Combinatorial Problem Solving

Overview

Constraint programming over finite domains. We (Beldiceanu, Carlsson) investigate solver architectures and filtering algorithms, using SICStus Prolog and its CLP(FD) solver as our research platform. The research is focused on global constraints, with the ultimate goal of developing the next generation of constraint programming tools. We are actively pursuing the following topics:

• A systematic classification of global constraints into constraint families. (Draft).
• Using this classification for designing languages for modeling, visualization, and expressing heuristics.
• Searching for essential principles from which one can derive several constraint propagation algorithms.
• Development of efficient constraint algorithms that reuse or adapt existing work from data structures, graph theory, and geometry.

Prolog technology. We (Carlsson, Danielsson, Mildner) develop and maintain SICStus Prolog and Quintus Prolog which run on UNIX and Windows platforms. Both Prologs have hundreds of licenses and offer full Prolog and powerful extensions.

SICStus Prolog is our platform for both constraint programming research and Prolog implementation research. In a recent Master's Thesis project, the benefits of different virtual machine instruction encodings for SICStus Prolog were investigated.

Projects

• SICStus Prolog
• Quintus Prolog
• Global Constraints
• NET-WMS

• Dispensation Order Generator for DNA Sequencing
• GENFUNK
• Trading Agent Competition
• A case study on airport crew rostering
• A study on using the case global constraint for configuration problems
• A study on optimization methods for configuration problems (SICS Technical Report T99-04)
• Frequency planning for cellular telephone networks
• Optimization of print mask design for inkjet printers
• TACIT
• Verification and optimization using constraints and logic

Researchers

• Mats Carlsson, Ph.D., Docent, group leader.
• Magnus Ågren, Ph.D.
• Per Mildner, Ph.D.
• Per Danielsson

Publications

• N. Beldiceanu, P. Flener, and X. Lorca. Combining tree partitioning, precedence, and incomparability constraints. Constraints, 13(4):459-489, 2008.

• Nicolas Beldiceanu, Mats Carlsson, and Emmanuel Poder. New filtering for the cumulative constraint in the context of non-overlapping rectangles. In L. Perron and M.A. Trick, editors, CPAIOR, volume 5015 of LNCS, pages 21-35, Paris, 2008. Springer.

• Mats Carlsson, Nicolas Beldiceanu, and Julien Martin. A geometric constraint over k-dimensional objects and shapes subject to business rules. Technical Report T2008-04, Swedish Institute of Computer Science, 2008.

• Mats Carlsson, Nicolas Beldiceanu, and Julien Martin. A geometric constraint over k-dimensional objects and shapes subject to business rules. In P.J. Stuckey, editor, Proc. CP'2008, volume 5202 of LNCS, pages 220-234. Springer-Verlag, 2008.

• Nicolas Beldiceanu. Introduction to the special issue on global constraints. Constraints, 12(1):1-2, 2007.

• Nicolas Beldiceanu and Xavier Lorca. Necessary condition for path partitioning constraints. In Pascal Van Hentenryck and Laurence A. Wolsey, editors, CPAIOR, volume 4510 of Lecture Notes in Computer Science, pages 141-154. Springer, 2007.

• Nicolas Beldiceanu and Emmanuel Poder. A continuous multi-resources umulative constraint with positive-negative resource consumption-production. In Pascal Van Hentenryck and Laurence A. Wolsey, editors, CPAIOR, volume 4510 of Lecture Notes in Computer Science, pages 214-228. Springer, 2007.

• N. Beldiceanu, M. Carlsson, E. Poder, R. Sadek, and C. Truchet. A generic geometrical constraint kernel in space and time for handling polymorphic k-dimensional objects. In C. Bessiere, editor, Proc. CP'2007, volume 4741 of LNCS, pages 180-194. Springer, 2007.

• N. Beldiceanu, M. Carlsson, E. Poder, R. Sadek, and C. Truchet. A generic geometrical constraint kernel in space and time for handling polymorphic k-dimensional objects. Technical Report T2007-08, Swedish Institute of Computer Science, 2007.

• Nicolas Beldiceanu, Mats Carlsson, Sophie Demassey, and Therry Petit. Global constraint catalog: Past, present and future. Constraints, 12(1):21-62, 2007. DOI 10.1007/s10601-006-9010-8.

