Higher-Order Positive Set Constraints

Authors:
Jean Goubault-Larrecq
Affiliations:
-
Venue:
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Year:
2002

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Abstract

We introduce a natural notion of positive set constraints on simply-typed 驴-terms. We show that satisfiability of these so-called positive higher-order set constraints is decidable in 2-NEXPTIME. We explore a number of subcases solvable in 2-DEXPTIME, among which higher-order definite set constraints, a.k.a., emptiness of higher-order pushdown processes. This uses a first-order clause format on so-called shallow higher-order patterns, and automated deduction techniques based on ordered resolution with splitting. This technique is then applied to the task of approximating success sets for a restricted subset of 驴-Prolog, 脿 la Fr眉hwirth et al.