TerminWeb: Termination Analyzer for Logic Programs

The TerminWeb analyser is a semantic based termination analyser for logic programs. It is uniqueness in that it is based on a semantics which makes the termination properties observable. Its implementation is obtained as an abstraction of an interpreter which computes the termination semantics of a given program. TerminWeb supports termination checking and inference with respect to semi-linear norms; type-based norms; and a combination of several norms. 1 Overview of TerminWeb The TerminWeb analyser [8] is a semantic based termination analyser for logic programs, which focuses on universal termination. The analyser is implemented in SICStus Prolog and is available in two versions: on-line via WWW and stand-alone. The early version of TerminWeb analyser was developed, in [2], out of a collaboration with TerminLog [7]. The main contribution of [2] is basing termination analysis on semantics. Namely, providing a semantics which makes the termination properties of a program observable. The semantics adopted in [2] is called the binary unfolding semantics first presented in [4] where it was shown to make the notion of calls observable. The semantic objects are binary clauses. A binary clause of the form p(s̄)← q(t̄) indicates that a call to p is eventually followed by a call to q. Note that each pair of subsequent calls p(s̄) and q(t̄) are represented by at least one binary clause and that the loops in the program are represented by binary clauses of the form p(t̄)← p(s̄). Using the binary unfolding semantics, a termination analyser is obtained by approximating this semantics with respect to size and instantiation information. Then, this information is used to verify that each loop (recursive binary clause) has a decreasing measure over a well-founded domain. Note that in contrast to classic techniques, where a single global decreasing measure is required for proving termination, TerminWeb requires only a local decreasing measure for each loop. The core of TerminWeb is a simple abstract meta-interpreter which approximates the binary unfolding semantics. The approximation is over a domain to represent size and