• N. Beldiceanu, P. Flener, and X. Lorca. Partitionnement de graphes par des arbres sous contraintes de degré. In L. Henocque, editor, Proc. Journées Francophones de Programmation par Contraintes (JFPC'06). Association Française de Programmation par Contraintes, 2006.

• Nicolas Beldiceanu, Mats Carlsson, Sophie Demassey, and Thierry Petit. Graph properties based filtering. Technical Report T2006-10, Swedish Institute of Computer Science, 2006.

• Nicolas Beldiceanu, Mats Carlsson, Sophie Demassey, and Thierry Petit. Graph properties based filtering. In F. Benhamou, editor, CP'2006, Principles and Practice of Constraint Programming, volume 4204 of LNCS, pages 59-74. Springer, 2006.

• Nicolas Beldiceanu, Mats Carlsson, and Sven Thiel. Sweep synchronisation as a global propagation mechanism. Computers & Operations Research, 3(10):2835-2851, 2006.

• Nicolas Beldiceanu, Irit Katriel, and Xavier Lorca. Undirected forest constraints. In J. Christopher Beck and Barbara M. Smith, editors, CPAIOR, volume 3990 of Lecture Notes in Computer Science, pages 29-43. Springer, 2006.

• Mats Carlsson. The SICStus Prolog finite domain constraint programming library. In CP-TOOLS-06 workshop at CP 2006, 2006.

• Christian Schulte and Mats Carlsson. Finite domain constraint programming systems. In F. Rossi, P. van Beek, and T. Walsh, editors, Handbook of Constraint Programming, chapter 14. Elsevier, 2006.

• Erik Aurell, Mats Carlsson, Jan Ekman, and Per Kreuger. Genfunk. Technical Report T2005-17, Swedish Institute of Computer Science, 2005.

• Nicolas Beldiceanu, Mats Carlsson, Romuald Debruyne, and Thierry Petit. Reformulation of global constraints based on constraint checkers. Constraints, 10(4), 2005.

• Nicolas Beldiceanu, Mats Carlsson, and Jean-Xavier Rampon. Global constraint catalog. Technical Report T2005-08, Swedish Institute of Computer Science, 2005.

• Nicolas Beldiceanu, Mats Carlsson, Jean-Xavier Rampon, and Charlotte Truchet. Graph invariants as necessary conditions for global constraints. In P. van Beek, editor, CP'2005, Principles and Practice of Constraint Programming, volume 3709 of LNCS, pages 92-106. Springer, 2005.

• Nicolas Beldiceanu, Mats Carlsson, Jean-Xavier Rampon, and Charlotte Truchet. Graph invariants as necessary conditions for global constraints. Technical Report T2005-07, Swedish Institute of Computer Science, 2005.

• Nicolas Beldiceanu, Pierre Flener, and Xavier Lorca. The tree constraint. In Roman Barták and Michela Milano, editors, CPAIOR, volume 3524 of Lecture Notes in Computer Science, pages 64-78. Springer, 2005.

• Nicolas Beldiceanu, Thierry Petit, and Guillaume Rochart. Bounds of graph characteristics. In Peter van Beek, editor, CP, volume 3709 of Lecture Notes in Computer Science, pages 742-746. Springer, 2005.

• Mats Carlsson. Dispensation order generation for pyrosequencing. ERCIM News, (60), 2005.

• Ludovic Langevine. Explication systématique des contraintes indexicales. In C. Solnon, editor, Proc. Premières Journées Francophones de Programmation par Contraintes (JFPC'05). Association Française de Programmation par Contraintes, 2005.

• Ludovic Langevine. Systematic explanation of indexical constraints. In M. Carlsson, F. Fages, B. Hnich, and F. Rossi, editors, Proc. CSCLP 2005: Joint Annual Workshop on Constraint Solving and Constraint Logic Programming. ERCIM/CologNet, 2005.

• Adam Ameur, Erik Aurell, Mats Carlsson, and Jakub Orzechowski Westholm. Global gene expression analysis by combinatorial optimization. In Silico Biology, 4(0020), 2004.

• Nicolas Beldiceanu and Thierry Petit. Cost evaluation of soft global constraints. In Jean-Charles Régin and Michel Rueher, editors, CPAIOR, volume 3011 of Lecture Notes in Computer Science, pages 80-95. Springer, 2004.

