Title: Justifications in Constraint Handling Rules for Logical Retraction in Dynamic Algorithms,
Abstract: We present a straightforward source-to-source transformation that introduces
justifications for user-defined constraints into the CHR programming language.
Then a scheme of two rules suffices to allow for logical retraction (deletion,
removal) of constraints during computation. Without the need to recompute from
scratch, these rules remove not only the constraint but also undo all
consequences of the rule applications that involved the constraint. We prove a
confluence result concerning the rule scheme and show its correctness. When
algorithms are written in CHR, constraints represent both data and operations.
CHR is already incremental by nature, i.e. constraints can be added at runtime.
Logical retraction adds decrementality. Hence any algorithm written in CHR with
justifications will become fully dynamic. Operations can be undone and data can
be removed at any point in the computation without compromising the correctness
of the result. We present two classical examples of dynamic algorithms, written
in our prototype implementation of CHR with justifications that is available
online: maintaining the minimum of a changing set of numbers and shortest paths
in a graph whose edges change.