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Type-Directed Concurrency

Type-Directed Concurrency. Deepak Garg, Frank Pfenning {dg+, fp+}@cs.cmu.edu Carnegie Mellon University. Design Goals. Build a language starting from a logic Functional and concurrent features should arise from logical principles Write precise specifications for functions in the types

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Type-Directed Concurrency

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  1. Type-Directed Concurrency Deepak Garg, Frank Pfenning {dg+, fp+}@cs.cmu.edu Carnegie Mellon University

  2. Design Goals • Build a language starting from a logic • Functional and concurrent features should arise from logical principles • Write precise specifications for functions in the types • Functional reduction should be type-safe • Concurrent computation should not interfere with functional type-safety Type-Directed Concurrency. CONCUR 2005

  3. Outline • Design goals • Computation-as-proof reduction, Computation-as-proof search, Computation-as-proof search and reduction • Introduction to CLL • fCLL: Functional core • lCLL: Concurrent core • Related Work and Conclusion Type-Directed Concurrency. CONCUR 2005

  4. Computation-as-proof reduction • Curry-Howard isomorphism • Strong guarantees about values computed by a program (type-safety) • Captures behavior of full programs, not their interacting components • Works very well for functional programs • Unsuited for concurrent languages, and reactive systems in general Type-Directed Concurrency. CONCUR 2005

  5. Computation-as-proof search • Logic programming languages (Prolog, …) • Programs are sets of logic formulae (Rules, facts and a goal) • Computation is proof-search (Proving the goal from the rules and facts) • Captures dynamics of concurrent programs (FCP, Concurrent Prolog, …) • Hard to capture functional features Type-Directed Concurrency. CONCUR 2005

  6. Computation-as-proof search and reduction • Add proof-terms to a logic programming language • Interpret proof-terms as programs • Synthesize proofs-terms on the fly • Alternate proof search with reduction of synthesized proof-terms • Captures both concurrent and functional features! Type-Directed Concurrency. CONCUR 2005

  7. Example (N: A!B), (M: A) FACTS Proof reduction Functional reduction, parallelism (V: A!B), (U: A) Proof search Synchronization (V U): B Proof reduction Functional reduction W: B ?: B GOAL Type-Directed Concurrency. CONCUR 2005

  8. Where we are … • Design goals • Computation-as-proof reduction, Computation-as-proof search, Computation-as-proof search and reduction • Introduction to CLL • fCLL: Functional core of CLL • lCLL: Concurrent core of CLL • Related Work and Conclusion Type-Directed Concurrency. CONCUR 2005

  9. Introduction to CLL • Typed programming language • Logical design • Functional features from proof reduction • Concurrent features from proof synthesis • Type system based on a variant of intuitionistic linear logic Type-Directed Concurrency. CONCUR 2005

  10. What CLL is and isn’t • Foundational/conceptual language • Prototype implementation • Not a full-fledged language yet • Functional part: • Type-safety • Concurrent part: • Preserves well-typedness of terms • No progress guarantee: Computations may deadlock Type-Directed Concurrency. CONCUR 2005

  11. CLL: Layered design • Three layer design • fCLL: Functional language • lCLL: Concurrent + Functional language • Concurrent computation can call functional computation • full-CLL: Concurrent + Functional language • Functional computation can call upon concurrent computation • Omitted from this talk Type-Directed Concurrency. CONCUR 2005

  12. Underlying Logic • Intuitionistic • captures functional specifications • Linear • captures concurrency in lCLL • Equipped with a monad • captures effects (deadlocks) in full-CLL • used in communication • First-order (dependent types) • precise functional specifications • model communication channels, process ids, etc. in lCLL Type-Directed Concurrency. CONCUR 2005

  13. Where we are … • Design Goals • Computation-as-proof reduction, Computation-as-proof search, Computation-as-proof search and reduction • Introduction to CLL • fCLL: Functional core of CLL • lCLL: Concurrent core of CLL • Related Work and Conclusion Type-Directed Concurrency. CONCUR 2005

  14. fCLL: Type Syntax Type-Directed Concurrency. CONCUR 2005

  15. fCLL: Program Syntax • Programs (P) divided into syntactic classes Type-Directed Concurrency. CONCUR 2005

  16. Linear variables: Non-linear variables: fCLL: Semantics • Call-by-value reduction semantics • Typing judgments: Type-Directed Concurrency. CONCUR 2005

  17. fCLL: Type-Safety • Type-preservation: If P : T and P reduces to P’, then P’ : T. • Progress: If P : T, then P is a value or P reduces. Type-Directed Concurrency. CONCUR 2005

  18. Where we are … • Design Goals • Computation-as-proof reduction, Computation-as-proof search, Computation-as-proof search and reduction • Introduction to CLL • fCLL: Functional core of CLL • lCLL: Concurrent core of CLL • Related Work and Conclusion Type-Directed Concurrency. CONCUR 2005

  19. lCLL: Concurrent Core of CLL • Computation-as-proof search and reduction • Functional part: • Includes all of fCLL directly • Concurrent part: • Arises from proof-synthesis • Resembles asynchronous -calculus in communication primitives • CHAM presentation Type-Directed Concurrency. CONCUR 2005