• Nicolas Beldiceanu and Emmanuel Poder. The period constraint. In Bart Demoen and Vladimir Lifschitz, editors, ICLP, volume 3132 of Lecture Notes in Computer Science, pages 329-342. Springer, 2004.

• Nicolas Beldiceanu, Mats Carlsson, and Thierry Petit. Deriving filtering algorithms from constraint checkers. In M. Wallace, editor, CP'2004, Principles and Practice of Constraint Programming, volume 3258 of LNCS. Springer, 2004. Extended version available as SICS Tech Report T2004-08.

• Nicolas Beldiceanu, Irit Katriel, and Sven Thiel. Filtering algorithms for the same constraint. In Jean-Charles Régin and Michel Rueher, editors, CPAIOR, volume 3011 of Lecture Notes in Computer Science, pages 65-79. Springer, 2004.

• Nicolas Beldiceanu, Irit Katriel, and Sven Thiel. Gcc-like restrictions on the ame constraint. In Boi Faltings, Adrian Petcu, François Fages, and Francesca Rossi, editors, CSCLP, volume 3419 of Lecture Notes in Computer Science, pages 1-11. Springer, 2004.

• Mats Carlsson and Nicolas Beldiceanu. Dispensation order generation for pyrosequencing. In Yi-Ping Phoebe Chen, editor, Proc. APBC2004, volume 29 of Conferences in Research and Practice in Information technology, Dunedin, New Zealand, 2004. Australian Computer Society.

• Mats Carlsson and Nicolas Beldiceanu. From constraints to finite automata to filtering algorithms. In D. Schmidt, editor, Proc. ESOP2004, volume 2986 of LNCS, pages 94-108, Barcelona, 2004. Springer.

• Mats Carlsson and Nicolas Beldiceanu. Multiplex dispensation order generation for pyrosequencing. In CP'2004 Workshop on CSP Techniques with Immediate Application, 2004.

• Emmanuel Poder, Nicolas Beldiceanu, and Eric Sanlaville. Computing a lower approximation of the compulsory part of a task with varying duration and varying resource consumption. EJOR, 153:239-254, 2004.

• Emmanuel Poder, Nicolas Beldiceanu, and Eric Sanlaville. Computing a lower approximation of the compulsory part of a task with varying duration and varying resource consumption. European Journal of Operational Research, 153(1):239-254, 2004.

• N. Beldiceanu. Generic filtering algorithms for generic global constraints. Invited Talk, ERCIM Working Group on Constraints Workshop, 2003.

• Nicolas Beldiceanu, Mats Carlsson, and Sven Thiel. Sweep synchronization as a global propagation mechanism. In Proc. CP-AI-OR 2003, Montreal, 2003. Preprint available as SICS Tech Report T2003-02.

• M. Carlsson. Trolleri med villkorsprogrammering. Presentation at SICS Open House, 2003. Powerpoint slides, in Swedish.

• Magnus Ågren. Tracing and explaining the execution of CLP(FD) programs in SICStus Prolog. Master's thesis, Uppsala University, 2002. Also available as SICS Tech Report T2002-10.

• M. Ågren, T. Szeredi, N. Beldiceanu, and M. Carlsson. Tracing and explaining execution of CLP(FD) programs. In WLPE workshop at ICLP, Int. Conf. on Logic Programming, 2002.

• Erik Aurell, Magnus Boman, Mats Carlsson, Joakim Eriksson, Niclas Finne, Sverker Janson, Per Kreuger, and Lars Rasmusson. A constraint programming agent for automated trading. In 8th Int. Conf. of The Society for Computational Economics Computing in Economics and Finance, Aix-en-Provence, France, June 2002.

• N. Beldiceanu. Global constraints. Tutorial at CP'2002, Principles and Practice of Constraint Programming, 2002. Powerpoint slides.

• Nicolas Beldiceanu and Mats Carlsson. A new multi-resource cumulatives constraint with negative heights. In P. Van Hentenryck, editor, CP'2002, Principles and Practice of Constraint Programming, volume 2470 of LNCS, pages 63-79. Springer, 2002. Preprint available as SICS Tech Report T2001-11.

• Nicolas Beldiceanu, Mats Carlsson, and Sven Thiel. Cost-filtering algorithms for the two sides of the sum of weights of distinct values constraint. Technical Report T2002-14, Swedish Institute of Computer Science, 2002.

