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Dependent Types for Distributed Systems: Enhancing Confidence and Modularity

This work explores using dependent types to ensure high-confidence distributed system development by capturing termination properties and employing transient certificates. It introduces novel solutions to verify program behaviors and system properties, aiding in practical support for reliable distributed components.

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Dependent Types for Distributed Systems: Enhancing Confidence and Modularity

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  1. Dependent Types for Reasoning About Distributed Systems Paul Sivilotti - Ohio State Hongwei Xi - Cincinnati

  2. Motivation and Context • Aim: practical support for the development of high-confidence distributed systems • practical: • modularity (components) • low cost • high-confidence: • respects resource budget, private memory… • executes “correctly” Dependent Types for Distributed Components

  3. Gaining confidence that program text satisfies required behavior Specifying com-ponent behavior and reasoning about its com-position Component A Properties Program Text of A . . . System Properties Component B Properties Program Text of B . . . Component C Properties Program Text of C . . . Two Challenges Dependent Types for Distributed Components

  4. Certificates temporal logic local properties Two Synergistic Solutions • Dependent Types • enriched types • familiar, low cost • Typically not tied to real programs • Typically not used for reasoning about progress • Synergy: locality • Surprising Connection: termination Dependent Types for Distributed Components

  5. “Transient”: A Certificate for Progress • Transient P for component C means: • progress: if P ever becomes true, it eventually becomes false • locality: guaranteed by an action of C alone • More formally: • transient P  a  C : [ P  wp.a.P ] Dependent Types for Distributed Components

  6. System: every client request is eventually satisfied Client: token is eventually returned transient holding Token-passing Layer E.g.: Mutual Exclusion Client C Client D Client B Client A Client E Dependent Types for Distributed Components

  7. Client Program *[ non CS ! request ? token //holding is true CS: ninetyone(0); ! token //holding is false ] • To prove transient holding, show • CS terminates (ie ninetyone terminates) Dependent Types for Distributed Components

  8. Dependent Types • Dependent types are types that can depend on the values of expressions • Examples • int(i) is a singleton type that contains the only integer equal to i • intarray(n) is the type for integer arrays of size n. Dependent Types for Distributed Components

  9. McCarthy’s 91 Function {i:nat} /* metric: max(0, 101-i) */ [j:int | (i <= 100  j = 91)  (i > 100  j = i-10)] int(j) ninetyone (x:int(i)) { if (x <= 100) { return ninetyone (ninetyone (x+11)); } else { return (x-10); } } Dependent Types for Distributed Components

  10. Cost Effectiveness • In general, termination of a program is difficult to prove • However, critical sections tend to be small and manageable • More importantly, we provide the programmer with a range of choices • higher effort  lower effort • higher benefit  lower benefit Dependent Types for Distributed Components

  11. Spectrum of Choices • Static Check • Programmer provides a metric • Type-checker verifies monotonicity of metric • Dynamic Check • Programmer provides a metric • Type-checker inserts run-time tests to check monotonicity of metric • Checkpointing • Programmer does not provide a metric • Checkpoint taken before “dangerous” action Dependent Types for Distributed Components

  12. Feasibility of Project • Certificates • A tool (cidl) for testing transient in CORBA objects has been implemented • Transient, and other local certificates, have been applied to several examples • Dependent Types • A dependently typed language (Xanadu) has been formalized and prototyped • Xanadu applied to several examples Dependent Types for Distributed Components

  13. Synergy of Collaboration • Paul: • Use transient properties to reason about progress in distributed systems • Use locally-checkable component properties to establish global system properties • Hongwei: • Design a dependent type system to capture termination properties • Implement a type-checker to verify captured termination properties Dependent Types for Distributed Components

  14. Future Goals • Research topics • Certification of mobile code for distributed systems • Build high confidence systems • External Funding • NSF (OS/Compiler & SE/Language) • DARPA (high-confidence computing) Dependent Types for Distributed Components

  15. Summary of Proposed Work • Extend dependent types to capture termination • Characterize certificates that can be supported by dependent types • Key qualities: • modular • holistic • high-confidence, not proof Dependent Types for Distributed Components

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