Abstract. The n-pebble tree transducer was recently proposed as a model for XML query languages. The four main results on deterministic transducers are: First, (1) the translation τ of an n-pebble tree transducer can be realized by a composition of n + 1 0-pebble tree transducers. Next, the pebble tree transducer is compared with the macro tree transducer, a well-known model for syntax-directed semantics, with decidable type checking. The 0-pebble tree transducer can be simulated by the macro tree transducer, which, by the first result, implies that (2) τ can be realized by an (n+1)-fold composition of macro tree transducers. Conversely, every macro tree transducer can be simulated by a composition of 0-pebble tree transducers. Together these simulations prove that (3) the composition closure of n-pebble tree transducers equals that of macro tree transducers (and that of 0-pebble tree transducers). Similar results hold in the nondeterministic case. Finally, (4) the output languages of deterministic n-pebble tree transducers form a hierarchy with respect to the number n of pebbles. 1

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 to do so, given two macro tree transducers under appropriate restrictions, we construct a single macro tree transducer that implements the composition of the two original ones. The imposed restrictions are more liberal than those in the literature on macro tree transducer composition, thus generalising previous results.

We study the question of efficiency improvement or deterioration for a semantics-preserving program transformation technique for (lazy) functional languages, based on composition of restricted macro tree transducers. By annotating programs to reflect the intensional property ``computation time'' explicitly in the computed output and by manipulating such annotations, we formally prove syntactic conditions under which the composed program is guaranteed to be not less efficient than the original program with respect to the number of call-by-name reduction steps required to reach normal form. Under additional conditions the guarantee also holds for call-by-need semantics. The criteria developed can be checked automatically and efficiently, and thus are suitable for integration into an optimizing compiler.

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 theory of tree transducers, we develop an automatic transformation technique. It transforms accumulative functional programs into non-accumulative ones, which are much better suited for automated verification by induction theorem provers. Hence, in contrast to classical program transformations aiming at improving the e#ciency, the goal of our deaccumulation technique is to improve the provability.