Transformations of Logic Programs on Infinite Lists

We consider an extension of logic programs, called \omega-programs, that can be used to define predicates over infinite lists. \omega-programs allow us to specify properties of the infinite behavior of reactive systems and, in general, properties of infinite sequences of events. The semantics of \omega-programs is an extension of the perfect model semantics. We present variants of the familiar unfold/fold rules which can be used for transforming \omega-programs. We show that these new rules are correct, that is, their application preserves the perfect model semantics. Then we outline a general methodology based on program transformation for verifying properties of \omega-programs. We demonstrate the power of our transformation-based verification methodology by proving some properties of Buechi automata and \omega-regular languages.Comment: 37 pages, including the appendix with proofs. This is an extended version of a paper published in Theory and Practice of Logic Programming, see belo

More on Unfold/Fold Transformations of Normal Programs: Preservation of Fitting's Semantics

The unfold/fold transformation system defined by Tamaki and Sato was meant for definite programs. It transforms a program into an equivalent one in the sense of both the least Herbrand model semantics and the Computed Answer Substitution semantics. Seki extended the method to normal programs and specialized it in order to preserve also the finite failure set. The resulting system is correct wrt nearly all the declarative semantics for normal programs. An exception is Fitting's model semantics. In this paper we consider a slight variation of Seki's method and we study its correctness wrt Fitting's semantics. We define an applicability condition for the fold operation and we show that it ensures the preservation of the considered semantics through the transformation

Automated Termination Proofs for Logic Programs by Term Rewriting

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a logic program into a term rewrite system (TRS) and then analyze termination of the resulting TRS instead. Thus, transformational approaches make all methods previously developed for TRSs available for logic programs as well. However, the applicability of most existing transformations is quite restricted, as they can only be used for certain subclasses of logic programs. (Most of them are restricted to well-moded programs.) In this paper we improve these transformations such that they become applicable for any definite logic program. To simulate the behavior of logic programs by TRSs, we slightly modify the notion of rewriting by permitting infinite terms. We show that our transformation results in TRSs which are indeed suitable for automated termination analysis. In contrast to most other methods for termination of logic programs, our technique is also sound for logic programming without occur check, which is typically used in practice. We implemented our approach in the termination prover AProVE and successfully evaluated it on a large collection of examples.Comment: 49 page

Transformation-Based Bottom-Up Computation of the Well-Founded Model

We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by Brass and Dix for disjunctive programs. However, even if we restrict their framework to nondisjunctive programs, their residual program can grow to exponential size, whereas for function-free programs our program remainder is always polynomial in the size of the extensional database (EDB). We show that particular orderings of our transformations (we call them strategies) correspond to well-known computational methods like the alternating fixpoint approach, the well-founded magic sets method and the magic alternating fixpoint procedure. However, due to the confluence of our calculi, we come up with computations of the well-founded model that are provably better than these methods. In contrast to other approaches, our transformation method treats magic set transformed programs correctly, i.e. it always computes a relevant part of the well-founded model of the original program.Comment: 43 pages, 3 figure

Program transformation for functional circuit descriptions

We model sequential synchronous circuits on the logical level by signal-processing programs in an extended lambda calculus Lpor with letrec, constructors, case and parallel or (por) employing contextual equivalence. The model describes gates as (parallel) boolean operators, memory using a delay, which in turn is modeled as a shift of the list of signals, and permits also constructive cycles due to the parallel or. It opens the possibility of a large set of program transformations that correctly transform the expressions and thus the represented circuits and provides basic tools for equivalence testing and optimizing circuits. A further application is the correct manipulation by transformations of software components combined with circuits. The main part of our work are proof methods for correct transformations of expressions in the lambda calculus Lpor, and to propose the appropriate program transformations