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Advances in Logical Programming Environments

Advances in Logical Programming Environments. Programming. Logic. Communications. Secure software infrastructure. Stuart Allen Mark Bickford Robert Constable Richard Eaton Christoph Kreitz Lori Lorigo. Project goals.

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Advances in Logical Programming Environments

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  1. Advances in Logical Programming Environments Programming Logic Communications Secure software infrastructure Stuart Allen Mark Bickford Robert Constable Richard Eaton Christoph Kreitz Lori Lorigo

  2. Project goals Build openLogical Programming Environment -integrate programming language and logic-share libraries of formalized mathematics-enable cooperation among formal systems-local reflection and code transformations Application to reliable embedded systems-semantics-based transformation and optimization-high-assurance software components and systems-formal component design

  3. Progress • Nuprl LPE - new implementation with open architecture- formal documentation mechanisms- development of class theory- local reflection for weaving aspects • Application to networked systems -optimizationof protocol stacks- compositional protocol verification-formal design of adaptive systems

  4. LPE Architecture • Cooperating processes • Library as persistent database- basis for sharing mathematics • Ability to connect to external systems • Cooperating inference engines • Multiple user interfaces • Reflective system structure

  5. Formal Documentation • Create documentation from formal objects- formal design expertise in “readable” form-screen display, LaTeX articles, HTML documents • Comments contain references to objects- formal content browsable while reading text • Display objects determine term presentation - print representation (screen/LaTeX macros)-suppressing formal parameters-preferences vs. parentheses

  6. Class theory provides IOA formalisms IOA Ocaml(Ensemble) Java/JVM Ocaml Language Formalized in Nuprl External System Formalizes JVM Formal Class Theory • Extends Nuprl’s type theory • Provides expressive type constructs- Union, Intersection, Subtyping, Records, Modules • Supports formalization and composition of -Abstract specifications + concrete code of components-Modular verifications 

  7. Weaving and local reflection • Add properties to code Message Passing with Total Order Fault Tolerance Transform Total Order code to include rejoining & view-change code Fault Tolerant System with Total Order • Weaving asformal method requires local reflection-thms about semantical effect of syntactical transformations- reasoning about refinement + meta-properties

  8. Formal Optimization • Optimize component-based network systems • generate fast-path for common case • compress message headers • Automate with Nuprl LPE (demo available) • Identify Common Case Predicates • Component code + CCP -> optimization theorem • System composition -> theorem composition • Composed theorem -> new system code Fast, abstract, verifiably correct results, speedup factor 3-4

  9. Incremental through proof inheritance: • (A = P)  (A  B = P) • A  B intersects: • states, actions • initial states, transitions Total = total ETO = total  view Total Induction: 1. A  I = I 2. B  I = I 3. A.init  B.init  I A  B = I ETO View View = view Compositional Protocol Verification

  10. switch spec spec Formal Design of Adaptive Systems Joint work with Robbert Van Renesse, Xiaoming Liu, Ken Birman • Adapt system to suit run-time dynamics • - system upgrades • - changing conditions (higher security levels, …) • - use optimal implementations of components • Usually complicated • Building block approach • - generic switching protocol • constructshybrid protocolsfrom simpler ones • - flexible, easy to prove correct

  11. Switching Protocol P1 P2 Switching Protocols: basic model • Normal mode • -forward messages to current protocol • - receive messages from current protocol • Switching Mode • -deliver messages from previous protocol • - buffer messages sent in the new protocol

  12. meta- properties What kind of properties will be preserved by switching? Reliability? Prioritized Delivery? Integrity? Total Order? Confidentiality? Virtual Synchrony? In other words, what are the properties of these properties ? Inject formal methods at earliest design stage

  13. switch spec spec spec network network Using the Nuprl LPE we proved that six meta-properties are sufficient for protocols to work correctly under a switching protocol

  14. Formal Model of Communication • Communication property - predicate P on traces • Trace - List tr ofsend and receive events Send(p,m) : message p sent by process m Deliver(p,m) : message p received by process m

  15. Reliability • p,m. Send(p, m)  tr  q. Deliver(q,m)  tr • Integrity (T: set of trusted processes) • qT. Deliver(q,m)  tr  pT. Send(p,m)  tr • Confidentiality • qT. Deliver(q,m)  tr  pT. Send(p,m)  tr ) • Total order • q1,q2,m1,m2. Deliver(q1,m1)  tr  Deliver(q2,m1)  tr •  Deliver(q1,m2)  tr  Deliver(q2,m2)  tr •  Deliver(q1,m1) < Deliver(q1, m2) •  Deliver(q2,m1) < Deliver(q2, m2) Properties, formalized

  16. Meta-property • Predicate M on properties of protocols  • Expressed by relation R between traces tru,trl above and below a protocol layer M(P)tru,trl. P(trl)  trlR tru P(tru) • Requires capability for higher order reasoning

  17. Meta-properties for Switching } Safety Asynchrony Layered Communication Delayable Send-enabled } Memoryless Protocol Switching Composable Rdelay (tru ,trl)  swap-adjacent(trl,tru) for e1,e2 with e1=Send(p,m1)  e2 = Deliver(p,m2) Rasync (tru ,trl)  swap-adjacent(trl,tru) for e1,e2 with process(e1)  process(e2) Switchable(P)Msafety (P) …  Mcomposable (P) Rcomposable (tru ,trl1,trl2) trl1trl2=[]  interleave(tru,trl1,trl2) … Rsend-e (tru ,trl)  tru= trl@ [Send(p1,m1),..,Send(pn,mn)] Rmemoryless (tru ,trl)  tru= trl- [e | msg(e){m1,..,mn}] Rsafety (tru ,trl)  trl tru

  18. Verifying Hybrid Protocols Nuprlproof developed in parallel to implementation P.tru,trl.switch_invariant(tru,trl) Switchable(P)  (P(pr1(trl))  P(pr2(trl)))  P(tru) • Switchable properties are preserved if the switch • implementation satisfies a switch invariant • tru results from swapping trl events with different origin • messages sent by different protocols must be delivered • in the same order Formal design at same pace as “informal” one

  19. Lessons learned • The component-based approach is ideal for building adaptive systems • Employing formal techniques at every design stage is of great use for building efficient network systems • The LPE is capable of supporting “real” design - its theory is very expressive- reflection supports reasoning about program transformation • Automation still needs to be increased • More experience from applications is necessary

  20. Plans • Design & verification of new programs - New hybrid protocols (adaptivity)- Probabilistic protocols (scalability) • Extend scope of automation- Domain-specific reasoning strategies- Connect external inference engines - Formalize design knowledge (e.g. as theorems)- Techniques for automated system (code) synthesis • Develop and deploy full reflection mechanism • Build formal infrastructure for practitioners- Include library of formally documented mathematics 

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