1. PathLP – Path-based Logic Programming Mira Balaban, Igal Khitron Computer Science Department Ben-Gurion University Mini-project-course Fall 20131

2. PathLP compact logic programming A compact logic programming language Inspired from – Object-Oriented Logic Programming languages: F-Logic (Kifer, Lausen, Wu 1995) FLORA-2 (http://flora.sourceforge.net/, 2009)http://flora.sourceforge.net/ – Object-Oriented database and web query languages : XSQL (Kifer, Kim, Sagiv 1992) XPATH – a query language over XML documents (http://www.w3schools.com/xpath/). (http://www.w3schools.com/xpath/) guarded path expressions Supports reasoning over guarded path expressions typing notions: Supports typing notions: – Hierarchy – Membership Mini-project-course Fall 20132

3. PathLP status PathLP is still under development by Mira Balaban, Igal Khitron, Michael Kifer (alphabetical order). Intended for: – Formal support for Model-Level Integrated Development Environments : Simultaneous reasoning over multiple models – Reasoning over applications that support hierarchical structures, like Access policy in Network Management Publications: – Mira Balaban and Michael Kifer: "An Overview of F-OML: An F-Logic Based Object Modeling Language", ECEASST'11 36."An Overview of F-OML: An F-Logic Based Object Modeling Language" – Mira Balaban and Michael Kifer: "Logic Based Model-Level Software Development with F- OML", MoDELS'2011."Logic Based Model-Level Software Development with F- OML" – Igal Khitron, Michael Kifer, Mira Balaban: “PathLP: A Logic Programming Language of Path Expressions”, PLDE 2012. Application: Version 1.4 PathLP1.4 PathLP1.4 Mini-project-course Fall 20133

4. Model-level IDE – Needed modeling services modeling Provide a modeling constraint language for extending UML diagrams: – Object Constraint Language (OCL) – PathLP Verification Verification of UML diagrams design patterns Specification of design patterns. Reasoning Reasoning about UML diagrams Testing Testing UML diagrams Model Model refactoring Meta-modeling Meta-modeling : – DSML specification – Formalize UML specification Mini-project-course Fall 20134

5. Model-level IDE – Integration with a modeling platform Diagrammatic models Diagrammatic models – concrete external syntax. Mini-project-course Fall 20135 Modeling services model 1 model n … UML development platform model 1 -module … model n -module Underlying formal modeling language transformations

6. Model-level IDE – Integration with a modeling platform Diagrammatic models Diagrammatic models – concrete external syntax. Mini-project-course Fall 20136 model 1 -module … model n -module F-OM L PathLP Modeling services model 1 model n … UML development platform transformations

7. PathLP constructs Path expressions Facts Rules Constraints Queries Mini-project-course Fall 20137

8. PathLP: Object path expressions constants, variables,., guards Consist of constants, variables,., guards objects Denote objects ?C.friend.student[?S].name The names of a student s of a friend of c, for some bindings s and c to variables ?S and ?C Mini-project-course Fall 2013 constant variable guard 8 denotation c friend student s name student … … …

9. PathLP: Object path expressions & Query formulas Query formula: John.childWith(Mary)[?C].name[?N], ?C:Student,?C.ageAt(2010)<20 The name ?N of ?C, who is a child with Mary of John, is a student and whose age at 2010 is less than 20 Mini-project-course Fall 2013 elementary formula 9 denotation John ?C Student childWith(Mary) name … … ageAt(2010) n<20 elementary formula ?N

10. PathLP: Type path expressions Person!spouse[Person]{0..1} The type of spouse s of nodes of type Person (nodes pointed by spouse edges) is Person (or a subtype of Person ), and there is at most 1 such edge Assume – ?n1.spouse[?n2] – Mini-project-course Fall 201310 ?n1 spouse ?n2 Cardinality constraint

11. PathLP: Type path expressions Person!spouse[Person]{0..1} The type of spouse s of nodes of type Person is Person (or a subtype of Person ), and there is at most 1 such edge Assume – ?n1.spouse[?n2] – ?n1:Person Mini-project-course Fall 201311 Person ?n1 spouse ?n2

12. PathLP: Type path expressions Person!spouse[Person]{0..1} The type of spouse s of nodes of type Person is Person (or a subtype of Person ), and there is at most 1 such edge Assume – ?n1.spouse[?n2] – ?n1:Person Mini-project-course Fall 201312 and Person ?n1 IF at most 1 spouse edge spouse ?n2 THEN  ?n2:Person

