Given a program P, an unfold/fold program transformation system derives a sequence of programs P = P0, P1,:::, Pn, such that Pi+1 is derived from Pi by application of either an unfolding or a folding step. Existing unfold/fold transformation systems for definite logic programs differ from one another mainly in the kind of folding transformations they permit at each step. Some allow folding using a single (possibly recursive) clause while others permit folding using multiple non-recursive clauses. However, none allow folding using multiple recursive clauses that are drawn from some previous program in the transformation sequence. In this paper we develop a parameterized framework for unfold/fold transformations by suitably abstracting and extending the proofs of existing transformation systems. Various existing unfold/fold transformation systems can be obtained by instantiating the parameters of the framework. This framework enables us to not only understand the relative strengths and limitations of these systems but also construct new transformation systems. Specifically we present a more general transformation system that permits folding using multiple recursive clauses that can be drawn from any previous program in the transformation sequence. This new transformation system is also obtained by instantiating our parameterized framework.

Abstract not found

This paper makes several contributions towards a clarified view of schema-based program development. First, we propose that schemata can be understood, formalized, and used in a simple way: program development schemata are derived rules. We mean this in the standard sense of a derived rule of inference in logic. A schema like Figure i can be formulated as a rule stating that the conclusion follows from the premises defining F, G, and the applicability conditions. By deriving the rule in an axiomatic theory, we validate a semantic statement about it: the conclusion of the rule holds in every model where both the axioms of the theory and the premises of the rule are true. Hence, by selecting a language to work in we control which development schemata are formalizable, and by selecting a theory we determine which schemata are derivable

Naive parallel implementation of nondeterministic systems (such as a theorem proving system) and languages (such as a logic, constraint, or a concurrent constraint language) can result in poor performance. We present three optimization schemas based on flattening of the computation tree, procrastination of overheads, and sequentialization of computations that can be systematically applied to parallel implementations of non-deterministic systems/languages to reduce the parallel overhead and to obtain improved efficiency of parallel execution. The effectiveness of these schemas is illustrated by applying them to the ACE parallel logic programming system. Performance data presented shows that considerable improvement in performance can result. 1

We consider the replacement transformation operation, a very general and powerful transformation, and study under which conditions it preserves universal termination besides computed answer substitutions. With this safe replacement we can significantly extend the safe unfold/fold transformation sequence presented in [11]. By exploiting typing information, more useful conditions can be defined and we may deal with some special cases of replacement very common in practice, namely switching two atoms in the body of a clause and the associativity of a predicate. This is a first step in the direction of exploiting a Pre/Post specification on the intended use of the program to be transformed. Such specification can restrict the instances of queries and clauses to be considered and then relax the applicability conditions on the transformation operations.

Since the early days of programming and automated reasoning, researchers have developed methods for systematically constructing programs from their specifications. Especially the last decade has seen a flurry of activities including the advent of specialized conferences, such as LOPSTR, covering the synthesis of programs in computational logic. In this paper we analyze and compare three state-of-the-art methods for synthesizing recursive programs in computational logic. The three approaches are constructive/deductive synthesis, schema-guided synthesis, and inductive synthesis. Our comparison is carried out in a systematic way where, for each approach, we describe the key ideas and synthesize a common running example. In doing so, we explore the synergies between the approaches, which we believe are necessary in order to achieve progress over the next decade in this field.

Several induction theorem provers have been developed which support mechanized verification of functional programs. Unfortunately, a major problem is that they often fail in verifying tail recursive functions (which correspond to imperative programs). However, in practice imperative programs are used almost exclusively. We present an automatic transformation to tackle this problem. It transforms functions which are hard to verify into functions whose correctness can be shown by the existing provers. In contrast to classical program transformations, the aim of our technique is not to increase efficiency, but to increase veriability. Therefore, this paper introduces a novel application area for program transformations and it shows that such techniques can in fact solve some of the most urgent current challenge problems in automated verification and induction theorem proving.

In a seminal paper [38] Prof. Robert Kowalski advocated the paradigm Algorithm = Logic + Control which was intended to characterize program executions. Here we want to illustrate the corresponding paradigm Program Derivation = Rules + Strategies which is intended to characterize program derivations, rather than executions. During program execution, the Logic component guarantees that the computed results are correct, that is, they are true facts in the intended model of the given program, while the Control component ensures that those facts are derived in an efficient way. Likewise, during program derivation, the Rules component guarantees that the derived programs are correct and the Strategies component ensures that the derived programs are efficient.

A combinatory form of definite clausal logic programs is introduced based on a system of predicate-forming operators. This variable-free canonical form of definite clauses provides a form of combinatorial completeness. The language form comes with a simple compositional model-theoretical semantics, construing the operators as quasi higher-order predicates. In particular the semantics enables an alternative model-theoretical fixpoint construction, accomplished solely by iterated union, intersection, a generalised projection, and list construction and destruction. This compositional semantics is proved equivalent to the usual fixpoint semantics for pure logic programs. It is proved, further, that the introduced operator language can be reduced literally to terms in an ordinary first order logic programming environment by means of established metalogic programming techniques. This reduction enables execution of combinatory programs using standard resolution technique. Keyword...

In the rule-based equivalent transformation (RBET) paradigm, where computation is based on meaning-preserving transformation of declarative descriptions, a set of rewriting rules is regarded as a program. The syntax for a large class of rewriting rules is determined. The incorporation of meta-variables of two different kinds enables precise control of rewriting-rule instantiations. As a result, the applicability of rewriting rules and the results of rule applications can be rigorously specified. A theoretical basis for justifying the correctness of rewriting rules is established. Reverse transformation operation in the RBET framework is discussed, and it is shown that a correct rewriting rule is reversible, i.e., a correct rewriting rule can in general be constructed by syntactically reversing another correct rewriting rule.