Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial deduction, is to exploit partial knowledge about the input. It is achieved through a well-automated application of parts of the Burstall-Darlington unfold/fold transformation framework. The main challenge in developing systems is to design automatic control that ensures correctness, efficiency, and termination. This survey and tutorial presents the main developments in controlling partial deduction over the past 10 years and analyses their respective merits and shortcomings. It ends with an assessment of current achievements and sketches some remaining research challenges.

Abstract. Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems.

this paper we assume that a system makes transitions from states to states and its evolution can be formalized using a computation tree which is dened as follows. Given a system S and its initial state s 0 , the root of the computation tree for S is s 0 , and every node s i of the computation tree for S has a child node s j i there exists in S a transition from state s i to state s j , called a successor state of s i . The set of all states of a system may be nite or innite. We assume that in every system for every state s i there exists at least one successor state

The reduction of nondeterminism can increase efficiency when specializing programs. We consider constraint logic programs and we propose a technique which by making use of a new transformation rule, called clause splitting, allows us to generate efficient, specialized programs which are deterministic. We have applied our technique to the specialization of pattern matching programs.

The goal of automated verification is the definition of a logical framework where hardware or software systems can be formally specified and formal proofs about their properties can be given in a fully automatic way. This involves defining formalisms for encoding systems and the properties of interest. During the last years many logic-based techniques have been developed for automatically verifying properties of systems, the most successful of them being model checking [3]. The success of model checking is mostly due to the use of a particular data structure, Binary Decision Diagrams, which provide a very compact symbolic representation of a possibly very large, but finite, set of states. In order to overcome this finiteness restriction, some effort is now being put into the integration of abstraction and deduction techniques with model checking [15]. Recent papers also demonstrate the usefulness of (constraint) logic programming as a basis for the verification of finite...