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Deriving a compiler and interpreter for a Multi-level

Yun-Yan Chi, profile picture
Yun-Yan Chi

The document describes deriving a uniform compiler and virtual machine (VM) that uses low-level code generation. It discusses defunctionalizing continuations, currying a primitive recursive evaluator, and generating VM instructions from high-level code to enable run-time computation. The goal is a single approach that can compile source code to low-level VM instructions.

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Deriving a Uniform Compiler and VM with Low-Level Code Generation Jaiyalas
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont type Compt = Compt Term Int -> Env -> Cont -> Val VM Val eval appK for Low-Level Code Generation Cont eval :: Term -> Compt Term appK :: Cont -> Val -> Val Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val type Compt = [Inst] Val Defunctionalizing Continuations eval appK appC Cont data Inst = Number Int Compt Term | Access Int VM Val eval appK | Lambda Compt for Low-Level Code Generation Cont | Push Compt Term | Enter Val Currying & | Leave Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val eval Source Code Val Defunctionalizing Continuations eval appK appC Cont VM Instructions Compt Term appC High-Level Code appK VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval eval appK Source Code for Low-Level Code Generation Cont Term VM Instructions Val Currying & eval Primitive Recursive Evaluator appK appC Cont appC VM Instructions appK Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
eval Source Code VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation
Demo feval3.hs compile exp6 run $ compile exp6 run $ compile $ deq $ run $ compile exp6 feval42.hs compile exp6 run $ compile exp6 run $ deq $ run $ compile exp6
Non-Uniform Compilation and Failure of Low-Level Code Generation
eval Source Code, Level VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation
Term evaluator Uniform Term Val Val Defunctionalizing Continuations eval appK appC Cont type Compt = Compt Term Int -> Env -> Cont -> Val VM Val eval appK for Low-Level Code Generation Cont eval :: Term -> Compt Term appK :: Cont -> Val -> Val Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Non-Uniform Val Defunctionalizing Continuations eval appK appC Cont Compt Term type Compt = VM Val eval appK -> Cont -> Val Env for Low-Level Code Generation Cont eval :: Term -> Int ->Compt Term appK :: Cont -> Val -> Val Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term type Compt = [Inst] evaluator Term Val data Inst = Number Int Val | Access Int Defunctionalizing eval appK appC Cont Continuations | Lambda Compt | Push Compt Compt Term | Enter L = 0 VM Val eval LeaveappK for | Low-Level Code Generation Cont | Plus Compt Term | QLit Int Val Currying & Primitive|Recursive Evaluator QVar Int eval appK appC Cont | PushQAbs Compt Int L > 0 Term | PushQApp Compt Compt Val eval | PushQNextappK Defunctionalizing Run-Time Computation | PushQPrev Cont | PushQAdd Compt
Enter compiler Next , 0 PushQNext compiler Next , 1
Enter compiler o r m Next , 0 n if n - U PushQNext N o compiler Next , 1
eval Source Code, Level L=0 L>0 VM Instructions appC appCQ High-Level Code appK appKQ High-Level Code /Jainon/nonnifeval3.hs
VM Instructions appC appCQ appK appKQ Interpretation Compilation VM
Demo Jainon/nonnifeval3.hs compile exp6 run $ compile exp6 run $ compile $ deq $ run $ compile exp6
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
Term evaluator Term Val Val Defunctionalizing eval appK appC Cont ? Continuations Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
compiler Source Code, Level L=0 L>0 VM Instructions VM | QLit Int L>0 | QVar Int | PushQAbs Compt Int | PushQApp Compt | PushQNext | PushQPrev | PushQAdd Compt
compiler Source Code, Level L=0 L>0 VM Instructions VM o r m n if | QLit Int | QVar Int U L>0 | PushQAbs Compt Int | PushQApp Compt | PushQNext | PushQPrev | PushQAdd Compt
data Inst = Lv0Numer Int | Lv0Access Int | Lv0Lambda Compt | Lv0... | Lv1Number Int | Lv1Access Int | Lv1... | ... | LvnNumber Int | Lvn ...
data Inst = Lv0Numer Int | Lv0Access Int | Lv0Lambda Compt | Lv0... | Lv1Number Int | Lv1Access Int | Lv1... | ... | LvnNumber Int | Lvn ...
Source Code, Level compiler Instructions VMn VM Result
Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
(Next (Next (Add (Lit 2) (Lit 3)))) Compiler [Enter,PushQNext,PushQAdd [QLit 2],QLit 3] VM Quot [PushQNext,PushQAdd [QLit 2],QLit 3]
(Next (Next (Add (Lit 2) (Lit 3)))) Compiler [Enter,PushQNext,PushQAdd [QLit 2],QLit 3] VM ? ? ? l = v e e Quot [PushQNext,PushQAdd [QLit 2],QLit 3] L
dmdq = demote + deq /Jainon/nonnifeval42o.hs
Quot [PushQNext,PushQAdd [QLit 2],QLit 3] dmdq [Enter,PushQAdd [QLit 2],QLit 3] VM Quot [PushQAdd [QLit 2],QLit 3]
Quot [PushQAdd [QLit 2],QLit 3] dmdq [Plus [Number 2],Number 3] VM Val 5
Demo exp7 = (Next (Next (App (Abs (Prev (Prev (Add (Lit 11) (Lit 13))))) (Prev (App (Abs (Var 0)) (Next (Add (Lit 1) (Lit 3))))))))
Demo Jainon/nonnifeval42o.hs compile exp7 run $ compile exp7 run $ dmdq $ run $ compile exp7 run $ dmdq $ run $ dmdq $ run $ compile exp7
END