13. PathLP: Type path expressions Person!spouse[Person]{0..1} The type of spouse s of nodes of type Person is Person (or a subtype of Person ), and there is at most 1 such edge Assume – ?n1.spouse[?n2] – ?n1:Person Mini-project-course Fall 201313 and Person ?n1 spouse IF at most 1 spouse edge spouse ?n2 THEN Type edge spouse …  ?n2:Person

14. PathLP: Facts – specify assertions John.spouse[Mary]; John.child[Bob]; John.child[Bill]; – John has a spouse Mary and children Bob and Bill (and possibly others) Type hierarchy and membership assertions: : Bob:CS_teaching_committee; :: CS_teaching_committee::Teaching_committee; : Teaching_committee:Committee; :: Committee::Group; – Bob CS_teaching_committee Teaching_committee Committee Group ! A type assertion: Person!spouse[Person]{0..1}; – The type of spous es of Person is Person, or one of its subtypes, and the cardinality constraint is {0..1} Mini-project-course Fall 201314

15. PathLP: Rules, Constraints, Queries Rules Rules – specify implications: – ?A:advisor :- ?T:Thesis, ?T.author.advisor[?A].read[?T],?A:Professor; ?A is an advisor if ?A has read a thesis ?T of an author that ?A advises Constraints Constraints – restrict legal states: – !- ?P:Professor, not ?P.degree[PhD]; forbid states with a professor ?P that does not have a PhD degree Queries Queries – trigger computation – ?- ?A:Professor, ?A.review[?Thesis], ?A.supervise.thesis-of[?Thesis]; Find a professor that reviews a thesis of somebody s/he supervises. A more compact expression: ?- ?A:Professor,?A.review.author.advisor[?A]; Mini-project-course Fall 201315

16. PathLP – as a basis for Object-Oriented modeling Defines entities: paths – Inter-related by paths typed – Possibly typed inclusion inclusion “::” membership membership “:” Multi-level Multi-level modeling: – Unrestricted “ :: “ and “ : “ Polymorphism: Polymorphism: – Parameterized – Parameterized path expressions – Type hierarchy Mini-project-course Fall 201316 Object navigation Class Class hierarchy Object creation; Testing Reflection Patterns Model query Static analysis

17. PathLP – implementation Beta version 1.4: – pathlp.sf.net (Igal Khitron) pathlp.sf.net – Compiler and interpreter – In XSB prolog open source tabling prolog supports well-founded negation – Windows, Linux, Unix – Large test cases: 200,000 facts Mini-project-course Fall 201317

18. Mini-Project subject – Develop a Graph Services library in PathLP An example library: JGraphTJGraphT From the JGraphT home page: – JGraphT is a free Java graph library that provides mathematical graph-theory objects and algorithms. JGraphT supports various types of graphs including: directed and undirected graphs. graphs with weighted / unweighted / labeled or any user-defined edges. various edge multiplicity options, including: simple-graphs, multigraphs, pseudographs. unmodifiable graphs - allow modules to provide "read-only" access to internal graphs. listenable graphs - allow external listeners to track modification events. subgraphs graphs that are auto-updating subgraph views on other graphs. all compositions of above graphs. – Although powerful, JGraphT is designed to be simple and type-safe (via Java generics). For example, graph vertices can be of any objects. You can create graphs based on: Strings, URLs, XML documents, etc; you can even create graphs of graphs! This code example shows how.code example Mini-project-course Fall 201318

19. Mini-Project subject – Develop a Graph Services library in PathLP Why having “yet another JGraphT” in PathLP?JGraphT Mini-project-course Fall 201319

20. Mini-Project subject – Develop a Graph Service library in PathLP Why having “yet another JGraphT” in PathLP?JGraphT What are the special features of Logic Programming languages? – Reasoning! – Answer queries! – Analysis! Mini-project-course Fall 201320

21. Graph representation in PathLP Directed graph: – Facts: n1.edge[n2]; n1.edge[n3]; n1.edge[n4]; n2.edge[n3]; n2.edge[n5]; n4.edge[n2]; n4.edge[n4]; n5.edge[n2]; n5.edge[n4]; Mini-project-course Fall 201321 n1 n2 n4n3 n5

