TY - JOUR

T1 - A general framework for automatic termination analysis of logic programs

AU - Dershowitz, Nachum

AU - Lindenstrauss, Naomi

AU - Sagiv, Yehoshua

AU - Serebrenik, Alexander

PY - 2001

Y1 - 2001

N2 - This paper describes a general framework for automatic termination analysis of logic programs, where we understand by "termination" the finiteness of the LD-tree constructed for the program and a given query. A general property of mappings from a certain subset of the branches of an infinite LD-tree into a finite set is proved. From this result several termination theorems are derived, by using different finite sets. The first two are formulated for the predicate dependency and atom dependency graphs. Then a general result for the case of the query-mapping pairs relevant to a program is proved (cf. [29, 21]). The correctness of the TermiLog system described in [22] follows from it. In this system it is not possible to prove termination for programs involving arithmetic predicates, since the usual order for the integers is not well-founded. A new method, which can be easily incorporated in TermiLog or similar systems, is presented, which makes it possible to prove termination for programs involving arithmetic predicates. It is based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case. Finally several possible extensions are outlined.

AB - This paper describes a general framework for automatic termination analysis of logic programs, where we understand by "termination" the finiteness of the LD-tree constructed for the program and a given query. A general property of mappings from a certain subset of the branches of an infinite LD-tree into a finite set is proved. From this result several termination theorems are derived, by using different finite sets. The first two are formulated for the predicate dependency and atom dependency graphs. Then a general result for the case of the query-mapping pairs relevant to a program is proved (cf. [29, 21]). The correctness of the TermiLog system described in [22] follows from it. In this system it is not possible to prove termination for programs involving arithmetic predicates, since the usual order for the integers is not well-founded. A new method, which can be easily incorporated in TermiLog or similar systems, is presented, which makes it possible to prove termination for programs involving arithmetic predicates. It is based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case. Finally several possible extensions are outlined.

KW - Abstract interpretation

KW - Constraints

KW - Termination of logic programs

UR - http://www.scopus.com/inward/record.url?scp=0034952407&partnerID=8YFLogxK

U2 - 10.1007/s002000100065

DO - 10.1007/s002000100065

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AN - SCOPUS:0034952407

SN - 0938-1279

VL - 12

SP - 117

EP - 156

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

IS - 1-2

ER -