1. Matthew Fluet Cornell University
Monadic Regions
Matthew Fluet
Cornell University

2. 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 )  

3. 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

4. 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

5. 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 

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

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

8. 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 

9. 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

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

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

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