• Mats Carlsson and Nicolas Beldiceanu. Arc-consistency for a chain of lexicographic ordering constraints. Technical Report T2002-18, Swedish Institute of Computer Science, 2002.

• Mats Carlsson and Nicolas Beldiceanu. Revisiting the lexicographic ordering constraint. Technical Report T2002-17, Swedish Institute of Computer Science, 2002.

• M. Carlsson and C. Schulte. Finite domain constraint programming systems. Tutorial at CP'2002, Principles and Practice of Constraint Programming, 2002. Powerpoint slides.

• Nicolas Beldiceanu. Pruning for the minimum constraint family and for the number of distinct values constraint family. In T. Walsh, editor, CP'2001, Principles and Practice of Constraint Programming, volume 2239 of LNCS, pages 211-224. Springer, 2001. Preprint available as SICS Tech Report T2000-10.

• Nicolas Beldiceanu. Pruning for the minimum constraint family and for the number of distinct values constraint family. In Toby Walsh, editor, CP, volume 2239 of Lecture Notes in Computer Science, pages 211-224. Springer, 2001.

• N. Beldiceanu and M. Carlsson. Sweep as a generic pruning technique applied to constraint relaxation. In Soft'01 workshop at CP'2001, Principles and Practice of Constraint Programming, 2001.

• N. Beldiceanu and Mats Carlsson. Constructive cardinality. Technical Report T2001-15, Swedish Institute of Computer Science, 2001.

• Nicolas Beldiceanu and Mats Carlsson. Revisiting the cardinality operator and introducing the cardinality-path constraint family. In P. Codognet, editor, ICLP'2001, Int. Conf. on Logic Programming, volume 2237 of LNCS, pages 59-73. Springer, 2001. Preprint available as SICS Tech Report T2000-11A.

• Nicolas Beldiceanu and Mats Carlsson. Sweep as a generic pruning technique applied to the non-overlapping rectangles constraint. In T. Walsh, editor, CP'2001, Principles and Practice of Constraint Programming, volume 2239 of LNCS, pages 377-391. Springer, 2001. Preprint available as SICS Tech Report T2001-13.

• Nicolas Beldiceanu, Qi Guo, and Sven Thiel. Non-overlapping constraints between convex polytopes. In T. Walsh, editor, CP'2001, Principles and Practice of Constraint Programming, volume 2239 of LNCS, pages 392-407. Springer, 2001. Preprint available as SICS Tech Report T2001-12.

• Nicolas Beldiceanu, Qi Guo, and Sven Thiel. Non-overlapping constraints between convex polytopes. In Toby Walsh, editor, CP, volume 2239 of Lecture Notes in Computer Science, pages 392-407. Springer, 2001.

• M. Carlsson. Finite domain constraints in SICStus Prolog. CICLOPS Workshop at CP'2001, Principles and Practice of Constraint Programming, 2001. Invited talk.

• G. Gupta, E. Pontelli, K. Ali, M. Carlsson, and M. Hermenegildo. Parallel execution of Prolog programs. ACM Transaction on Programming Languages and Systems, 23(4):1-131, 2001.

• Per Kreuger, Mats Carlsson, Thomas Sjöland, and Emil Åström. Sequence dependent task extensions for trip scheduling. Technical Report T2001-14, Swedish Institute of Computer Science, 2001.

• Henrik Nässén. Optimizing the SICStus virtual machine instruction set. Master's thesis, Uppsala University, 2001. Also available as SICS Tech Report T2001-01.

• Henrik Nässén, Mats Carlsson, and Konstantinos Sagonas. Instruction merging and specializing in the SICStus Prolog virtual machine. In PPDP'01, Principles and Practice of Declarative Programming. ACM, 2001.

• Nicolas Beldiceanu. Global constraints as graph properties on a structured network of elementary constraints of the same type. In Rina Dechter, editor, CP, volume 1894 of Lecture Notes in Computer Science, pages 52-66. Springer, 2000.

• Nicolas Beldiceanu. Global constraints as graph properties on structured network of elementary constaints of the same type. In R. Dechter, editor, CP'2000, Principles and Practice of Constraint Programming, volume 1894 of LNCS, pages 52-66. Springer, 2000. Preprint available as SICS Tech Report T2000-01.