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Deriving a compiler and interpreter for a Multi-level

  • 1. Deriving a Uniform Compiler and VM with Low-Level Code Generation Jaiyalas
  • 2. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 3. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 4. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 5. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 6. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont type Compt = Compt Term Int -> Env -> Cont -> Val VM Val eval appK for Low-Level Code Generation Cont eval :: Term -> Compt Term appK :: Cont -> Val -> Val Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 7. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 8. Term evaluator Term Val type Compt = [Inst] Val Defunctionalizing Continuations eval appK appC Cont data Inst = Number Int Compt Term | Access Int VM Val eval appK | Lambda Compt for Low-Level Code Generation Cont | Push Compt Term | Enter Val Currying & | Leave Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 9. Term evaluator Term Val eval Source Code Val Defunctionalizing Continuations eval appK appC Cont VM Instructions Compt Term appC High-Level Code appK VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 10. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 11. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval eval appK Source Code for Low-Level Code Generation Cont Term VM Instructions Val Currying & eval Primitive Recursive Evaluator appK appC Cont appC VM Instructions appK Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 12. eval Source Code VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation
  • 13. Demo feval3.hs compile exp6 run $ compile exp6 run $ compile $ deq $ run $ compile exp6 feval42.hs compile exp6 run $ compile exp6 run $ deq $ run $ compile exp6
  • 14. Non-Uniform Compilation and Failure of Low-Level Code Generation
  • 15. eval Source Code, Level VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation VM Instructions (Run-Time Computation) Level Environment appC VM Instructions appK Continuation
  • 16. Term evaluator Uniform Term Val Val Defunctionalizing Continuations eval appK appC Cont type Compt = Compt Term Int -> Env -> Cont -> Val VM Val eval appK for Low-Level Code Generation Cont eval :: Term -> Compt Term appK :: Cont -> Val -> Val Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 17. Term evaluator Term Val Non-Uniform Val Defunctionalizing Continuations eval appK appC Cont Compt Term type Compt = VM Val eval appK -> Cont -> Val Env for Low-Level Code Generation Cont eval :: Term -> Int ->Compt Term appK :: Cont -> Val -> Val Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 18. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 19. Term type Compt = [Inst] evaluator Term Val data Inst = Number Int Val | Access Int Defunctionalizing eval appK appC Cont Continuations | Lambda Compt | Push Compt Compt Term | Enter L = 0 VM Val eval LeaveappK for | Low-Level Code Generation Cont | Plus Compt Term | QLit Int Val Currying & Primitive|Recursive Evaluator QVar Int eval appK appC Cont | PushQAbs Compt Int L > 0 Term | PushQApp Compt Compt Val eval | PushQNextappK Defunctionalizing Run-Time Computation | PushQPrev Cont | PushQAdd Compt
