P.M. van den Broek

Static analysis of functional programs

In this paper, the static analysis of programs in the functional programming language Miranda is described based on two graph models. A new control-flow graph model of Miranda definitions is presented, and a model with four classes of caligraphs. Standard software metrics are applicable to these models. A Miranda front end for Prometrixt, a tool for the automated analysis of flowgraphs and callgraphs, has been developed. This front end produces the flowgraph and callgraph representations of Miranda programs. Some features of the metric analyser are illustrated with an example program. The tool provides a promising access to standard metrics on functional programs.

Exact Membership Functions for the Fuzzy Weighted Average

The problem of computing the fuzzy weighted average, where both attributes and weights are fuzzy numbers, is well studied in the literature. Generally, the approach is to apply Zadeh’s extension principle to compute α-cuts of the fuzzy weighted average from the α-cuts of the attributes and weights for fixed values of α∈[0..1]; this means that all values of the membership functions of the fuzzy weighted average are computed separately. In this paper, we generalise this approach in such a way that α is considered to be a parameter; this enables us to compute exact analytical membership functions for the fuzzy weighted average in case the attributes and weights are triangular or trapeizoidal fuzzy numbers. To illustrate the power of our algorithms, they are applied to the examples from the literature, providing exact membership functions in each case.

Programmers Performance on Structured versus Nonstructured Function Definitions

A control-flow model for functional programs is used in an experimental comparison of the performance of programmers on structured versus nonstructured Miranda function definitions. The performance is taken as a measure of the comprehensibility of functional programs. The experimental set-up is similar to the Scanlan study (1989). However, in the present study, a two-factor repeated measures design is used in the statistical analysis. The control-flow model appears to be useful in the shaping of the experiment. A significantly better performance has been found for structured function definitions on both dependent variables: the time needed to answer questions about the function definitions and the proportion correct answers. Moreover, for structured function definitions, a counter-intuitive result has been obtained: there are significantly fewer errors in larger definitions than in smaller ones.

A Generalised Approach to Software Structure Metrics

The aim of this paper is to generalise the Fenton-Whitty-Kaposi (FWK) approach to structure software metrics by considering arbitrary sets of decomposition operations for flowgraphs. In the FWK approach decomposition of flowgraphs is unique, but the number of associated metric functions is not finite and these functions are all independent. In general, the decomposition of flowgraphs is not unique, which leads to constraints on the associated metric functions. Here we derive these constraints explicitly for two special cases, where we consider only the two operations sequencing and nesting as decomposition operations. It is shown that the two resulting classes of structure metrics are contained in the class of recursive structure metrics of the FWK approach.

Validation of structure metrics: a case study

A framework for the validation of axiomatic structure metrics is presented. In a case study, the comprehensibility of type expressions in the functional programming language Miranda has been investigated. A structure metric for the comprehensibility of type expressions has been developed together with internal and external axioms. This structure metric has been validated experimentally. The calibrated metric function results in a good prediction of the comprehensibility. >

Comparison of two graph-rewrite systems

We compare the two graph-rewrite systems of Ehrig and Raoult. First a common domain is identified where both systems may be applied. It is shown that on this domain a Raoult rewritin exists if an Ehrig rewriting exists, but not vice versa. Out main result is that when both systems give a rewriting, these rewritings are isomorphic.

A new programming technique for lazy functional languages

In this paper we present a new programming technique for lazy functional programming languages. The technique is embedded in a programming methodology which is based on divide and conquer: the division of problems into subproblems. Such a division will be represented by a call graph. A class of program schemes, which implement call graphs, is derived based on Johnsson’s approach to attribute evaluation in attribute grammars. The key idea is to consider the passing of arguments to functions and the return of results by functions in a call graph as the propagation of inherited and synthesized attributes, respectively, in an attribute grammar. The new technique is illustrated by several small examples and a case study: the design and implementation of a compiler generator.

Axiomatic testing of structure metrics

Axiomatic testing of software metrics is described, based on axioms from representational measurement theory. In a case study, the axioms are given for the formal relational structure and the empirical relational structure. Two approaches to axiomatic testing are elaborated: deterministic testing and probabilistic testing. >Axiomatic testing of software metrics is described, based on axioms from representational measurement theory. In a case study, the axioms are given for the formal relational structure and the empirical relational structure. Two approaches to axiomatic testing are elaborated: deterministic testing and probabilistic testing.<<ETX>>

Rankings from Fuzzy Pairwise Comparisons

We propose a new method for deriving rankings from fuzzy pairwise comparisons. It is based on the observation that quantification of the uncertainty of the pairwise comparisons should be used to obtain a better crisp ranking, instead of a fuzzified version of the ranking obtained from crisp pairwise comparisons. With our method, a crisp ranking is obtained by solving a linear programming problem, when the fuzzy pairwise comparisons are fuzzy triangular numbers. Our method simplifies the recent method by Mikhailov

Musical equational programs: a functional approach

In this paper we solve musical equational programs by means of higher order functions. The initial solution is written in a functional programming language (Miranda1). It is shown how a solution in an imperative language (Pascal) can be obtained by elimination of the higher order functions.