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2010   1   8
• Hindley-Milner style polymorphic type
                 inference: low cost of inference by
                 unification to model intra-procedural
                 dependencies of values
               • the flow of values between functions
                 characterized by instantiations of
                 polymorphic types
               • polymorphic version of Steensgaard’s algo.
               • flow-insensitive, context-sensitive
2010   1   8
2010   1   8
2010   1   8
• 2: type constraint
               • 3: constraint resolution algorithm
               • 4: Computing global flow information
                • by type instantiation graph
               • 5: Experiments

2010   1   8
Flow-Query



               • each sub-expression is annotated by a label l
               • “Do values arising at label l in the program
                                            1
                 flow to a program point lablled l2?”
               • by tracing path on the type instantiation graph

2010   1   8
2010
1
8
                                                            Normalized dereference set size




                                                                    0
                                                                        20
                                                                               40
                                                                                       60
                                                                                             80
                                                                                                   100
                                                 co
                                                   m




       18
                                                       pr
                                                          e   ss


                                                              li
                                                   m
                                                    88
                                                      ks
                                                        im

                                                       ijp
                                                          eg




                      Monomorphic
                                                            go



                                       Benchmark
                                                        pe
                                                           r   l

                      Polymorphic
                                                     vo
                                                        rte
                                                           x

                                                         gc
                                                            c




                                                                   Analysis time (us per node)
                                             co
                                                                    0
                                                                         500
                                                                                    1000
                                                                                            1500
                                                                                                   2000




                                               m
                                                     pr
                                                        e   ss


                                                            li
                                                 m
                                                  88
            Monomorphic




                                                    ks
                                                      im

                                                     ijp
                                                        eg


                                                         go
                                     Benchmark

            Instantiation overhead




                                                       pe
                                                          r   l
                                                    vo
                                                       rte
                                                          x

                                                        gc
                                                           c
            Flow step overhead
2010
1
8
                                                         Multiple of #Nodes
                                                          Monomorphic
                                      co




                                                         0
                                                               6
                                                                      12
                                        m
                                             pr                               18
                                                e   ss


                                                    li
                                          m
                                           88
                                             ks
                                               im

                                             ijp
                                                eg



       #Nodes: Polymorphic
                              Benchmark         go

                                              pe
                                                 r   l
                                            vo
                                               rte
                                                  x
       #Instantiation edges




                                               gc
                                                  c
2010   1   8
2010   1   8
2010   1   8
2010   1   8
2010   1   8
2010   1   8

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Scalablecontext sensiteveflowanalysis-100107093234-phpapp02

  • 1. 2010 1 8
  • 2. • Hindley-Milner style polymorphic type inference: low cost of inference by unification to model intra-procedural dependencies of values • the flow of values between functions characterized by instantiations of polymorphic types • polymorphic version of Steensgaard’s algo. • flow-insensitive, context-sensitive 2010 1 8
  • 3. 2010 1 8
  • 4. 2010 1 8
  • 5. • 2: type constraint • 3: constraint resolution algorithm • 4: Computing global flow information • by type instantiation graph • 5: Experiments 2010 1 8
  • 6. Flow-Query • each sub-expression is annotated by a label l • “Do values arising at label l in the program 1 flow to a program point lablled l2?” • by tracing path on the type instantiation graph 2010 1 8
  • 7. 2010 1 8 Normalized dereference set size 0 20 40 60 80 100 co m 18 pr e ss li m 88 ks im ijp eg Monomorphic go Benchmark pe r l Polymorphic vo rte x gc c Analysis time (us per node) co 0 500 1000 1500 2000 m pr e ss li m 88 Monomorphic ks im ijp eg go Benchmark Instantiation overhead pe r l vo rte x gc c Flow step overhead
  • 8. 2010 1 8 Multiple of #Nodes Monomorphic co 0 6 12 m pr 18 e ss li m 88 ks im ijp eg #Nodes: Polymorphic Benchmark go pe r l vo rte x #Instantiation edges gc c
  • 9. 2010 1 8
  • 10. 2010 1 8
  • 11. 2010 1 8
  • 12. 2010 1 8
  • 13. 2010 1 8
  • 14. 2010 1 8