• Nicolas Beldiceanu. Sweep as a generic pruning technique. Technical Report T2000-08, Swedish Institute of Computer Science, 2000. Also in Proc. TRICS workshop at CP'2000, Principles and Practice of Constraint Programming.

• Helmut Simonis, Abderrahmane Aggoun, Nicolas Beldiceanu, and Eric Bourreau. Complex constraint abstraction: Global constraint visualisation. In Pierre Deransart, Manuel V. Hermenegildo, and Jan Maluszynski, editors, Analysis and Visualization Tools for Constraint Programming, volume 1870 of Lecture Notes in Computer Science, pages 299-317. Springer, 2000.

• J. Yen, M. Carlsson, M. Chang, J.M. García, and H. Nguyen. Constraint solving for inkjet print mask design. Journal of Imaging Science and Technology, 44(5), September/October 2000.

• Mats Carlsson and Greger Ottosson. A comparison of CP, IP and hybrids for configuration problems. Technical Report T99-04, Swedish Institute of Computer Science, 1999.

• Mats Carlsson, Per Kreuger, and Emil Åström. Constraint-based resource allocation and scheduling in steel manufacturing. In G. Gupta, editor, Practical Aspects of Declarative Languages, volume 1551 of LNCS, pages 335-349, San Antonio, 1999. Springer.

• J. Yen, M. Carlsson, M. Chang, J.M. García, and H. Nguyen. Constraint solving for inkjet print mask design. In NIP15: Int. Conf. on Digital Printing Technologies, Orlando, FL, 1999. The Society for Imaging Science and Technology.

• Jesper Eskilson and Mats Carlsson. SICStus MT---a multithreaded execution environment for SICStus Prolog. In C. Palamidessi, H. Glaser, and K. Meinke, editors, Programming Languages: Implementations, Logics, and Programs, volume 1490 of LNCS, pages 36-53, Pisa, 1998. Springer.

• J. Yen, M. Carlsson, M. Chang, J.M. Garcia, and H. Nguyen. Constraint solving for inkjet print mask design. Technical report, HPL-98-133, Hewlett-Packard Company, July 1998.

• Mats Carlsson, Greger Ottosson, and Björn Carlson. An open-ended finite domain constraint solver. In H. Glaser, P. Hartel, and H. Kuchen, editors, Programming Languages: Implementations, Logics, and Programming, volume 1292 of LNCS, pages 191-206. Springer, 1997.

• Per Kreuger, Mats Carlsson, Jan Olsson, Thomas Sjöland, and Emil Åström. The TUFF train scheduler. In G. Puebla, editor, ILPS'97 Workshop on Tools and Environments for (Constraint) Logic Programmins, 1997.

• Per Kreuger, Mats Carlsson, Jan Olsson, Thomas Sjöland, and Emil Åström. The TUFF train scheduler--two duration trip scheduling on single track networks. In A. Davenport, editor, CP'97 Workshop on Industrial Constraint-Driven Scheduling, 1997.

• Mats Carlsson and Greger Ottosson. Anytime frequency allocation with soft constraints. In J. Burg, M. Leconte, and R. Yap, editors, CP'96 Pre-conf. Workshop on Applications, 1996.

• Björn Carlson and Mats Carlsson. Compiling and executing disjunctions of finite domain constraints. In L. Sterling, editor, ICLP'95, Int. Conf. on Logic Programming, MIT Press Series in Logic Programming. The MIT Press, 1995.

• Björn Carlson, Sverker Janson, and Mats Carlsson. The implementation of AKL(FD). In J. Lloyd, editor, ILPS'95, Int. Logic Programming Symposium, MIT Press Series in Logic Programming. The MIT Press, 1995.

• Mats Carlsson et al. SICStus Prolog User's Manual. Swedish Institute of Computer Science, release 3 edition, 1995. ISBN 91-630-3648-7.

• Björn Carlson, Mats Carlsson, and Daniel Diaz. Entailment of finite domain constraints. In P. Van Hentenryck, editor, ICLP'94, Int. Conf. on Logic Programming, MIT Press Series in Logic Programming, S. Margherita Ligure, Italy, 1994. The MIT Press.

• Mats Carlsson and Mats Grindal. Automatic frequency assignment for cellular telephones using constraint satisfaction techniques. In D.S. Warren, editor, ICLP'93, Int. Conf. on Logic Programming, MIT Press Series in Logic Programming, pages 647-665, Budapest, 1993. The MIT Press.

