Scaling termination proofs by a characterisation of cycles in CHR
نویسندگان
چکیده
outputs relate to inputs by a match transition relation, given by a dependency analysis. Definition 4 (Match transition relation). A match transition of a CHR program P is an ordered pair M(i, j,k,l) = (out(i, j), in(k,l)), expressing a dependency between an output out(i, j) = (C(i, j),Gi) of OutP and an input in(k,l) = (C(k,l),Gk) of I nP, for which ∃θ : CT |= ((C(i, j) = C(k,l))∧Gi∧Gk)θ holds. The match transition relation M is the set of all match transitions M(i, j,k,l) in P. ¤ Notice that a match transition exists if the output and input it connects represent sets of constraints with a non-empty intersection: ℘(out(i, j))∩℘(in(k,l)) 6= / 0. Example 4 (GCD cont.). We obtain for the GCD program the following match transition relation: M = {M(2,1,2,1),M(2,1,2,2),M(2,2,1,1),M(2,2,2,1),M(2,2,2,2)}. Note that the first output of the second rule does not match with the input of the first rule as their intersection ℘(out(2,1))∩℘(in(1,1)) = / 0. ¤ For a program P, we call NP = 〈I nP,OutP,TP,MP〉 its CHR net.
منابع مشابه
Scaling termination proofs by a characterization of cycles in CHR
In the current paper, we discuss cycles in Constraint Handling Rules for the purpose of scaling termination proofs. In order to obtain a useful characterization, our approach differs from the ones used in other declarative languages, such as Logic Programming and Term Rewrite Systems. Due to multi-headed rules, the notion of a cycle is not in direct correspondence with the recursive calls of a ...
متن کاملImproved Termination Analysis of CHR Using Self-sustainability Analysis
In the past few years, several successful approaches to termination analysis of Constraint Handling Rules (CHR) have been proposed. In parallel to these developments, for termination analysis of Logic Programs (LP), recent work has shown that a stronger focus on the analysis of the cycles in the strongly connected components (SCC) of the program is very beneficial, both for precision and effici...
متن کاملTermination Analysis of CHR Revisited
Today, there exist two distinct direct approaches to prove termination of CHR programs. Both are applicable on separate classes of CHR programs. One approach, by T. Frühwirth, proves termination of CHR programs without propagation rules. A second approach deals with CHR programs with propagation rules. Due to its extended scope to such programs, it fails to prove termination for a class of CHR ...
متن کاملAutomating Termination Proofs for CHR
We propose a constraint-based approach towards automated termination analysis of Constraint Handling Rules (CHR). Similar to such approaches for Logic Programming (LP), we define a symbolic level mapping on atoms of the program and express termination conditions using these. Then, we search for an assignment to the symbolic coefficients, validating the termination conditions. However, different...
متن کاملA new approach to termination analysis of CHR
We present a new approach to termination analysis of Constraint Handling Rules (CHR). Unlike current approaches, our approach has no restrictions on the kind of rules in the CHR program. We propose a termination condition that verifies conditions imposed on the dynamic process of adding constraints to the store, instead of a termination argument based on the comparison of sizes of consecutive c...
متن کامل