1. CLF: A Concurrent Logical Framework David Walker Princeton (with I. Cervesato, F. Pfenning, K. Watkins)

2. 2 Outline What is a logical framework? Logical frameworks & security CLF: a concurrent logical framework

3. 3 Logical Frameworks a logical framework is a meta-language for representing deductive systems sample deductive systems logics of all kinds first-order logic, higher-order logic, temporal logic,... programming languages ML, lambda calculus, pi calculus specification languages set theory, type theory, multi-set rewriting,... compilers translations between languages or logics

4. 4 Logical Frameworks meta-logical frameworks logical frameworks logics proofs Twelf, Nuprl, HOL,... Automath, Nuprl, HOL, LF,... FOL, linear logic, temporal logic (A and B) => C represent properties of logics represent logics represent proofs

5. 5 Logical Frameworks meta-logical frameworks logical frameworks programming languages programs Twelf, Nuprl, HOL,... Automath, Nuprl, HOL, LF,... C, ML, Java lambda calculus if (n > 17) {...} represent properties of programming langs represent programming langs represent programs

6. 6 Tasks for Logical Frameworks Represent syntax of a logic of a programming language Represent valid rules of inference inference rules (modus ponens, law of the excluded middle) of a logic typing rules, operational rules of a language Represent valid deductions valid proofs well-typed programs, valid executions

7. 7 Outline What is a logical framework? Logical frameworks & security CLF: a concurrent logical framework

8. 8 Application I: proof-carrying X Proof-carrying code [Necula, Lee] Attach a proof of some safety property to mobile code Represent and check the proof in LF Proof-carrying authentication [Appel, Felten] Attach a proof of access rights to database query, service request Represent and check the proof in LF

9. 9 Application II: Mechanical Reasoning Increase our confidence in system properties through the following process 1. Represent algorithm, deductive system 2. Prove adequacy of representation 3. Prove security properties within the framework LF normally small, simple and trustworthy eg: LF has two type constructors Appel et al. (100k lines LF, 0 soundness bugs) Step 2 is least trustworthy

10. 10 Application II: Mechanical Reasoning Authentication protocols Extremely difficult to get correct Highly concurrent Errors are costly Many different specification languages informal notation, security logics, MSR, spi calculus,... Represent protocols, languages & their properties/relationships in a logical fwrk

11. 11 Outline What is a logical framework? Logical frameworks & security CLF: a concurrent logical framework

12. 12 Logical framework design Logical framework design resembles programming language design Simple logical frameworks are like simple programming languages few features = simple, trustworthy implementation but limited expressiveness expressive enough in principle but awkward and unmanageable in practice adequacy may be unclear, difficult to prove

13. 13 The LF family of Logical Frameworks Automath [De Bruijn], LF [Harper et al.] Dependent types, intuitionistic functions Represents pure PL, logics Higher-order abstract syntax Linear LF [Cervesato, Pfenning] LF + linear functions, additive pairs Represents state, effectful programming paradigms Resource-conscious logics

14. 14 Concurrent LF (CLF) Linear LF + a concurrency monad The monad encapsulates a concurrent computation Represents concurrent programming paradigms MSR specifications of security protocols, pi- calculus, CML, Petri nets

15. 15 CLF types Linear LF types + concurrency monad Represent the state of a concurrent computation A,B ::= a |  x:A.B | A -o B | T | A & B | {S} S ::= A | 1 | S 1  S 2 |  x:A.S | !A

16. 16 Pure CLF terms Pure Linear LF terms + concurrent computations A monad encapsulates computations within the pure language pure terms M,N ::= c | x:A.M | M N |... | {E}

17. 17 Effectful CLF computations Computation E processes the ambient state A let expression represents a step in a computation Patterns p introduce new state computations E ::= let {p} = M in E | F patterns p ::= x:A | 1 | p 1  p 2 |  x:A.p | !x states F ::= M | 1 | F 1  F 2 | [M,F] | !M

18. 18 Example key : type. msg : type. encrypt : key -> msg -> msg. wire : msg -> type. send :  M:msg.{wire M}. rec :  M:msg.wire M -o {1}. { let {m:wire M} = send M in let {m’:wire M’} = send M’ in let {1} = rec M’ m’ in let {1} = rec M m in... } CLF signature:Valid Computation:

19. 19 Concurrency equations LF and related dependent type theories provide a notion of definitional equality When M  N, the framework cannot distinguish M and N We extend the LF equality: The framework cannot distinguish the order of independent computation steps let {p} = M in let {p’} = M’ in E  let {p’} = M’ in let {p} = M in E (M,M’ do not contain variables in p,p’)

20. 20 Example { let {m:wire M} = send M in let {1} = rec M m in let {m’:wire M’} = send M’ in let {1} = rec M’ m’ in... } Valid Computation:Equivalent Computation: { let {m:wire M} = send M in let {m’:wire M’} = send M’ in let {1} = rec M’ m’ in let {1} = rec M m in... }

21. 21 Results Definition and meta-theory of CLF A new presentation of LF dependent type theory based on canonical forms Decidability of type checking Examples and applications Representation of Petri nets, synchronous and asynchronous pi-calculus with proofs of adequacy Novel, modular representation of CML in CLF Representation of MSR & examples

22. 22 Further reading Cervesato, Pfenning, Walker, Watkins. A concurrent logical framework. January 2002 (submitted). Forthcoming technical reports: Watkins et al. A concurrent logical framework I: Judgments and properties. Cervesato et al. A concurrent logical framework II: Examples and applications.

23. 23 Future work Implementation and logic programming operational semantics for CLF Represent, check and execute concurrent computations Meta-logical reasoning about concurrent computations Properties of concurrent computations, bisimulation Automatic proof search

24. 24 Conclusions Study of logical frameworks is an important aspect of the development of secure and reliable systems CLF enables concise and adequate representations of concurrent languages