Matthew Fluet Cornell University Monadic Regions Matthew Fluet Cornell University

Introduction Draw together two lines of research Region-based memory management Regions delimit lifetimes of objects new .e Monadic encapsulation of effects Embed imperative features in pure languages runST :: .(s. ST s )  

Introduction Encode Tofte-Talpin region calculus in System F with monadic sub-language Features runST serves as inspiration runRGN – encapsulate region computation newRGN – encapsulate a single region Sufficient polymorphism to encode region polymorphism

FRGN = System F + RGN monad Monadic (sub)-language Monadic types and operations RGN r  – monadic region computations RGNVar r  – region allocated values RGNHandle r – region handles

FRGN = System F + RGN monad Create and read region allocated values allocRGNVar :: ,r.   RGNHandle r  RGN r (RGNVar r ) readRGNVar :: ,r. RGNVar r   RGN r 

FRGN = System F + RGN monad Encapsulate and run a monadic computation runRGN :: .(r. RGNHandle r  RGN r )  

FRGN = System F + RGN monad Encapsulate a region newRGN :: ,r.(s. RGNHandle s  RGN s )  RGN r 

FRGN = System F + RGN monad Encapsulate a region newRGN :: ,r.(s. r  s  RGNHandle s  RGN s )  RGN r α  ≡ ,r,s. RGN r   RGN s 

Single Effect Calculus LIFO stack of regions imposes a partial order on live (allocated) regions Regions lower on the stack outlive regions higher on the stack A single region can serve as a witness for a set of effects Region appears as a single effect in place of the set

new .e  newRGN (.w.h. e) Translation Type-preserving translation from Single Effect Calculus to FRGN new .e  newRGN (.w.h. e)

Conclusion Monadic encoding of effects applicable to region calculi Trivial (syntactic) equality on types Encapsulation within monad

FRGN = System F + RGN monad Monadic unit and bind returnRGN :: ,r.   RGN r  thenRGN :: ,,r. RGN r   (  RGN r )  RGN r 