Erlang meets Dependent Types

Talk given at SPLS St Andrews, June 2015.

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

Transcript

1. Erlang meets Dependent Types
   Archibald Samuel Elliott1 Edwin Brady1
   1University of St Andrews
   SPLS St Andrews, 15 June 2015
   

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3. Erlang & Concurrency Dependent Types Example Compiler Conclusion
   Erlang
   • Actor-based Concurrent Programming Language
   • !,receive, and spawn
   • Mailbox per Process
   • Isolated Processes
   • Dynamically Typed
   • dialyzer
   • OTP: Behaviours
   Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
   

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4. Erlang & Concurrency Dependent Types Example Compiler Conclusion
   Idris
   • Dependently-typed Programming Language
   • “Pacman complete” — Brady
   • Types are Values and Values are Types
   • IR-Happy!
   Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
   

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5. Erlang & Concurrency Dependent Types Example Compiler Conclusion
   A Problematic Program
   1 -module(lock_srv ).
   -behaviour(gen_server ).
   handle_call(lock , _From , unlocked) →
   {reply , grant , locked};
   6 handle_call(lock , _From , locked) →
   {reply , wait , locked};
   handle_call(unlock , _From , _) →
   {reply , ok , unlocked}.
   11 %% Other gen_server callbacks elided
   Listing 1: Simple Concurrent Lock Service in Erlang using
   gen_server.
   Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
   

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6. Erlang & Concurrency Dependent Types Example Compiler Conclusion
   In Idris?
   1 module Locks
   data LockReq = Lock | Unlock
   4 data LockLockResp = Grant | Wait
   total
   LockResp : LockReq → Type
   LockResp Lock = LockLockResp
   9 LockResp Unlock = Unit
   data LockSt = Locked | Unlocked
   total
   14 lock : LockSt → (m : LockReq)
   → (LockResp m, LockSt)
   lock Locked Lock = (Wait , Locked)
   lock Unlocked Lock = (Grant , Locked)
   lock _ Unlock = ((), Unlocked)
   Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
   

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7. Erlang & Concurrency Dependent Types Example Compiler Conclusion
   RPC Framework
   1 data RPCLang : (r : Type)
   2 → (r → Type)
   → Type where
   MkRPCLang : {req : Type}
   → {resp : (req → Type )}
   → RPCLang req resp
   7
   data RPCRef : RPCLang _ _ → Type where
   MkRPCRef : Ptr → RPCRef l
   rpc : {l : RPCLang req resp}
   12 → RPCRef l
   → (m : req)
   → EIO (resp m)
   Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
   

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8. Erlang & Concurrency Dependent Types Example Compiler Conclusion
   Generic Processes
   1 data Process : Type → Type∗ → Type
   data ProcRef : Type → Type
   6
   spawn : Process l’ a → Process l (ProcRef l’)
   receive : Process l l
   11
   send : ProcRef l’ → l’ → Process l ()
   16 become : Process l a → (a → Process l’ b)
   → Process l’ b
   Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
   

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9. Erlang & Concurrency Dependent Types Example Compiler Conclusion
   And Back Up To OTP
   1 data GSL : (cl : Type) → (cl → Type) → Type → Type
   3
   GSP : Type → Type
   data GSRef : (GSL _ _ _) → Type
   8
   call : {l : GSL cl cr ct} → GSRef l → (m : cl)
   → GSP (cr m)
   13
   cast : {l : GSL _ _ ct} → GSRef l → ct → GSP Unit
   Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
   

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10. Erlang & Concurrency Dependent Types Example Compiler Conclusion
    And Becoming Too Dependent
    1 data GFL : (st : Type) → (se : Type)
    → (se → st → Type)
    → Type → Type where
    MkGFL : (st : Type) → (se : Type)
    → (ser : (se → st → Type ))
    6 → (e : Type) → GFL st se ser e
    GFP : Type → Type
    data GFRef : (GFL _ _ _ _)
    11 → Type where
    MkGFRef : {l : GFL _ _ _ _}
    → ErlPid
    → GFRef l
    16 sync_send_event : {l : GFL st se ser e} → GFRef l
    → (ev : se) → GFP ???
    Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
    

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11. Erlang & Concurrency Dependent Types Example Compiler Conclusion
    Idris IRs
    Idris has several IRs, but only some for Code Generation
    • Lambda Terms
    • Defunctionalised Terms
    • Applicative Normal Form
    • Bytecode
    Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
    

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12. Erlang & Concurrency Dependent Types Example Compiler Conclusion
    Defunctionalised IR
    Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
    

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13. Erlang & Concurrency Dependent Types Example Compiler 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
    Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types
    

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