Theory of linear and integer programming
Theory of linear and integer programming
Polyhedral functions and multiparametric linear programming
Journal of Optimization Theory and Applications
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Solution of parametrized linear inequalities by fourier elimination and its applications
Journal of Optimization Theory and Applications
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
The CLP( R ) language and system
ACM Transactions on Programming Languages and Systems (TOPLAS)
A canonical form for generalized linear constraints
Journal of Symbolic Computation
Practical tools for reasoning about linear constraints
Fundamenta Informaticae - Special issue: logics for artificial intelligence
Global analysis of constraint logic programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
From logic programming to Prolog
From logic programming to Prolog
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Parameterized polyhedra and their vertices
International Journal of Parallel Programming
Optimizing compilation of CLP( R )
ACM Transactions on Programming Languages and Systems (TOPLAS)
Solving systems of strict polynomial inequalities
Journal of Symbolic Computation
Abstracting numeric constraints with Boolean functions
Information Processing Letters
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
On proving left termination of constraint logic programs
ACM Transactions on Computational Logic (TOCL)
Higher-Precision Groundness Analysis
Proceedings of the 17th International Conference on Logic Programming
Approaches to the Incremental Detection of Implicit Equalities with the Revised Simplex Method
PLILP '98/ALP '98 Proceedings of the 10th International Symposium on Principles of Declarative Programming
Consistency, Redundancy, and Implied Equalities in Linear Systems
Consistency, Redundancy, and Implied Equalities in Linear Systems
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Worst-case groundness analysis using definite Boolean functions
Theory and Practice of Logic Programming
Not necessarily closed convex polyhedra and the double description method
Formal Aspects of Computing
Average-Case Analysis of the Double Description Method and the Beneath-Beyond Algorithm
Discrete & Computational Geometry
Typing Linear Constraints for Moding CLP(${\cal R}$) Programs
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Theoretical Computer Science
A termination analyzer for Java bytecode based on path-length
ACM Transactions on Programming Languages and Systems (TOPLAS)
Adding constraint solving to mercury
PADL'06 Proceedings of the 8th international conference on Practical Aspects of Declarative Languages
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We present a type system for linear constraints over the reals intended for reasoning about the input-output directionality of variables. Types model the properties of definiteness, range width or approximation, lower and upper bounds of variables in a linear constraint. Several proof procedures are presented for inferring the type of a variable and for checking validity of type assertions. We rely on theory and tools for linear programming problems, linear algebra, parameterized polyhedra and negative constraints. An application of the type system is proposed in the context of the static analysis of constraint logic programs. Type assertions are at the basis of the extension of well-moding from pure logic programming. The proof procedures (both for type assertion validity and for well-moding) are implemented and their computational complexity is discussed. We report experimental results demonstrating the efficiency in practice of the proposed approach.