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Erlang meets Dependent Types

Erlang meets Dependent Types

Talk given at SPLS St Andrews, June 2015.

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

Sam Elliott

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

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  2. 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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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. Erlang & Concurrency Dependent Types Example Compiler Conclusion
    Defunctionalised IR
    Archibald Samuel Elliott, Edwin Brady Erlang meets Dependent Types

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  12. 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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