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Solving Inclusion Constraints between intensional sets

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Abstract

Tools allowing set manipulations are generally accepted by the logic programming community as providing a very "ad-hoc" formulation of a number of problems. Most of the existing approaches to deal with sets in a constraint logic programming framework work with extensional (finite) sets, or (infinite) regular sets using tree automatas. But intensional sets are often forbidden, or supposed to be finite. In this paper, starting from the initial syntax of Prolog, we propose an extended logical programming language including the data-structure of intensional set formalizing set comprehension and cartesian product. We describe a solving algorithm manipulating inclusion constraints containing set variables through suitable rules. Our method is a way to overcome the finiteness restrictions concerning intensional sets into logical programming language. 1 Introduction Set constraints are naturally involved in many computer science areas and there is a large agreement about their value [6]. For ...

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... (3) f(0; 10; 10); (1; 11; 10)g E (for each triple must exist an execution after which the state is this triple) constraints to bind the set variables (4) E f(x; y; z) j x 2 S 1^y 2 S 2^z 2 S 3 g (the set of reachable states is included in the cartesian product of set of reachable values of each state variable) Table 3.2 : an example of set speci cation An algorithm allowing to test the satis ability of such a speci cation (i.e. to test if there exists a solution) has been developed ( 11,13]), but we do not present it here. It uses rewriting techniques to transform set constraints in order to get a logical formula without any set variable. ...
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