Backtracable State with Linear Assumptions, Continuations and Hidden Accumulator Grammars

A set of executable specifications and efficient implementations of backtrackable state persisting over the current AND-continuation is investigated

At a specification level, our primitive operations are linear and intuitionistic implications, having as consequent the current continuation. On top of them, we introduce a form of hypothetical assumptions which use no explicit quantifiers and have an easy and efficient implementation on top of logic programming systems featuring backtrackable destructive assignment and global variables

A variant of Extended DCGs handling multiple streams without the need of a preprocessing technique, Hidden Accumulator Grammars (HAGs), are specified in terms of linear assumptions. For HAGs, efficiency comparable to that of preprocessing techniques is obtained through a WAM-level implementation of backtrackable destructive assignment, supporting nondeterministic execution based on value-trailing, while collapsing to a form of in-place update in case of deterministic execution

When more precise information about the location where linear assumptions are used is available, either HAGs or a continuation based representation (multi-headed clauses) allows an efficient implementation

Not restricted to Prolog, the techniques described in the paper are portable to logic programming languages like Life, Lolli and λProlog