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In this appendix to the article " Composition of functions with accumulating parameters " we prove Theorem 5.2 of that paper, showing that Construction 5.1 produces an mtt that is equivalent to the composition of the two given ones. Firstly, we will formalise the idea of " walking upwards " in the intermediate result to obtain the context parameters of… (More)

We present a technique to prevent the construction of intermediate data structures in functional programs, which is based on results from the theory of tree transducers. We rst decompose function deen-itions, which correspond to macro tree transducers, into smaller pieces. Under certain restrictions these pieces can be composed to an attributed tree… (More)

In this paper we i n troduce a new formal model for the concept of syntax{directed semantics , called macro attributed t r ee t r ansducer (for short: mat tree transducer). This model is based on (noncircular) attributed tree transducers and on macro tree transducers. In the rst type of transducer, semantic values are computed by means of meaning names… (More)

Many functional programs with accumulating parameters are contained in the class of macro tree transducers. We present a program transformation technique that can be used to solve the efficiency problems due to creation and consumption of intermediate data structures in compositions of such functions, where classical deforestation techniques fail. In order… (More)

We compare transformations for the elimination of intermediate results in rst-order functional programs. We choose the well known deforestation technique of Wadler and composition techniques from the theory of tree transducers, of which the implementation of functional programs yet does not take advantage. We identify syntactic classes of function… (More)

We study the problem to transform functional programs, which intensively use append functions (like inefficient list reversal), into programs, which use accumulating parameters instead (like efficient list reversal). We give an (automatic) transformation algorithm for our problem and identify a class of functional programs, namely restricted 2-modular tree… (More)

The concept of attributed tree transducer is a formal model for studying properties of attribute grammars. In this paper, for output languages of noncircular, producing, and visiting attributed tree transducers, we i n troduce and prove a pumping lemma. We apply this pumping lemma to gain two results: (1) there is no noncircular, producing, and visiting… (More)

The concept of macro tree transducer is a formal model for studying properties of syntax{directed translations. In this paper, for output languages of producing, nondeleting, and noncopying macro tree transducers, we introduce a pumping lemma. We apply the pumping lemma to gain the following result: there is no producing and nondeleting macro tree… (More)

Several induction theorem provers were developed to verify functional programs mechanically. Unfortunately, automated verification usually fails for functions with accumulating arguments. In particular, this holds for tail-recursive functions that correspond to imperative programs , but also for programs with nested recursion. Based on results from the… (More)