. Proving the congruence between a direct semantics and a continuation semantics is often surprisingly complicated considering that direct-style -terms can be transformed into continuation style automatically. However, transforming the representation of a direct-style semantics into continuation style usually does not yield the expected representation of a continuation-style semantics (i.e., one written by hand). The goal of our work is to automate the transformation between textual representations of direct semantics and of continuation semantics. Essentially, we identify properties of a direct-style representation (e.g., totality), and we generalize the transformation into continuation style accordingly. As a result, we can produce the expected representation of a continuation semantics, automatically. It is important to understand the transformation between representations of direct and of continuation semantics because it is these representations that get processed in any kind of ...

In this paper we present an analysis technique for isolating dead code in higher-order functional programs. First, we formalize what it means for a program fragment to contribute to the value returned by the program. Next, we provide a purely declarative specification of a subset of terms which constitute dead code. This is done by a refinement of the set-based semantics technique, developed by Nevin Heintze, by the introduction of a concept of demand. We then develop a demand-driven set-based analysis to compute dead code specified by the declarative specification. The demand-driven set-based analysis developed in this paper is polynomial time, in the size of the input program. 1 Introduction Elimination of dead code is a standard optimisation performed by modern compilers for imperative languages. But compilers for higher-order programming languages perform only extremely naive kinds of dead code elimination. The principal benefit associated with the elimination of dead code in fir...

We definea novel inference system for strictness and totality analysis for the simplytyped lazy lambda-calculus with constants and fixpoints. Strictness information identifies those terms that definitely denote bottom (i.e. do not evaluate to WHNF) whereas totality information identifies those terms that definitely do not denote bottom (i.e. do evaluate to WHNF). The analysis is presented as an annotated type system allowing conjunctions only at "top-level". We give examples of its use and prove the correctness with respect to a natural-style operational semantics. 1 Introduction Strictness analysis has proved useful in the implementation of lazy functional languages as Miranda, Lazy ML and Haskell: when a function is strict it is safe to evaluate its argument before performing the function call. Totality analysis is equally useful but has not be adopted so widely: if the argument to a function is known to terminate then it is safe to evaluate it before performing the function call [1...

. This paper examines the transformation of call-by-need terms into continuation -passing style (CPS). It begins by presenting a simple transformation of call-by-need terms into program graphs and a reducer for such graphs. From this, an informal derivation is carried out, resulting in a translation from terms into self-reducing program graphs, where the graphs are represented as CPS terms involving storage operations. Though informal, the derivation proceeds in simple steps, and the resulting translation is taken to be our canonical CPS transformation for call-by-need terms. In order to define the CPS transformation more formally, two alternative presentations are given. The first takes the form of a continuation semantics for the call-by-need language. The second presentation follows Danvy and Hatcliff 's two-stage decomposition of the call-by-name CPS transformation, resulting in a similar two-stage CPS transformation for call-by-need. Finally, a number of practical matters are...

Interpretations Roberto Giacobazzi ? Francesco Ranzato ?? ? Dipartimento di Informatica, Universit`a di Pisa Corso Italia 40, 56125 Pisa, Italy giaco@di.unipi.it ?? Dipartimento di Matematica Pura ed Applicata, Universit`a di Padova Via Belzoni 7, 35131 Padova, Italy franz@hilbert.math.unipd.it Abstract. We define the inverse operation for disjunctive completion, introducing the notion of least disjunctive basis for an abstract domain D: this is the most abstract domain inducing the same disjunctive completion as D. We show that the least disjunctive basis exists in most cases, and study its properties in relation with reduced product of abstract interpretations. The resulting framework is powerful enough to be applied to arbitrary abstract domains for analysis, providing advanced algebraic methods for domain manipulation and optimization. These notions are applied to abstract domains for analysis of functional and logic programming languages. 1 Introduction It is widely ackn...

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.

Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation introduced in [21] for Horn logic to a fragment of higher-order HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.

Abstract. This article presents a way of implementing abstract interpretations that can be very efficient. The improvement lies in the use of a symbolic representation of boolean functions called Typed Decision Graphs (TDGs), a refinement of Binary Decision Diagrams. A general procedure for using this representation in abstract interpretation is given; we examine in particular the possibility of encoding higher order functions into TDGs. Moreover, this representation is used to design a widening operator based on the size of the objects represented, so that abstract interpretations will not fail due to insufficient memory. This approach is illustrated on strictness analysis of higher-order functions, showing a great increase in efficiency. 1

Research into providing support for long term data in lazy functional programming systems is presented in this thesis. The motivation for this work has been to reap the benefits of integrating lazy functional programming languages and persistence. The benefits are . the programmer need not write code to support long term data since this is provided as part of the programming system . persistent data can be used in a type safe way since the programming language type system applies to data with the whole range of persistence . the benefits of lazy evaluation are extended to the full lifetime of a data value. Whilst data is reachable, any evaluation performed on the data persists. A data value changes monotonically from an unevaluated state towards a completely evaluated state over time. . interactive data intensive applications such as functional databases can be developed. These benefits are realised by the development of models for persistence in lazy functional programming systems. Tw...

. Higher-order functions and the ability to create new functions at runtime, either by partial application or -abstraction of existing functions, are important features of functional languages. Since these runtimecreated functions may outlive their creating functions, it is necessary to represent all functional parameters by closures in a memory area which is not affected by the termination of function calls, i.e. in a heap component. Such a closure contains the original function, which may be a closure again, and the bindings of the parameters used (by the partial application) . It many cases, however, it is possible to avoid this expensive heap allocation and use the run-time stack or even statically allocated closures. Often a closure created for a partial application is used only locally and will never be part of the result of the creating function. In these cases, the closure may be allocated on the stack. This approach is feasible in eager and lazy languages. If we can additional...