  20. lCLL: Syntax fCLL values with types fCLL programs with types Replicable Linear Type-Directed Concurrency. CONCUR 2005

  21. Type Constructs in lCLL • Each construct has an intuitive meaning Type-Directed Concurrency. CONCUR 2005

  22. Interaction Example Server: Listens on channel k Computes factorials Client: Listens on channel k’ k <6> Objective: compute factorial(6) Compute factorial(6) = 720 Return 720and terminate k’ <720> Type-Directed Concurrency. CONCUR 2005

  23. Modeling messages in lCLL • Channels k, k’,… modeled as index terms • messint : type constructor of arity 1 • (messintk) is the type of integer messages on channel k Type-Directed Concurrency. CONCUR 2005

  24. Server Process 3. Send computed result on channel k’ 1. Wait for message “y” on channel k 2. Extract content of y and compute its factorial Type-Directed Concurrency. CONCUR 2005

  25. Client Process Wait for message “x” on channel k’, and return content of x Send message 6 on channel k Parallel composition Type-Directed Concurrency. CONCUR 2005

  26. lCLL: Semantics • Type-directed rewrite semantics • Three alternating rewrite phases: • fCLL’s functional reduction (proof-term reduction) • Structural decomposition • Synchronization (proof-term synthesis) Type-Directed Concurrency. CONCUR 2005

  27. 1. Functional reduction • Applies to all non-values in a configuration • If P : T, then P’ : T by fCLL’s type-preservation theorem! Type-Directed Concurrency. CONCUR 2005

  28. 2. Structural decomposition • Resemble -calculus structural decomposition Type-Directed Concurrency. CONCUR 2005

  29. 3. Synchronization • Takes several values in a configuration and links them to form a larger program • Site of all communication • Directed by types • Three golden rules: • Applies to asynchronoustypes only • Applies to values only • Result must have type {S} Type-Directed Concurrency. CONCUR 2005

  30. Synchronization examples Type-Directed Concurrency. CONCUR 2005

  31. Incorrect Synchronizations Not of type {S} Not a value Type-Directed Concurrency. CONCUR 2005

  32. Why have a monad {…} • Atomicity - {…} determines how far each synchronization will go Type-Directed Concurrency. CONCUR 2005

  33. Interaction Example Server: Listens on channel k Computes factorials Client: Listens on channel k’ k <6> Objective: compute factorial(6) Compute factorial(6) = 720 Return 720and terminate k’ <720> Type-Directed Concurrency. CONCUR 2005

  34. Example: Execution in lCLL Type-Directed Concurrency. CONCUR 2005

  35. Example: Execution in lCLL Type-Directed Concurrency. CONCUR 2005

  36. Are the rewrite rules ad-hoc? • No! • Rewrite rules obtained from a proof search procedure by adding proof-terms • See paper for details Type-Directed Concurrency. CONCUR 2005

  37. What does lCLL give us? • A “well-typedness” preservation result: If every program in a lCLL configuration is well-typed with the type indicated, then after any number of rewrite steps, the same property still holds. • Concurrent computation does not interfere with functional type-safety! Type-Directed Concurrency. CONCUR 2005

  38. What lCLL lacks … • Concurrent computations in lCLL may deadlock • Reason: Linear logic is not expressive enough Type-Directed Concurrency. CONCUR 2005

  39. Where we are … • Design Goals • Computation-as-proof reduction, Computation-as-proof search, Computation-as-proof search and reduction • Introduction to CLL • fCLL: Functional core of CLL • lCLL: Concurrent core of CLL • Related Work and Conclusion Type-Directed Concurrency. CONCUR 2005

  40. Closely Related Work • Facile, CML, Concurrent Haskell, JOCaml • Combine functional and concurrent prog. • Type Systems for -calculus [Kobayashi ’03], [Igarashi, Kobayashi ’03], [Yoshida ’04], [Kobayashi, Pierce, Turner ’95], … • Properties like type-safety, deadlock freedom • Computational Interpretations of Linear Logic [Abramsky ’93] • Classical linear logic and concurrency Type-Directed Concurrency. CONCUR 2005

  41. Closely Related Work • MSR Framework [Cervesato ’04] • Rewriting as logical rules • CLF [Cervesato, Pfenning, Walker, Watkins ’03], LolliMon [ Lopez, Pfenning, Polakow, Watkins’05] • Share the same underlying logic • Lots more … Type-Directed Concurrency. CONCUR 2005

  42. Future Work • A realistic implementation • Challenges • Low level of concurrency in CLL • Linear functional programming • Type inference • Reasoning about deadlock freedom and program correctness Type-Directed Concurrency. CONCUR 2005

  43. Conclusion • CLL • Built from a logic • Functional part arises from proof reduction • Concurrent part arises from proof search • Type-safety for functional reduction • Concurrency does not interfere with functional type-safety Type-Directed Concurrency. CONCUR 2005

  44. In the paper … • Multi-sorted index terms • Existential types • Creating channel names • Encoding the asynchronous -calculus • A three phase classification of fCLL programs • Terms, expressions and monadic terms Type-Directed Concurrency. CONCUR 2005

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