Reversible Computations in Logic Programming

[EN] In this work, we say that a computation is reversible if one can find a procedure to undo the steps of a standard (or forward) computation in a deterministic way. While logic programs are often invertible (e.g., one can use the same predicate for adding and for subtracting natural numbers), computations are not reversible in the above sense. In this paper, we present a so-called Landauer embedding for SLD resolution, the operational principle of logic programs, so that it becomes reversible. A proof-of-concept implementation of a reversible debugger for Prolog that follows the ideas in this paper has been developed and is publicly available.This work is partially supported by the EU (FEDER) and the Spanish MCI/AEI under grants TIN2016-76843-C4-1-R/PID2019-104735RB-C41, by the Generalitat Valenciana under grant Prometeo/2019/098 (DeepTrust), and by the COST Action IC1405 on Reversible Computation - extending horizons of computing.Vidal, G. (2020). Reversible Computations in Logic Programming. Springer. 246-254. https://doi.org/10.1007/978-3-030-52482-1_15S246254Apt, K.: From Logic Programming to Prolog. Prentice Hall, Upper Saddle River (1997)Ducassé, M.: Opium: an extendable trace analyzer for prolog. J. Log. Program. 39(1–3), 177–223 (1999). https://doi.org/10.1016/S0743-1066(98)10036-5Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)Lanese, I., Palacios, A., Vidal, G.: Causal-consistent replay debugging for message passing programs. In: Pérez, J.A., Yoshida, N. (eds.) FORTE 2019. LNCS, vol. 11535, pp. 167–184. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21759-4_10Lloyd, J.: Foundations of Logic Programming, 2nd edn. Springer, Berlin (1987). https://doi.org/10.1007/978-3-642-83189-8O’Callahan, R., Jones, C., Froyd, N., Huey, K., Noll, A., Partush, N.: Engineering record and replay for deployability: Extended technical report (2017). CoRR abs/1705.05937, http://arxiv.org/abs/1705.05937Ströder, T., Emmes, F., Schneider-Kamp, P., Giesl, J., Fuhs, C.: A linear operational semantics for termination and complexity analysis of ISO prolog. In: Vidal, G. (ed.) LOPSTR 2011. LNCS, vol. 7225, pp. 237–252. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32211-2_16Undo Software: Increasing software development productivity with reversible debugging (2014). https://undo.io/media/uploads/files/Undo_ReversibleDebugging_Whitepaper.pd

Biabduction (and related problems) in array separation logic

We investigate array separation logic (\mathsf {ASL}), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of memory. This logic provides a language for compositional memory safety proofs of array programs. We focus on the biabduction problem for this logic, which has been established as the key to automatic specification inference at the industrial scale. We present an \mathsf {NP} decision procedure for biabduction in \mathsf {ASL}, and we also show that the problem of finding a consistent solution is \mathsf {NP}-hard. Along the way, we study satisfiability and entailment in \mathsf {ASL}, giving decision procedures and complexity bounds for both problems. We show satisfiability to be \mathsf {NP}-complete, and entailment to be decidable with high complexity. The surprising fact that biabduction is simpler than entailment is due to the fact that, as we show, the element of choice over biabduction solutions enables us to dramatically reduce the search space