  • 20. Enter compiler Next , 0 PushQNext compiler Next , 1
  • 21. Enter compiler o r m Next , 0 n if n - U PushQNext N o compiler Next , 1
  • 22. eval Source Code, Level L=0 L>0 VM Instructions appC appCQ High-Level Code appK appKQ High-Level Code /Jainon/nonnifeval3.hs
  • 23. VM Instructions appC appCQ appK appKQ Interpretation Compilation VM
  • 24. Demo Jainon/nonnifeval3.hs compile exp6 run $ compile exp6 run $ compile $ deq $ run $ compile exp6
  • 25. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 26. Term evaluator Term Val Val Defunctionalizing eval appK appC Cont ? Continuations Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 27. compiler Source Code, Level L=0 L>0 VM Instructions VM | QLit Int L>0 | QVar Int | PushQAbs Compt Int | PushQApp Compt | PushQNext | PushQPrev | PushQAdd Compt
  • 28. compiler Source Code, Level L=0 L>0 VM Instructions VM o r m n if | QLit Int | QVar Int U L>0 | PushQAbs Compt Int | PushQApp Compt | PushQNext | PushQPrev | PushQAdd Compt
  • 29. data Inst = Lv0Numer Int | Lv0Access Int | Lv0Lambda Compt | Lv0... | Lv1Number Int | Lv1Access Int | Lv1... | ... | LvnNumber Int | Lvn ...
  • 30. data Inst = Lv0Numer Int | Lv0Access Int | Lv0Lambda Compt | Lv0... | Lv1Number Int | Lv1Access Int | Lv1... | ... | LvnNumber Int | Lvn ...
  • 31. Source Code, Level compiler Instructions VMn VM Result
  • 32. Term evaluator Term Val Val Defunctionalizing Continuations eval appK appC Cont Compt Term VM Val eval appK for Low-Level Code Generation Cont Term Val Currying & Primitive Recursive Evaluator eval appK appC Cont Term Compt Defunctionalizing Val eval appK Run-Time Computation Cont
  • 33. (Next (Next (Add (Lit 2) (Lit 3)))) Compiler [Enter,PushQNext,PushQAdd [QLit 2],QLit 3] VM Quot [PushQNext,PushQAdd [QLit 2],QLit 3]
  • 34. (Next (Next (Add (Lit 2) (Lit 3)))) Compiler [Enter,PushQNext,PushQAdd [QLit 2],QLit 3] VM ? ? ? l = v e e Quot [PushQNext,PushQAdd [QLit 2],QLit 3] L
  • 35. dmdq = demote + deq /Jainon/nonnifeval42o.hs
  • 36. Quot [PushQNext,PushQAdd [QLit 2],QLit 3] dmdq [Enter,PushQAdd [QLit 2],QLit 3] VM Quot [PushQAdd [QLit 2],QLit 3]
  • 37. Quot [PushQAdd [QLit 2],QLit 3] dmdq [Plus [Number 2],Number 3] VM Val 5
  • 38. Demo exp7 = (Next (Next (App (Abs (Prev (Prev (Add (Lit 11) (Lit 13))))) (Prev (App (Abs (Var 0)) (Next (Add (Lit 1) (Lit 3))))))))
  • 39. Demo Jainon/nonnifeval42o.hs compile exp7 run $ compile exp7 run $ dmdq $ run $ compile exp7 run $ dmdq $ run $ dmdq $ run $ compile exp7
  • 40. END