Erlang Meets Dependent Types

Talk given at EdLambda, in July 2015.

Dissertation Link: http://lenary.co.uk/publications/dissertation/

Transcript

1. Erlang Meets Dependent Types
   Sam Elliott
   edλ, 14 July 2015
   

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2. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   Erlang
   • Actor-based Concurrent Programming Language
   • !, receive, and spawn
   • Mailbox per Isolated Process
   Sam Elliott Erlang Meets Dependent Types
   

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3. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   Erlang Advanced Features
   • Dynamically Typed
   • dialyzer
   • OTP: Behaviours
   Sam Elliott Erlang Meets Dependent Types
   

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4. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   Dependently-Typed Languages
   • Idris
   • Agda
   • Coq
   Sam Elliott Erlang Meets Dependent Types
   

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5. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   Idris
   • Dependently-typed Pure Programming Language
   • Types are Values
   • Values are Types
   • Programs and Proofs
   Sam Elliott Erlang Meets Dependent Types
   

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6. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   Idris IRs
   “Cross-platform Compilers for Functional Languages”
   • Idris
   • TT
   • TTcase
   • IRcase
   • IRlift
   • IRdefunc
   • IRANF
   • Idris Bytecode
   Sam Elliott Erlang Meets Dependent Types
   

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7. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   IRdefunc
   Sam Elliott Erlang Meets Dependent Types
   

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8. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   Actors
   data Actor : Type → Type → Type
   proc : Actor l ()
   Sam Elliott Erlang Meets Dependent Types
   

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9. Erlang Dependent Types Compiler Concurrency OTP Conclusion
   Actors
   data Actor : Type → Type → Type
   proc : Actor l ()
   recieve : Actor l l
   Sam Elliott Erlang Meets Dependent Types
   

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10. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    Actors
    data Actor : Type → Type → Type
    proc : Actor l ()
    recieve : Actor l l
    spawn : (Actor l’ a) → Actor l (ActorID l’)
    data ActorID : Type → Type
    pid : ActorID l
    Sam Elliott Erlang Meets Dependent Types
    

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11. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    Actors
    data Actor : Type → Type → Type
    proc : Actor l ()
    recieve : Actor l l
    spawn : (Actor l’ a) → Actor l (ActorID l’)
    data ActorID : Type → Type
    pid : ActorID l
    send : ActorID l’ → l’ → Actor l ()
    Sam Elliott Erlang Meets Dependent Types
    

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12. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    RPC
    data RPCLang : (r : Type)
    → (r → Type)
    → Type
    Sam Elliott Erlang Meets Dependent Types
    

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13. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    RPC
    data RPCLang : (r : Type)
    → (r → Type)
    → Type
    data LockReq = Lock | Unlock
    data LockLockResp = Grant | Wait
    total
    LockResp : LockReq → Type
    LockResp Lock = LockLockResp
    LockResp Unlock = Unit
    LockLang : RPCLang LockReq LockResp
    Sam Elliott Erlang Meets Dependent Types
    

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14. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    RPC II
    data RPCRef : RPCLang rq rs → Type
    rpc : {l : RPCLang rq rs}
    → RPCRef l
    → (m : rq)
    → EIO (rs m)
    Sam Elliott Erlang Meets Dependent Types
    

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15. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    RPC II
    data RPCRef : RPCLang rq rs → Type
    rpc : {l : RPCLang rq rs}
    → RPCRef l
    → (m : rq)
    → EIO (rs m)
    pid : RPCRef LockLang
    rpc pid Lock : LockLockResp
    rpc pid Unlock : Unit
    Sam Elliott Erlang Meets Dependent Types
    

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16. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    RPC III
    spawn : {l : RPCLang rq rs}
    → (r : rq → rs r)
    → EIO (RPCRef l)
    Sam Elliott Erlang Meets Dependent Types
    

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17. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    RPC III
    spawn : {l : RPCLang rq rs}
    → (r : rq → rs r)
    → EIO (RPCRef l)
    total
    lock : (m : LockReq) → LockResp m
    lock Lock = Grant -- Oh Crap!
    lock Unlock = ()
    Sam Elliott Erlang Meets Dependent Types
    

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18. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    RPC III
    spawn : {l : RPCLang rq rs}
    → (r : rq → rs r)
    → EIO (RPCRef l)
    total
    lock : (m : LockReq) → LockResp m
    lock Lock = Grant -- Oh Crap!
    lock Unlock = ()
    State? Side Effects?
    Sam Elliott Erlang Meets Dependent Types
    

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19. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    OTP
    • “Open Telecoms Platform”
    • Lots of great defaults
    • Generic Behaviours!
    • Supervisors!
    Sam Elliott Erlang Meets Dependent Types
    

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20. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    Generic Behaviours
    • gen server
    • gen fsm
    • gen event
    Sam Elliott Erlang Meets Dependent Types
    

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21. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    gen server
    data GSL : (cl : Type)
    → (cl → Type)
    → Type
    → Type
    data GSRef : GSL cl cr ct → Type
    Sam Elliott Erlang Meets Dependent Types
    

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22. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    gen server
    data GSL : (cl : Type)
    → (cl → Type)
    → Type
    → Type
    data GSRef : GSL cl cr ct → Type
    call : {l : GSL cl cr ct}
    → GSRef l
    → (m : cl)
    → EIO (cr m)
    cast : {l : GSL cl cr ct}
    → GSRef l
    → ct
    → EIO Unit
    Sam Elliott Erlang Meets Dependent Types
    

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23. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    gen server
    data GS : (GSL cl cr ct)
    → Type
    → Type
    → Type
    spawn : (GS l st i)
    → i
    → EIO (GSRef i)
    Sam Elliott Erlang Meets Dependent Types
    

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24. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    Conclusion
    • We can produce verified concurrent programs in Idris
    • We can compile these programs to work with Erlang
    • We can run verified programs in Erlang
    Sam Elliott Erlang Meets Dependent Types
    

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25. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    Read More
    Sam Elliott Erlang Meets Dependent Types
    

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26. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    Thanks To
    Edwin Brady
    Rob Stewart
    Skyscanner & Mike Moran
    Sam Elliott Erlang Meets Dependent Types
    

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27. Erlang Dependent Types Compiler Concurrency OTP Conclusion
    Any Questions?
    Sam Elliott Erlang Meets Dependent Types
    

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