22. Querying the directed graph Directed graph: – Facts: n1.edge[n2]; n1.edge[n3]; n1.edge[n4]; n2.edge[n3]; n2.edge[n5]; n4.edge[n2]; n4.edge[n4]; n5.edge[n2]; n5.edge[n4]; – Queries: ?- n1.edge[?N]; ?- ?N1.edge[?N2]; ?- ?N1.edge[?_N2],?_N2.edge[?N1]; ?- ?n.edge[?n]; ?- not n1.edge[n2]; ?- ?N._size(edge)[?edge_number],?edge_number<2 ; Mini-project-course Fall 201322 n1 n2 n4n3 n5

23. Reasoning about the directed graph Paths in the directed graph: – Rules: ?n1.path[?n2]:- ?n1.edge[?n2]; ?n1.path[?n2]:- ?n1.path[?n3],?n3.edge[?n2]; – Facts: n1.edge[n3];n4.edge[n2]; n1.edge[n4];n4.edge[n4]; n2.edge[n3];n5.edge[n2]; n2.edge[n5];n5.edge[n4]; – Queries: ?- n5.path[n5]; ?- ?N.path[n5]; ?- ?N.path[n5],?N != n5; ?- ?n.path[?n]; ?- not(n1.path[n1]); ?- n1.path[?N],not(?N.path[?N]); – Rule: ?n.selfPath[true]:- ?n.path[?n]; – Query: ?- ?N._size(selfpath)[?path_num],?path_num>1; Mini-project-course Fall 201323 n1 n2 n4n3 n5

24. Reasoning about the directed graph Adding path details and node typing: – Rules: ?N1.path([?N1,?N2])[?N2]:- ?N1.edge[?N2]; ?N1.path([?N1|?P])[?N3]:- ?N1.edge[?N2],?N2.path(?P)[?N3]; ?N1.loop[?N2]:- ?N1.edge[?N2],?N2.edge[?N1]; ?N.origin[true]:- ?N:Node,not ?N.enter_edge[true]; ?N.enter_edge[true]:- ?N1.edge[?N]; ?N.sink[true]:- ?N:Node,not ?N.leaving_edge[true]; ?N.leaving_edge[true]:- ?N.edge[?N1]; isolated(?N)[true] :- origin(?N)[true],sink(?N)[true]; – Facts: n1:Node; n2:Node; n3:Node; n4:Node; n5:Node; n6:Node; n1.edge[n3];n4.edge[n2]; n1.edge[n4];n4.edge[n4]; n2.edge[n3];n5.edge[n2]; n2.edge[n5];n5.edge[n4]; – Queries: ?- n5.path(?P)[n5]; ?- ?N.path(?P)[n5]; ?- ?N.path(?_P)[n5]; is the same as ?- ?N.path[n5]; ?- ?N.path(?_P)[n5],not ?_P.member[n4]; ?- ?N.loop[n5]; ?- ?N1.origin[true],?N2.origin[true],?N1!=?N2; ?- ?_N.isolated[true]); Mini-project-course Fall 201324 n1 n2 n4n3 n5 n6

25. Reasoning about the directed graph Adding labeled edges, edge typing, path typing: – Rules: ?P:Path :-?N1.path(?P)[?N2]; % Bad modeling! Why? ?P.nodes[?P] :- ?P:Path,?N1.path(?P)[?N2]; ?P.node[?N] :- ?P.nodes[?Node_list],?Node_list.member[?N]; ?E:Edge :- ?N1.edge(?E)[?N2]; ?E.source[?N] :- ?E:Edge,?N.edge(?E)[?N1]; – Facts: n1:Node; n2:Node; n3:Node; n4:Node; n5:Node; n6:Node; n1.edge[n3];n4.edge[n2]; n1.edge[n4];n4.edge[n4]; n2.edge[n3];n5.edge[n2]; n2.edge[n5];n5.edge(e54)[n4]; – Note the different design decision about the status of nodes and edges: Node typing is mandatory Edge typing is inferred Mini-project-course Fall 201325 n1 n2 n4n3 n5 n6 e54

