Inferring non-suspension conditions for logic programs with dynamic scheduling

Abstract

A logic program consists of a logic component and a control component. The former is a specification in predicate logic whereas the latter defines the order of sub-goal selection. The order of sub-goal selection is often controlled with delay declarations that specify that a sub-goal is to suspend until some condition on its arguments is satisfied. Reasoning about delay declarations is notoriously difficult for the programmer and it is not unusual for a program and a goal to reduce to a state that contains a sub-goal that suspends indefinitely. Suspending sub-goals are usually unintended and often indicate an error in the logic or the control. A number of abstract interpretation schemes have therefore been proposed for checking that a given program and goal cannot reduce to such a state. This paper considers a reversal of this problem, advocating an analysis that for a given program infers a class of goals that do not lead to suspension. This paper shows that this more general approach can have computational, implementational and user-interface advantages. In terms of user-interface, this approach leads to a lightweight point-and-click mode of operation in which, after directing the analyser at a file, the user merely has to inspect the results inferred by the analysis. In terms of implementation, the analysis can be straightforwardly realised as two simple fixpoint computations. In terms of computation, by modelling n! different schedulings of n sub-goals with a single Boolean function, it is possible to reason about the suspension behaviour of large programs. In particular, the analysis is fast enough to be applied repeatedly within the program development cycle. The paper also demonstrates that the method is precise enough to locate bugs in existing programs.

Logic + control: On program construction and verification

“…The proof of occur-check freedom is rather ad hoc. It should be added that non-floundering and termination can be determined by means of automatic tools, see Genaim and King (2008) for the former, and e.g. Nguyen et al (2011, and the references therein) for the latter.…”

“…Non-floundering -proof. Analysis tools, like that of Genaim and King (2008), can be used to demonstrate non-floundering of P 3 , for initial queries of the form (4.9), under a partial selection rule as described above (King 2012). To make the paper self-contained, we present an explicit proof.…”

Transforming floundering into success

“…The more recent approach of Genaim and King (2008) uses bottom-up analysis, and argues strongly for the practicality of bottom-up methods. A relatively standard bottom-up least fixed-point analysis is used to compute groundness dependencies for successful computed answers of all predicates using the Pos domain (positive Boolean functions).…”

“…However, this analysis assumes that a local computation rule is used. Programs such as submaxtree/2 (and examples given in Genaim and King 2008) have cyclic data-flow and do not work with a local computation rule, so the greatest fixed-point computation results in significant loss of precision. Our transformations make no assumptions about the computation rule other than that it is safe with respect to the delay declarations, so (in this respect) it can be more precise.…”

RedAlert: Determinacy inference for Prolog

“…To demonstrate, notice that if Ys is ground then the execution of vert(Zs,Ys,Xs) grounds Zs, which is sufficient for the earlier goal diag(Xs,Zs,Ys) to be deterministic as well. They achieve this by delaying execution of a goal until a mutual exclusion condition between its clauses is fulfilled and then using suspension inference (Genaim and King, 2008) to infer a determinacy condition for the goals that constitute the body of a clause. This allows them to infer the determinacy condition Xs ∨ Ys for the goal rot(Xs,Ys).…”