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Generating Precise and Concise Procedure Summaries

Generating Precise and Concise Procedure Summaries. Greta Yorsh Eran Yahav Satish Chandra. abstract domain & transformers. foo(…) { … }. summary of foo. Our Framework. Summary Generator. function from input to output abstract values. abstract domain & transformers. bar(…) {

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Generating Precise and Concise Procedure Summaries

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  1. Generating Precise and Concise Procedure Summaries Greta Yorsh Eran Yahav Satish Chandra

  2. abstract domain & transformers foo(…) { … } summary of foo Our Framework Summary Generator function from input to output abstract values

  3. abstract domain & transformers bar(…) { … foo(); … } summary of bar Our Framework Summary Generator summary of foo

  4. abstract domain & transformers library   Analyzer Our Framework (restricted) … Summary Generator client client client Summaries • precise • efficient • concise

  5. (A1) tr12 (A2) tr23 tr13 (A3) Example • Composition of transformers tr13  tr12  tr23 class DataReader { FileComp f; ... void setComponent(FileComp p) { this.f = p; } FileComp getComponent() { return this.f; } ... void nop() { FileComp t; t = getComponent(); setComponent(t); } } A1: A2: A3:

  6. … Main Challenge • Composition of transformers • Finite representation of iterated composition of transformers calling contexts loop iterations …

  7. tr12 tr23 tr13 Our Approach • Express constraints on intermediate states in terms of initial and final states • Restrict the representation of transformers • covers all basic statements • closed under composition • finite language

  8. Our Contributions • Framework for generating precise, efficient and concise summaries • language of transformers • composition algorithm • Instances of the framework include • known classes: IFDS, IDE • modular constant propagation with aliasing • modular typestate verification with aliasing • Prototype and evaluation for typestate

  9. tr12 tr23 tr13 Key Ideas • Transformers are defined using conditional micro-transformers • partition values into finite number of classes with uniform behavior • compose using case-splitting • restrict the way partitions defined • e.g., no quantifiers • Lift to aggregate domains • powerset, product, union • transformers follow domain structure • dependencies between components

  10. Simple Example: Tracking “Nullness” • Abstract value is a set of access paths • e.g., { x.f, y } must have null value • Abstract transformer tr operates pointwiseon individual access paths using trAP:tr(X) = X trAP() • Conditional micro-transformertrAP maps an access path  to a set of access paths

  11. { this.f, t } if  = this.f { } if  = t {  } if   t    this.f trAP() ≡  =this.f t  this.f =this.f this.f  t preconditions (under certain restrictions) Example: Conditional Micro-Transformer t = this.f

  12. (A1) tr12 (A2) 12 tr12(X) = X trAP() tr23 tr13 23 tr23(X) = X trAP() (A3) 12 23 tr13(X) = X (trAP  trAP )() Example: Composition Algorithm class DataReader { FileComp f; ... void setComponent(FileComp p) { this.f = p; } FileComp getComponent() { return this.f; } ... void nop() { FileComp t; t = getComponent(); setComponent(t); } } A1: A2: A3:

  13. trAP 12    this.f  t this.f  t this.f  t =t =t =t =t =t =t    t t t this.f this.f this.f trAP 23 Example: Composition Algorithm t = getComponent(); setComponent(t)  =this.f t  this.f t = getComponent() =this.f this.f  t substitution  :=  :=this.f  := t setComponent(t)

  14. Example: Composition Algorithm t = getComponent(); setComponent(t)  t  this.f =this.f =this.f := :=t :=this.f this.f t tthis.f  tt this.fthis.f  this.f t =t this.f=t t=t =t t=t this.f=t  t this.f t t this.f this.f t this.f          tthis.f

  15. t  this.f =this.f =this.f this.f  t t = getComponent(); setComponent(t) Example: Composition Algorithm t = getComponent(); setComponent(t)  t  this.f =this.f this.f t t=t t=t  t this.f   

  16. =this.f t  this.f t = getComponent() =this.f  this.f  t setComponent(t)  this.f  t =t =t  t  this.f  t this.f =this.f t = getComponent(); setComponent(t) =this.f this.f  t Basic Ingredients of Composition • Case splitting • Substitution • Consistency checking • Simplification • Invert operation (details in the paper)

  17. Related Work • Static determination of dynamic properties of recursive procedures [Cousot-Cousot ’79] • Functional approach [Sharir-Pnueli ‘81] • IFDS problems [Reps-Horwitz-Sagiv POPL’95] • IDE problems [Sagiv-Reps-Horwitz TCS ‘96] • Relevant Context Inference [Chatterjee-Ryder-Landi POPL’99]

  18. Summary • Language of transformers • Composition algorithm • The language is closed under composition • The language is expressive • Precise and concise procedure summaries

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