26. Reasoning about the directed graph Improved path modeling: – Rules: path(?node_list):Path :-?N1.path(?node_list)[?N2]; path(?node_list).nodes[?node_list] :-?N1.path(?node_list)[?N2]; ?P.node[?N] :- ?P.nodes[?Node_list], ?Node_list.member[?N]; ?P.first[?N] :- ?P:Path, ?P.nodes[ [?N|?rest_nodes] ]; ?P.last[?N] :- ?P:Path, ?P.nodes[?node_list], ?node_list.reverse[[?N|?rest_nodes]]; – Constraints: !- ?P:Path, ?P.first[?N1], ?P.last[?N2], ?P.nodes[?node_list], not ?N1.path(?node_list)[?N2]; – Facts: n1:Node; n2:Node; n3:Node; n4:Node; n5:Node; n6:Node; n1.edge[n3];n4.edge[n2]; n1.edge[n4];n4.edge[n4]; n2.edge[n3];n5.edge[n2]; n2.edge[n5];n5.edge(e54)[n4]; Mini-project-course Fall 201326 n1 n2 n4n3 n5 n6 e54

27. Reasoning about the directed graph Adding more constraints: – Rules: path(?node_list):Path :-?N1.path(?node_list)[?N2]; path(?node_list).nodes[?node_list] :-?N1.path(?node_list)[?N2]; ?E:Edge :- ?N1.edge(?E)[?N2]; ?E.source[?N] :- ?E:Edge,?N.edge(?E)[?N1]; – Constraint: !- ?E.source[?N1],?E.source[?N2], ?N1!=?N2; !- ?N1.path(?P)[?N2], ?P.member[?N],not ?N:Node; A single labeled edge between nodes: !- ?N1.edge(?L1)[?N2], ?N1.edge(?L2)[?N2], ?L1 != ?L2; A single labeled edge leaving a node: !- Node!edge(?L)[Node]{0..1}; Mini-project-course Fall 201327 n1 n2 n4n3 n5 n6 e54

28. Reasoning about the directed graph Adding path properties and sub-typing: – Rules: path(?node_list):Compact_Path :- path(?node_list):Path, ?node_list.compactList[true]; ?List.compactList[true] :- not ?L1.append([?N],?L2,[?N],?L3)[?List]; ?P:Cycle :- ?P:Path,?P.first[?N],?P.last[?N]; path(?node_list).length[?number] :- ?node_list.length[?number]; Compact_Path :: Path; Cycle :: Path; – Constraints: !- path(?node_list):Compact_Path, not ?node_list.compactList[true]; !- ?P:Cycle, ?P.first[?N1], ?P.last[?N2], ?N1 != ?N2; Mini-project-course Fall 201328 n1 n2 n4n3 n5 n6 e54

29. Reasoning about the directed graph Adding multiple graphs: – Rules: ?G.node[?N] :-?G.nodes[?Node_list],?Node_list.member[?N]; ?N.graph[?G] :-?G.node[?N]; ?G1.intersection(?G2)[?G] :- ?G1.nodes[?Ns1],?G2.nodes[?Ns2], ?G1.edges[?Es1],?G2.edges[?Es2], ?Ns1.intersection(?Ns2)[?Ns], ?Es1.intersection(?Es2)[?Es], ?G:Directed_graph,?G.nodes[?Ns],?G.edges[?Es]; ?G.is_empty[true] :- ?G:Directed_graph,?G.nodes[ [] ]; ?G1.disjoint[?G2] :- ?G1.intersection(?G2)[?G], ?G.is_empty[true]; ?G.path[?P]:- ?P.nodes[?Nodes_P],?G.nodes[?Nodes_G], ?Nodes_G.contains[?Nodes_P]; ?G:Cyclic_directed_graph :- ?G.path[?P],?P:Cycle; ?G:DAG :- not ?G:Cyclic_directed_graph; – A different modeling approach – using functional constructors: intersection(?G1,?G2):Directed_graph :- ?G1:Directed_graph,?G2:Directed_graph; intersection(?G1,?G2).nodes[intersection(?Ns1,?Ns2)] :- ?G1.nodes[?Ns1],?G2.nodes[?Ns2]; – A type Constraint: Directed_graph!nodes[List]{1..1}; – Facts: g1:Directed_graph; g1.nodes[[n1,n2,n3,n4,n5,n6]]; g1.edges[[e12,e13,e14,e25,e52,e23,e42,e44]]; Mini-project-course Fall 201329

30. 30Mini-project-course Fall 2013