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Agate: an Agda -to- Haskell compiler

Agate: an Agda -to- Haskell compiler. AIST / CVS Hiroyuki Ozaki (joint work with Makoto Takeyama). What is Agda?. Proof assistant based on Martin-L ö f type theory. Curry-Howard correspondence available for its core language

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Agate: an Agda -to- Haskell compiler

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  1. Agate:an Agda-to-Haskell compiler AIST / CVS Hiroyuki Ozaki (joint work with Makoto Takeyama)

  2. What is Agda? • Proof assistant based on Martin-Löf type theory. • Curry-Howard correspondence available for its core language ⇒ Proof language can be regarded as a functional programming language withdependent types. • Full language contains extension of packages, classes (therefore, monads), hidden arguments, metavariables, etc.

  3. Goal • To provide a tool for experimentation of programming with dependent types. • To achieve it, we need • implement the tool quickly • reasonably fast execution of the emitted code • deal with “side effects,” such as I/O.

  4. Requirements • Treat full Agda language • use parser of the current Agda implementation • Faster execution • compile, rather than interpret! • Quick implementation • make the target language be Haskell • Agda language is close to it and there is GHC which generates executable binaries of high quality • use Higher Order Abstract Syntax • to eliminate coding for variable substitution

  5. data Val = VAbs (Val -> Val) | VCon String [Val] | VStr [(String, Val)] | VIO (IO Val) | VString String apply :: Val -> Val -> Val apply (VAbs f) v = f v select :: Val -> String -> Val select (VStr bs) x = lookup x bs E.g., (∖x -> x) zero⇨ VAbs (∖x -> x) `apply` (VCon “zero” []) struct { inc = ∖x -> succ x; n = inc zero } ⇨let inc = VAbs (∖x -> succ `apply` x) n = inc `apply` zero in VStr [(“n”,n),(“inc”,inc)] Our HOAS Tree Untyped lambda calculus for representing Agda terms

  6. How to deal with IO Pass the buck to Haskell! posutulate IO :: Set -> Set posutulate putStr :: String -> IO Unit main :: IO Unit main = putStr “Hello World” x_main, x_putStr :: Val x_main = x_putStr `apply` VString “Hello World” x_putStr = VAbs (∖v -> VIO (putStr (deString v) >> return VUnit )) main :: IO Val main = deIO x_main data Val = … | VIO (IO Val) | VString String deIO (VIO m) = m deString (VString s) = s

  7. Performance GHC : Agate = 1 : 6 (execution time)

  8. Conclusion • FULL dependently typed functional language including IO, with a very sophisticated development environment • Running under Linux, Windows and MacOSX • Visit my homepage to download Agate! http://staff.aist.go.jp/hiroyuki.ozaki/ Availability

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