value. This was proposed for strict first-order programs, and a termination analysis of the pure untyped λ-calculus was subsequently obtained in this framework. We present a generalisation of this work, to handle realistic purely functional programming languages. From our general semantic framework, instances of the termination criterion are derived for both strict (call-by-value) and lazy (call-by-need) and proved sound. It is shown that nontrivial higher-order and lazy programs can be proved to terminate. It is further shown that the analysis of lazy programs requires techniques beyond previous work on size-change termination. Our analysis proceeds by extracting the call graph of a higher-order program, together with dataflow annotations; termination is then proved by showing that infinite paths in the

The major question examined by this paper is whether sufficient fine-grain parallelism can be obtained from programs written in a lazy functional language. To answer this question, we have implemented a prototype compiler based on a novel approach to strictness analysis (called abstract demand propagation) and we have compared this implementation strategy (optimized lazy) with other implementations, viz., pure lazy and lenient. Although the optimized lazy implementation improves significantly the efficiency of the resulting programs over the pure lazy approach, it was found that little parallelism can effectively be identified. This remains true even when a new notion of laziness --- speculative laziness --- is introduced, notion well suited to parallel machines as it based on a parallel notion of head-strictness instead of the traditional sequential one. Our experiments also showed that when a program's result is known to be finite, then strictness analysis can generate almost as mu...

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 ß-calculus which achieves asynchronous communication. We present the f...