• Abderrahmane Aggoun and Nicolas Beldiceanu. Extending chip in order to solve complex scheduling and placement problems. In Jean-Paul Delahaye, Philippe Devienne, Philippe Mathieu, and Pascal Yim, editors, JFPL, pages 51--, 1992.

• Mats Carlsson. A BDD-based approcah to multiple level combinational logic synthesis. In Al Roth, editor, Practical Applications of Prolog Conf. Al Roth, 1992.

• Abderrahmane Aggoun and Nicolas Beldiceanu. Overview of the chip compiler system. In ICLP, pages 775-789, 1991.

• Abderrahmane Aggoun and Nicolas Beldiceanu. Overview of the chip compiler system. In WCLP, pages 421-435, 1991.

• Mats Carlsson. Boolean constraints in SICStus Prolog. SICS Research Report T91:09, Swedish Institute of Computer Science, 1991.

• Mats Carlsson. The SICStus emulator. SICS Technical Report T91:15, Swedish Institute of Computer Science, 1991.

• Péter Szeredi, Mats Carlsson, and Rong Yang. Interfacing engines and schedulers in or-parallel Prolog systems. In E.H.L. Aarts, J. van Leeuwen, and M. Rem, editors, PARLE'91, Conf. on Parallel Architectures and Languages Europe, volume 506 of LNCS. Springer, 1991.

• Abderrahmane Aggoun and Nicolas Beldiceanu. Time stamps techniques for the trailed data in constraint logic programming systems. In Serge Bourgault and Mehmet Dincbas, editors, SPLT, pages 487-510, 1990.

• Mats Carlsson. Design and Implementation of an OR-Parallel Prolog Engine. SICS Dissertation Series 02, The Royal Institute of Technology, Stockholm, Stockholm, Sweden, May 1990.

• Mats Carlsson. A Prolog compiler and its extension for or-parallelism. SICS Research Report R90006, Swedish Institute of Computer Science, 1990.

• Mats Carlsson and Dan Sahlin. Variable shunting for the WAM. In J.W. Mills, editor, NACLP'90 Post-conf. Workshop on Logic Programming Architectures and Implementations, 1990. Also available as SICS Research Report R91:07.

• Mats Carlsson and Péter Szeredi. The Aurora abstract machine and its emulator. SICS Research Report R90005, Swedish Institute of Computer Science, 1990.

• E. Lusk, R. Butler, T. Disz, R. Olson, R. Overbeek, R. Stevens, D.H.D. Warren, A. Calderwood, P. Szeredi, P. Brand, M. Carlsson, A. Ciepielewski, and B. Hausman. The aurora or-parallel prolog system. New Generation Computing, 7(2,3):243-271, 1990.

• Péter Szeredi and Mats Carlsson. The engine-scheduler interface in the Aurora or-parallel Prolog system. Technical Report TR-90-09, University of Bristol, Computer Science Department, April 1990.

• M. Carlsson. On the efficiency of optimising shallow backtracking in compiled Prolog. In G. Levi and M. Martelli, editors, ICLP'89, Int. Conf. on Logic Programming, MIT Press Series in Logic Programming, pages 3-16, Lisbon, 1989. The MIT Press.

• Karen Appleby, Mats Carlsson, Seif Haridi, and Dan Sahlin. Garbage collection for Prolog based on WAM. Communications of the ACM, 31(6):719-740, June 1988.

• Mats Carlsson, Ken Danhof, and Ross Overbeek. A simplified approach to the implementation of AND-Parallelism in an OR-Parallel environment. In R.A. Kowalski and K.A. Bowen, editors, ICLP'88, Int. Conf. and Symposium on Logic Programming, MIT Press Series in Logic Programming, pages 1565-1577, Seattle, 1988. ALP, IEEE, The MIT Press.

• Younes Souissi and Nicolas Beldiceanu. Deterministic systems of sequential processes: Theory and tools. In Friedrich H. Vogt, editor, Concurrency, volume 335 of Lecture Notes in Computer Science, pages 380-400. Springer, 1988.

• M. Carlsson. Freeze, indexing, and other implementation issues in the WAM. In Jean-Louis Lassez, editor, ICLP'87, Int. Conf. on Logic Programming, MIT Press Series in Logic Programming, pages 40-58, Melbourne, 1987. The MIT Press.